Video encryption using chaotic masks in joint transform correlator

NASA Astrophysics Data System (ADS)

Saini, Nirmala; Sinha, Aloka

2015-03-01

A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.

A comparative analysis of chaotic particle swarm optimizations for detecting single nucleotide polymorphism barcodes.

PubMed

Chuang, Li-Yeh; Moi, Sin-Hua; Lin, Yu-Da; Yang, Cheng-Hong

2016-10-01

Evolutionary algorithms could overcome the computational limitations for the statistical evaluation of large datasets for high-order single nucleotide polymorphism (SNP) barcodes. Previous studies have proposed several chaotic particle swarm optimization (CPSO) methods to detect SNP barcodes for disease analysis (e.g., for breast cancer and chronic diseases). This work evaluated additional chaotic maps combined with the particle swarm optimization (PSO) method to detect SNP barcodes using a high-dimensional dataset. Nine chaotic maps were used to improve PSO method results and compared the searching ability amongst all CPSO methods. The XOR and ZZ disease models were used to compare all chaotic maps combined with PSO method. Efficacy evaluations of CPSO methods were based on statistical values from the chi-square test (χ 2 ). The results showed that chaotic maps could improve the searching ability of PSO method when population are trapped in the local optimum. The minor allele frequency (MAF) indicated that, amongst all CPSO methods, the numbers of SNPs, sample size, and the highest χ 2 value in all datasets were found in the Sinai chaotic map combined with PSO method. We used the simple linear regression results of the gbest values in all generations to compare the all methods. Sinai chaotic map combined with PSO method provided the highest β values (β≥0.32 in XOR disease model and β≥0.04 in ZZ disease model) and the significant p-value (p-value<0.001 in both the XOR and ZZ disease models). The Sinai chaotic map was found to effectively enhance the fitness values (χ 2 ) of PSO method, indicating that the Sinai chaotic map combined with PSO method is more effective at detecting potential SNP barcodes in both the XOR and ZZ disease models. Copyright © 2016 Elsevier B.V. All rights reserved.

Fractional Order Spatiotemporal Chaos with Delay in Spatial Nonlinear Coupling

NASA Astrophysics Data System (ADS)

Zhang, Yingqian; Wang, Xingyuan; Liu, Liyan; Liu, Jia

We investigate the spatiotemporal dynamics with fractional order differential logistic map with delay under nonlinear chaotic maps for spatial coupling connections. Here, the coupling methods between lattices are the nonlinear chaotic map coupling of lattices. The fractional order differential logistic map with delay breaks the limits of the range of parameter μ ∈ [3.75, 4] in the classical logistic map for chaotic states. The Kolmogorov-Sinai entropy density and universality, and bifurcation diagrams are employed to investigate the chaotic behaviors of the proposed model in this paper. The proposed model can also be applied for cryptography, which is verified in a color image encryption scheme in this paper.

A Simple Secure Hash Function Scheme Using Multiple Chaotic Maps

NASA Astrophysics Data System (ADS)

Ahmad, Musheer; Khurana, Shruti; Singh, Sushmita; AlSharari, Hamed D.

2017-06-01

The chaotic maps posses high parameter sensitivity, random-like behavior and one-way computations, which favor the construction of cryptographic hash functions. In this paper, we propose to present a novel hash function scheme which uses multiple chaotic maps to generate efficient variable-sized hash functions. The message is divided into four parts, each part is processed by a different 1D chaotic map unit yielding intermediate hash code. The four codes are concatenated to two blocks, then each block is processed through 2D chaotic map unit separately. The final hash value is generated by combining the two partial hash codes. The simulation analyses such as distribution of hashes, statistical properties of confusion and diffusion, message and key sensitivity, collision resistance and flexibility are performed. The results reveal that the proposed anticipated hash scheme is simple, efficient and holds comparable capabilities when compared with some recent chaos-based hash algorithms.

PSO algorithm enhanced with Lozi Chaotic Map - Tuning experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan

2015-03-10

In this paper it is investigated the effect of tuning of control parameters of the Lozi Chaotic Map employed as a chaotic pseudo-random number generator for the particle swarm optimization algorithm. Three different benchmark functions are selected from the IEEE CEC 2013 competition benchmark set. The Lozi map is extensively tuned and the performance of PSO is evaluated.

A novel color image encryption scheme using alternate chaotic mapping structure

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Zhao, Yuanyuan; Zhang, Huili; Guo, Kang

2016-07-01

This paper proposes an color image encryption algorithm using alternate chaotic mapping structure. Initially, we use the R, G and B components to form a matrix. Then one-dimension logistic and two-dimension logistic mapping is used to generate a chaotic matrix, then iterate two chaotic mappings alternately to permute the matrix. For every iteration, XOR operation is adopted to encrypt plain-image matrix, then make further transformation to diffuse the matrix. At last, the encrypted color image is obtained from the confused matrix. Theoretical analysis and experimental results has proved the cryptosystem is secure and practical, and it is suitable for encrypting color images.

Hysteresis compensation of the Prandtl-Ishlinskii model for piezoelectric actuators using modified particle swarm optimization with chaotic map.

PubMed

Long, Zhili; Wang, Rui; Fang, Jiwen; Dai, Xufei; Li, Zuohua

2017-07-01

Piezoelectric actuators invariably exhibit hysteresis nonlinearities that tend to become significant under the open-loop condition and could cause oscillations and errors in nanometer-positioning tasks. Chaotic map modified particle swarm optimization (MPSO) is proposed and implemented to identify the Prandtl-Ishlinskii model for piezoelectric actuators. Hysteresis compensation is attained through application of an inverse Prandtl-Ishlinskii model, in which the parameters are formulated based on the original model with chaotic map MPSO. To strengthen the diversity and improve the searching ergodicity of the swarm, an initial method of adaptive inertia weight based on a chaotic map is proposed. To compare and prove that the swarm's convergence occurs before stochastic initialization and to attain an optimal particle swarm optimization algorithm, the parameters of a proportional-integral-derivative controller are searched using self-tuning, and the simulated results are used to verify the search effectiveness of chaotic map MPSO. The results show that chaotic map MPSO is superior to its competitors for identifying the Prandtl-Ishlinskii model and that the inverse Prandtl-Ishlinskii model can provide hysteresis compensation under different conditions in a simple and effective manner.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Color encryption scheme based on adapted quantum logistic map

NASA Astrophysics Data System (ADS)

Zaghloul, Alaa; Zhang, Tiejun; Amin, Mohamed; Abd El-Latif, Ahmed A.

2014-04-01

This paper presents a new color image encryption scheme based on quantum chaotic system. In this scheme, a new encryption scheme is accomplished by generating an intermediate chaotic key stream with the help of quantum chaotic logistic map. Then, each pixel is encrypted by the cipher value of the previous pixel and the adapted quantum logistic map. The results show that the proposed scheme has adequate security for the confidentiality of color images.

Analysis of unstable periodic orbits and chaotic orbits in the one-dimensional linear piecewise-smooth discontinuous map

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajpathak, Bhooshan, E-mail: bhooshan@ee.iitb.ac.in; Pillai, Harish K., E-mail: hp@ee.iitb.ac.in; Bandyopadhyay, Santanu, E-mail: santanu@me.iitb.ac.in

2015-10-15

In this paper, we analytically examine the unstable periodic orbits and chaotic orbits of the 1-D linear piecewise-smooth discontinuous map. We explore the existence of unstable orbits and the effect of variation in parameters on the coexistence of unstable orbits. Further, we show that this structuring is different from the well known period adding cascade structure associated with the stable periodic orbits of the same map. Further, we analytically prove the existence of chaotic orbit for this map.

Chaotic attractors of relaxation oscillators

NASA Astrophysics Data System (ADS)

Guckenheimer, John; Wechselberger, Martin; Young, Lai-Sang

2006-03-01

We develop a general technique for proving the existence of chaotic attractors for three-dimensional vector fields with two time scales. Our results connect two important areas of dynamical systems: the theory of chaotic attractors for discrete two-dimensional Henon-like maps and geometric singular perturbation theory. Two-dimensional Henon-like maps are diffeomorphisms that limit on non-invertible one-dimensional maps. Wang and Young formulated hypotheses that suffice to prove the existence of chaotic attractors in these families. Three-dimensional singularly perturbed vector fields have return maps that are also two-dimensional diffeomorphisms limiting on one-dimensional maps. We describe a generic mechanism that produces folds in these return maps and demonstrate that the Wang-Young hypotheses are satisfied. Our analysis requires a careful study of the convergence of the return maps to their singular limits in the Ck topology for k >= 3. The theoretical results are illustrated with a numerical study of a variant of the forced van der Pol oscillator.

Clustering stock market companies via chaotic map synchronization

NASA Astrophysics Data System (ADS)

Basalto, N.; Bellotti, R.; De Carlo, F.; Facchi, P.; Pascazio, S.

2005-01-01

A pairwise clustering approach is applied to the analysis of the Dow Jones index companies, in order to identify similar temporal behavior of the traded stock prices. To this end, the chaotic map clustering algorithm is used, where a map is associated to each company and the correlation coefficients of the financial time series to the coupling strengths between maps. The simulation of a chaotic map dynamics gives rise to a natural partition of the data, as companies belonging to the same industrial branch are often grouped together. The identification of clusters of companies of a given stock market index can be exploited in the portfolio optimization strategies.

Statistical characterization of discrete conservative systems: The web map

NASA Astrophysics Data System (ADS)

Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino

2017-10-01

We numerically study the two-dimensional, area preserving, web map. When the map is governed by ergodic behavior, it is, as expected, correctly described by Boltzmann-Gibbs statistics, based on the additive entropic functional SB G[p (x ) ] =-k ∫d x p (x ) lnp (x ) . In contrast, possible ergodicity breakdown and transitory sticky dynamical behavior drag the map into the realm of generalized q statistics, based on the nonadditive entropic functional Sq[p (x ) ] =k 1/-∫d x [p(x ) ] q q -1 (q ∈R ;S1=SB G ). We statistically describe the system (probability distribution of the sum of successive iterates, sensitivity to the initial condition, and entropy production per unit time) for typical values of the parameter that controls the ergodicity of the map. For small (large) values of the external parameter K , we observe q -Gaussian distributions with q =1.935 ⋯ (Gaussian distributions), like for the standard map. In contrast, for intermediate values of K , we observe a different scenario, due to the fractal structure of the trajectories embedded in the chaotic sea. Long-standing non-Gaussian distributions are characterized in terms of the kurtosis and the box-counting dimension of chaotic sea.

A note on chaotic unimodal maps and applications.

PubMed

Zhou, C T; He, X T; Yu, M Y; Chew, L Y; Wang, X G

2006-09-01

Based on the word-lift technique of symbolic dynamics of one-dimensional unimodal maps, we investigate the relation between chaotic kneading sequences and linear maximum-length shift-register sequences. Theoretical and numerical evidence that the set of the maximum-length shift-register sequences is a subset of the set of the universal sequence of one-dimensional chaotic unimodal maps is given. By stabilizing unstable periodic orbits on superstable periodic orbits, we also develop techniques to control the generation of long binary sequences.

Randomly chosen chaotic maps can give rise to nearly ordered behavior

NASA Astrophysics Data System (ADS)

Boyarsky, Abraham; Góra, Paweł; Islam, Md. Shafiqul

2005-10-01

Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226-5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68-72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68-72], the resulting composed map has a periodic orbit which is stable.

Chaos analysis of viscoelastic chaotic flows of polymeric fluids in a micro-channel

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, C. P.; Lam, Y. C., E-mail: myclam@ntu.edu.sg; BioSystems and Micromechanics

2015-07-15

Many fluids, including biological fluids such as mucus and blood, are viscoelastic. Through the introduction of chaotic flows in a micro-channel and the construction of maps of characteristic chaos parameters, differences in viscoelastic properties of these fluids can be measured. This is demonstrated by creating viscoelastic chaotic flows induced in an H-shaped micro-channel through the steady infusion of a polymeric fluid of polyethylene oxide (PEO) and another immiscible fluid (silicone oil). A protocol for chaos analysis was established and demonstrated for the analysis of the chaotic flows generated by two polymeric fluids of different molecular weight but with similar relaxationmore » times. The flows were shown to be chaotic through the computation of their correlation dimension (D{sub 2}) and the largest Lyapunov exponent (λ{sub 1}), with D{sub 2} being fractional and λ{sub 1} being positive. Contour maps of D{sub 2} and λ{sub 1} of the respective fluids in the operating space, which is defined by the combination of polymeric fluids and silicone oil flow rates, were constructed to represent the characteristic of the chaotic flows generated. It was observed that, albeit being similar, the fluids have generally distinct characteristic maps with some similar trends. The differences in the D{sub 2} and λ{sub 1} maps are indicative of the difference in the molecular weight of the polymers in the fluids because the driving force of the viscoelastic chaotic flows is of molecular origin. This approach in constructing the characteristic maps of chaos parameters can be employed as a diagnostic tool for biological fluids and, more generally, chaotic signals.« less

An Extended Chaotic Maps-Based Three-Party Password-Authenticated Key Agreement with User Anonymity

PubMed Central

Lu, Yanrong; Li, Lixiang; Zhang, Hao; Yang, Yixian

2016-01-01

User anonymity is one of the key security features of an authenticated key agreement especially for communicating messages via an insecure network. Owing to the better properties and higher performance of chaotic theory, the chaotic maps have been introduced into the security schemes, and hence numerous key agreement schemes have been put forward under chaotic-maps. Recently, Xie et al. released an enhanced scheme under Farash et al.’s scheme and claimed their improvements could withstand the security loopholes pointed out in the scheme of Farash et al., i.e., resistance to the off-line password guessing and user impersonation attacks. Nevertheless, through our careful analysis, the improvements were released by Xie et al. still could not solve the problems troubled in Farash et al‥ Besides, Xie et al.’s improvements failed to achieve the user anonymity and the session key security. With the purpose of eliminating the security risks of the scheme of Xie et al., we design an anonymous password-based three-party authenticated key agreement under chaotic maps. Both the formal analysis and the formal security verification using AVISPA are presented. Also, BAN logic is used to show the correctness of the enhancements. Furthermore, we also demonstrate that the design thwarts most of the common attacks. We also make a comparison between the recent chaotic-maps based schemes and our enhancements in terms of performance. PMID:27101305

Fuzzy fractals, chaos, and noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zardecki, A.

1997-05-01

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

A method of recovering the initial vectors of globally coupled map lattices based on symbolic dynamics

NASA Astrophysics Data System (ADS)

Sun, Li-Sha; Kang, Xiao-Yun; Zhang, Qiong; Lin, Lan-Xin

2011-12-01

Based on symbolic dynamics, a novel computationally efficient algorithm is proposed to estimate the unknown initial vectors of globally coupled map lattices (CMLs). It is proved that not all inverse chaotic mapping functions are satisfied for contraction mapping. It is found that the values in phase space do not always converge on their initial values with respect to sufficient backward iteration of the symbolic vectors in terms of global convergence or divergence (CD). Both CD property and the coupling strength are directly related to the mapping function of the existing CML. Furthermore, the CD properties of Logistic, Bernoulli, and Tent chaotic mapping functions are investigated and compared. Various simulation results and the performances of the initial vector estimation with different signal-to-noise ratios (SNRs) are also provided to confirm the proposed algorithm. Finally, based on the spatiotemporal chaotic characteristics of the CML, the conditions of estimating the initial vectors using symbolic dynamics are discussed. The presented method provides both theoretical and experimental results for better understanding and characterizing the behaviours of spatiotemporal chaotic systems.

Robust PRNG based on homogeneously distributed chaotic dynamics

NASA Astrophysics Data System (ADS)

Garasym, Oleg; Lozi, René; Taralova, Ina

2016-02-01

This paper is devoted to the design of new chaotic Pseudo Random Number Generator (CPRNG). Exploring several topologies of network of 1-D coupled chaotic mapping, we focus first on two dimensional networks. Two topologically coupled maps are studied: TTL rc non-alternate, and TTL SC alternate. The primary idea of the novel maps has been based on an original coupling of the tent and logistic maps to achieve excellent random properties and homogeneous /uniform/ density in the phase plane, thus guaranteeing maximum security when used for chaos base cryptography. In this aim two new nonlinear CPRNG: MTTL 2 sc and NTTL 2 are proposed. The maps successfully passed numerous statistical, graphical and numerical tests, due to proposed ring coupling and injection mechanisms.

An information hiding method based on LSB and tent chaotic map

NASA Astrophysics Data System (ADS)

Song, Jianhua; Ding, Qun

2011-06-01

In order to protect information security more effectively, a novel information hiding method based on LSB and Tent chaotic map was proposed, first the secret message is Tent chaotic encrypted, and then LSB steganography is executed for the encrypted message in the cover-image. Compared to the traditional image information hiding method, the simulation results indicate that the method greatly improved in imperceptibility and security, and acquired good results.

Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan

2018-01-01

We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.

Composing chaotic music from the letter m

NASA Astrophysics Data System (ADS)

Sotiropoulos, Anastasios D.

Chaotic music is composed from a proposed iterative map depicting the letter m, relating the pitch, duration and loudness of successive steps. Each of the two curves of the letter m is based on the classical logistic map. Thus, the generating map is xn+1 = r xn(1/2 - xn) for xn between 0 and 1/2 defining the first curve, and xn+1 = r (xn - 1/2)(1 - xn) for xn between 1/2 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The m-model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. Based on this, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven- octaves range. At the composer's will and, for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. Compositions with endings of non-repeating note patterns result from values of r in the m-model that do not produce bifurcations. Scores of chaotic music composed from the m-model and the classical logistic model are presented.

Global bifurcations in fractional-order chaotic systems with an extended generalized cell mapping method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xiaojun; School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001; Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn

Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuousmore » change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.« less

Impact of hyperbolicity on chimera states in ensembles of nonlocally coupled chaotic oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Semenova, N.; Anishchenko, V.; Zakharova, A.

2016-06-08

In this work we analyse nonlocally coupled networks of identical chaotic oscillators. We study both time-discrete and time-continuous systems (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of chaotic non-hyperbolic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by numerical simulations for hyperbolic and non-hyperbolic cases.

Pseudo-Random Number Generator Based on Coupled Map Lattices

NASA Astrophysics Data System (ADS)

Lü, Huaping; Wang, Shihong; Hu, Gang

A one-way coupled chaotic map lattice is used for generating pseudo-random numbers. It is shown that with suitable cooperative applications of both chaotic and conventional approaches, the output of the spatiotemporally chaotic system can easily meet the practical requirements of random numbers, i.e., excellent random statistical properties, long periodicity of computer realizations, and fast speed of random number generations. This pseudo-random number generator system can be used as ideal synchronous and self-synchronizing stream cipher systems for secure communications.

On the efficiency of the image encryption and decryption by using logistic-sine chaotic system and logistic-tent chaotic system

NASA Astrophysics Data System (ADS)

Chiun, Lee Chia; Mandangan, Arif; Daud, Muhamad Azlan; Hussin, Che Haziqah Che

2017-04-01

We may secure the content of text, audio, image and video during their transmission from one party to another party via an open channel such as the internet by using cryptograph. Logistic-Sine System (LSS) is a combination on two 1D chaotic maps which are Logistic Map and Sine Map. By applying the LSS into cryptography, the image encryption and decryption can be performed. This study is focusing on the performance test of the image encryption and decryption processes by using the LSS. For comparison purpose, we compare the performance of the encryption and decryption by using two different chaotic systems, which are the LSS and Logistic-Tent System (LTS). The result shows that system with LSS is less efficient than LTS in term of encryption time but both systems have similar efficiency in term of decryption time.

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

NASA Astrophysics Data System (ADS)

Ouannas, Adel; Grassi, Giuseppe

2016-09-01

A new synchronization scheme for chaotic (hyperchaotic) maps with different dimensions is presented. Specifically, given a drive system map with dimension n and a response system with dimension m, the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states. The method, based on the Lyapunov stability theory and the pole placement technique, presents some useful features: (i) it enables synchronization to be achieved for both cases of n < m and n > m; (ii) it is rigorous, being based on theorems; (iii) it can be readily applied to any chaotic (hyperchaotic) maps defined to date. Finally, the capability of the approach is illustrated by synchronization examples between the two-dimensional Hénon map (as the drive system) and the three-dimensional hyperchaotic Wang map (as the response system), and the three-dimensional Hénon-like map (as the drive system) and the two-dimensional Lorenz discrete-time system (as the response system).

Improvement and empirical research on chaos control by theory of "chaos + chaos = order".

PubMed

Fulai, Wang

2012-12-01

This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos = order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ≥ 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos = order" also exist in the dynamics generated by non-Mandelbrot maps.

Generalized logistic map and its application in chaos based cryptography

NASA Astrophysics Data System (ADS)

Lawnik, M.

2017-12-01

The logistic map is commonly used in, for example, chaos based cryptography. However, its properties do not render a safe construction of encryption algorithms. Thus, the scope of the paper is a proposal of generalization of the logistic map by means of a wellrecognized family of chaotic maps. In the next step, an analysis of Lyapunov exponent and the distribution of the iterative variable are studied. The obtained results confirm that the analyzed model can safely and effectively replace a classic logistic map for applications involving chaotic cryptography.

A novel algorithm for thermal image encryption.

PubMed

Hussain, Iqtadar; Anees, Amir; Algarni, Abdulmohsen

2018-04-16

Thermal images play a vital character at nuclear plants, Power stations, Forensic labs biological research, and petroleum products extraction. Safety of thermal images is very important. Image data has some unique features such as intensity, contrast, homogeneity, entropy and correlation among pixels that is why somehow image encryption is trickier as compare to other encryptions. With conventional image encryption schemes it is normally hard to handle these features. Therefore, cryptographers have paid attention to some attractive properties of the chaotic maps such as randomness and sensitivity to build up novel cryptosystems. That is why, recently proposed image encryption techniques progressively more depends on the application of chaotic maps. This paper proposed an image encryption algorithm based on Chebyshev chaotic map and S8 Symmetric group of permutation based substitution boxes. Primarily, parameters of chaotic Chebyshev map are chosen as a secret key to mystify the primary image. Then, the plaintext image is encrypted by the method generated from the substitution boxes and Chebyshev map. By this process, we can get a cipher text image that is perfectly twisted and dispersed. The outcomes of renowned experiments, key sensitivity tests and statistical analysis confirm that the proposed algorithm offers a safe and efficient approach for real-time image encryption.

Gross-Pitaevski map as a chaotic dynamical system.

PubMed

Guarneri, Italo

2017-03-01

The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.

Horseshoes in a Chaotic System with Only One Stable Equilibrium

NASA Astrophysics Data System (ADS)

Huan, Songmei; Li, Qingdu; Yang, Xiao-Song

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.

Reverse bifurcation and fractal of the compound logistic map

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Liang, Qingyong

2008-07-01

The nature of the fixed points of the compound logistic map is researched and the boundary equation of the first bifurcation of the map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, the paper reveal the general features of the compound logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the map may emerge out of double-periodic bifurcation and (2) the chaotic crisis phenomena and the reverse bifurcation are found. At the same time, we analyze the orbit of critical point of the compound logistic map and put forward the definition of Mandelbrot-Julia set of compound logistic map. We generalize the Welstead and Cromer's periodic scanning technology and using this technology construct a series of Mandelbrot-Julia sets of compound logistic map. We investigate the symmetry of Mandelbrot-Julia set and study the topological inflexibility of distributing of period region in the Mandelbrot set, and finds that Mandelbrot set contain abundant information of structure of Julia sets by founding the whole portray of Julia sets based on Mandelbrot set qualitatively.

An authenticated image encryption scheme based on chaotic maps and memory cellular automata

NASA Astrophysics Data System (ADS)

Bakhshandeh, Atieh; Eslami, Ziba

2013-06-01

This paper introduces a new image encryption scheme based on chaotic maps, cellular automata and permutation-diffusion architecture. In the permutation phase, a piecewise linear chaotic map is utilized to confuse the plain-image and in the diffusion phase, we employ the Logistic map as well as a reversible memory cellular automata to obtain an efficient and secure cryptosystem. The proposed method admits advantages such as highly secure diffusion mechanism, computational efficiency and ease of implementation. A novel property of the proposed scheme is its authentication ability which can detect whether the image is tampered during the transmission or not. This is particularly important in applications where image data or part of it contains highly sensitive information. Results of various analyses manifest high security of this new method and its capability for practical image encryption.

Efficiency and security problems of anonymous key agreement protocol based on chaotic maps

NASA Astrophysics Data System (ADS)

Yoon, Eun-Jun

2012-07-01

In 2011, Niu-Wang proposed an anonymous key agreement protocol based on chaotic maps in [Niu Y, Wang X. An anonymous key agreement protocol based on chaotic maps. Commun Nonlinear Sci Simulat 2011;16(4):1986-92]. Niu-Wang's protocol not only achieves session key agreement between a server and a user, but also allows the user to anonymously interact with the server. Nevertheless, this paper points out that Niu-Wang's protocol has the following efficiency and security problems: (1) The protocol has computational efficiency problem when a trusted third party decrypts the user sending message. (2) The protocol is vulnerable to Denial of Service (DoS) attack based on illegal message modification by an attacker.

Chaotic map clustering algorithm for EEG analysis

NASA Astrophysics Data System (ADS)

Bellotti, R.; De Carlo, F.; Stramaglia, S.

2004-03-01

The non-parametric chaotic map clustering algorithm has been applied to the analysis of electroencephalographic signals, in order to recognize the Huntington's disease, one of the most dangerous pathologies of the central nervous system. The performance of the method has been compared with those obtained through parametric algorithms, as K-means and deterministic annealing, and supervised multi-layer perceptron. While supervised neural networks need a training phase, performed by means of data tagged by the genetic test, and the parametric methods require a prior choice of the number of classes to find, the chaotic map clustering gives a natural evidence of the pathological class, without any training or supervision, thus providing a new efficient methodology for the recognition of patterns affected by the Huntington's disease.

Short-term cascaded hydroelectric system scheduling based on chaotic particle swarm optimization using improved logistic map

NASA Astrophysics Data System (ADS)

He, Yaoyao; Yang, Shanlin; Xu, Qifa

2013-07-01

In order to solve the model of short-term cascaded hydroelectric system scheduling, a novel chaotic particle swarm optimization (CPSO) algorithm using improved logistic map is introduced, which uses the water discharge as the decision variables combined with the death penalty function. According to the principle of maximum power generation, the proposed approach makes use of the ergodicity, symmetry and stochastic property of improved logistic chaotic map for enhancing the performance of particle swarm optimization (PSO) algorithm. The new hybrid method has been examined and tested on two test functions and a practical cascaded hydroelectric system. The experimental results show that the effectiveness and robustness of the proposed CPSO algorithm in comparison with other traditional algorithms.

Transition from complete synchronization to spatio-temporal chaos in coupled chaotic systems with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-06-01

We study the transition from coherence (complete synchronization) to incoherence (spatio-temporal chaos) in ensembles of nonlocally coupled chaotic maps with nonhyperbolic and hyperbolic attractors. As basic models of a partial element we use the Henon map and the Lozi map. We show that the transition to incoherence in a ring of coupled Henon maps occurs through the appearance of phase and amplitude chimera states. An ensemble of coupled Lozi maps demonstrates the coherence-incoherence transition via solitary states and no chimera states are observed in this case.

Chaotic orbits obeying one isolating integral in a four-dimensional map

NASA Astrophysics Data System (ADS)

Muzzio, J. C.

2018-02-01

We have recently presented strong evidence that chaotic orbits that obey one isolating integral besides energy exist in a toy Hamiltonian model with three degrees of freedom and are bounded by regular orbits that isolate them from the Arnold web. The interval covered by those numerical experiments was equivalent to about one million Hubble times in a galactic context. Here, we use a four-dimensional map to confirm our previous results and to extend that interval 50 times. We show that, at least within that interval, features found in lower dimension Hamiltonian systems and maps are also present in our study, e.g. within the phase space occupied by a chaotic orbit that obeys one integral there are subspaces where that orbit does not enter and are, instead, occupied by regular orbits that, if tori, bound other chaotic orbits obeying one integral and, if cantori, produce stickiness. We argue that the validity of our results might exceed the time intervals covered by the numerical experiments.

Neural network representation and learning of mappings and their derivatives

NASA Technical Reports Server (NTRS)

White, Halbert; Hornik, Kurt; Stinchcombe, Maxwell; Gallant, A. Ronald

1991-01-01

Discussed here are recent theorems proving that artificial neural networks are capable of approximating an arbitrary mapping and its derivatives as accurately as desired. This fact forms the basis for further results establishing the learnability of the desired approximations, using results from non-parametric statistics. These results have potential applications in robotics, chaotic dynamics, control, and sensitivity analysis. An example involving learning the transfer function and its derivatives for a chaotic map is discussed.

Audio signal encryption using chaotic Hénon map and lifting wavelet transforms

NASA Astrophysics Data System (ADS)

Roy, Animesh; Misra, A. P.

2017-12-01

We propose an audio signal encryption scheme based on the chaotic Hénon map. The scheme mainly comprises two phases: one is the preprocessing stage where the audio signal is transformed into data by the lifting wavelet scheme and the other in which the transformed data is encrypted by chaotic data set and hyperbolic functions. Furthermore, we use dynamic keys and consider the key space size to be large enough to resist any kind of cryptographic attacks. A statistical investigation is also made to test the security and the efficiency of the proposed scheme.

Enhanced smartcard-based password-authenticated key agreement using extended chaotic maps.

PubMed

Lee, Tian-Fu; Hsiao, Chia-Hung; Hwang, Shi-Han; Lin, Tsung-Hung

2017-01-01

A smartcard based password-authenticated key agreement scheme enables a legal user to log in to a remote authentication server and access remote services through public networks using a weak password and a smart card. Lin recently presented an improved chaotic maps-based password-authenticated key agreement scheme that used smartcards to eliminate the weaknesses of the scheme of Guo and Chang, which does not provide strong user anonymity and violates session key security. However, the improved scheme of Lin does not exhibit the freshness property and the validity of messages so it still fails to withstand denial-of-service and privileged-insider attacks. Additionally, a single malicious participant can predetermine the session key such that the improved scheme does not exhibit the contributory property of key agreements. This investigation discusses these weaknesses and proposes an enhanced smartcard-based password-authenticated key agreement scheme that utilizes extended chaotic maps. The session security of this enhanced scheme is based on the extended chaotic map-based Diffie-Hellman problem, and is proven in the real-or-random and the sequence of games models. Moreover, the enhanced scheme ensures the freshness of communicating messages by appending timestamps, and thereby avoids the weaknesses in previous schemes.

An Improvement of Robust and Efficient Biometrics Based Password Authentication Scheme for Telecare Medicine Information Systems Using Extended Chaotic Maps.

PubMed

Moon, Jongho; Choi, Younsung; Kim, Jiye; Won, Dongho

2016-03-01

Recently, numerous extended chaotic map-based password authentication schemes that employ smart card technology were proposed for Telecare Medical Information Systems (TMISs). In 2015, Lu et al. used Li et al.'s scheme as a basis to propose a password authentication scheme for TMISs that is based on biometrics and smart card technology and employs extended chaotic maps. Lu et al. demonstrated that Li et al.'s scheme comprises some weaknesses such as those regarding a violation of the session-key security, a vulnerability to the user impersonation attack, and a lack of local verification. In this paper, however, we show that Lu et al.'s scheme is still insecure with respect to issues such as a violation of the session-key security, and that it is vulnerable to both the outsider attack and the impersonation attack. To overcome these drawbacks, we retain the useful properties of Lu et al.'s scheme to propose a new password authentication scheme that is based on smart card technology and requires the use of chaotic maps. Then, we show that our proposed scheme is more secure and efficient and supports security properties.

Enhanced smartcard-based password-authenticated key agreement using extended chaotic maps

PubMed Central

Lee, Tian-Fu; Hsiao, Chia-Hung; Hwang, Shi-Han

2017-01-01

A smartcard based password-authenticated key agreement scheme enables a legal user to log in to a remote authentication server and access remote services through public networks using a weak password and a smart card. Lin recently presented an improved chaotic maps-based password-authenticated key agreement scheme that used smartcards to eliminate the weaknesses of the scheme of Guo and Chang, which does not provide strong user anonymity and violates session key security. However, the improved scheme of Lin does not exhibit the freshness property and the validity of messages so it still fails to withstand denial-of-service and privileged-insider attacks. Additionally, a single malicious participant can predetermine the session key such that the improved scheme does not exhibit the contributory property of key agreements. This investigation discusses these weaknesses and proposes an enhanced smartcard-based password-authenticated key agreement scheme that utilizes extended chaotic maps. The session security of this enhanced scheme is based on the extended chaotic map-based Diffie-Hellman problem, and is proven in the real-or-random and the sequence of games models. Moreover, the enhanced scheme ensures the freshness of communicating messages by appending timestamps, and thereby avoids the weaknesses in previous schemes. PMID:28759615

Robust and efficient biometrics based password authentication scheme for telecare medicine information systems using extended chaotic maps.

PubMed

Lu, Yanrong; Li, Lixiang; Peng, Haipeng; Xie, Dong; Yang, Yixian

2015-06-01

The Telecare Medicine Information Systems (TMISs) provide an efficient communicating platform supporting the patients access health-care delivery services via internet or mobile networks. Authentication becomes an essential need when a remote patient logins into the telecare server. Recently, many extended chaotic maps based authentication schemes using smart cards for TMISs have been proposed. Li et al. proposed a secure smart cards based authentication scheme for TMISs using extended chaotic maps based on Lee's and Jiang et al.'s scheme. In this study, we show that Li et al.'s scheme has still some weaknesses such as violation the session key security, vulnerability to user impersonation attack and lack of local verification. To conquer these flaws, we propose a chaotic maps and smart cards based password authentication scheme by applying biometrics technique and hash function operations. Through the informal and formal security analyses, we demonstrate that our scheme is resilient possible known attacks including the attacks found in Li et al.'s scheme. As compared with the previous authentication schemes, the proposed scheme is more secure and efficient and hence more practical for telemedical environments.

Failure detection in high-performance clusters and computers using chaotic map computations

DOEpatents

Rao, Nageswara S.

2015-09-01

A programmable media includes a processing unit capable of independent operation in a machine that is capable of executing 10.sup.18 floating point operations per second. The processing unit is in communication with a memory element and an interconnect that couples computing nodes. The programmable media includes a logical unit configured to execute arithmetic functions, comparative functions, and/or logical functions. The processing unit is configured to detect computing component failures, memory element failures and/or interconnect failures by executing programming threads that generate one or more chaotic map trajectories. The central processing unit or graphical processing unit is configured to detect a computing component failure, memory element failure and/or an interconnect failure through an automated comparison of signal trajectories generated by the chaotic maps.

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levnajić, Zoran; Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106; Mezić, Igor

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone,more » and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.« less

Ergodic theory and visualization. II. Fourier mesochronic plots visualize (quasi)periodic sets.

PubMed

Levnajić, Zoran; Mezić, Igor

2015-05-01

We present an application and analysis of a visualization method for measure-preserving dynamical systems introduced by I. Mezić and A. Banaszuk [Physica D 197, 101 (2004)], based on frequency analysis and Koopman operator theory. This extends our earlier work on visualization of ergodic partition [Z. Levnajić and I. Mezić, Chaos 20, 033114 (2010)]. Our method employs the concept of Fourier time average [I. Mezić and A. Banaszuk, Physica D 197, 101 (2004)], and is realized as a computational algorithms for visualization of periodic and quasi-periodic sets in the phase space. The complement of periodic phase space partition contains chaotic zone, and we show how to identify it. The range of method's applicability is illustrated using well-known Chirikov standard map, while its potential in illuminating higher-dimensional dynamics is presented by studying the Froeschlé map and the Extended Standard Map.

Chaotic diffusion in the Gliese-876 planetary system

NASA Astrophysics Data System (ADS)

Martí, J. G.; Cincotta, P. M.; Beaugé, C.

2016-07-01

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disc, and a natural consequence of irregular motion. In this paper, we show that resonant multiplanetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over time-scales comparable to their age. Using the GJ-876 system as an example, we analyse the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincaré maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, the stochastic borders of the Laplace resonance seem to prevent the complete destruction of the system. We characterize the diffusion for small ensembles along the parameters of the outermost planet. Finally, we perform a stability analysis of the inherent chaotic, albeit stable Laplace resonance, by linking the behaviour of the resonant variables of the configurations to the different sub-structures inside the three-body resonance.

Mammographic images segmentation based on chaotic map clustering algorithm

PubMed Central

2014-01-01

Background This work investigates the applicability of a novel clustering approach to the segmentation of mammographic digital images. The chaotic map clustering algorithm is used to group together similar subsets of image pixels resulting in a medically meaningful partition of the mammography. Methods The image is divided into pixels subsets characterized by a set of conveniently chosen features and each of the corresponding points in the feature space is associated to a map. A mutual coupling strength between the maps depending on the associated distance between feature space points is subsequently introduced. On the system of maps, the simulated evolution through chaotic dynamics leads to its natural partitioning, which corresponds to a particular segmentation scheme of the initial mammographic image. Results The system provides a high recognition rate for small mass lesions (about 94% correctly segmented inside the breast) and the reproduction of the shape of regions with denser micro-calcifications in about 2/3 of the cases, while being less effective on identification of larger mass lesions. Conclusions We can summarize our analysis by asserting that due to the particularities of the mammographic images, the chaotic map clustering algorithm should not be used as the sole method of segmentation. It is rather the joint use of this method along with other segmentation techniques that could be successfully used for increasing the segmentation performance and for providing extra information for the subsequent analysis stages such as the classification of the segmented ROI. PMID:24666766

Chaotic dynamics around cometary nuclei

NASA Astrophysics Data System (ADS)

Lages, José; Shevchenko, Ivan I.; Rollin, Guillaume

2018-06-01

We apply a generalized Kepler map theory to describe the qualitative chaotic dynamics around cometary nuclei, based on accessible observational data for five comets whose nuclei are well-documented to resemble dumb-bells. The sizes of chaotic zones around the nuclei and the Lyapunov times of the motion inside these zones are estimated. In the case of Comet 1P/Halley, the circumnuclear chaotic zone seems to engulf an essential part of the Hill sphere, at least for orbits of moderate to high eccentricity.

A novel chaos-based image encryption algorithm using DNA sequence operations

NASA Astrophysics Data System (ADS)

Chai, Xiuli; Chen, Yiran; Broyde, Lucie

2017-01-01

An image encryption algorithm based on chaotic system and deoxyribonucleic acid (DNA) sequence operations is proposed in this paper. First, the plain image is encoded into a DNA matrix, and then a new wave-based permutation scheme is performed on it. The chaotic sequences produced by 2D Logistic chaotic map are employed for row circular permutation (RCP) and column circular permutation (CCP). Initial values and parameters of the chaotic system are calculated by the SHA 256 hash of the plain image and the given values. Then, a row-by-row image diffusion method at DNA level is applied. A key matrix generated from the chaotic map is used to fuse the confused DNA matrix; also the initial values and system parameters of the chaotic system are renewed by the hamming distance of the plain image. Finally, after decoding the diffused DNA matrix, we obtain the cipher image. The DNA encoding/decoding rules of the plain image and the key matrix are determined by the plain image. Experimental results and security analyses both confirm that the proposed algorithm has not only an excellent encryption result but also resists various typical attacks.

Dynamic Analysis of the Carotid-Kundalini Map

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Liang, Qingyong; Meng, Juan

The nature of the fixed points of the Carotid-Kundalini (C-K) map was studied and the boundary equation of the first bifurcation of the C-K map in the parameter plane is presented. Using the quantitative criterion and rule of chaotic system, the paper reveals the general features of the C-K Map transforming from regularity to chaos. The following conclusions are obtained: (i) chaotic patterns of the C-K map may emerge out of double-periodic bifurcation; (ii) the chaotic crisis phenomena are found. At the same time, the authors analyzed the orbit of critical point of the complex C-K Map and put forward the definition of Mandelbrot-Julia set of the complex C-K Map. The authors generalized the Welstead and Cromer's periodic scanning technique and using this technology constructed a series of the Mandelbrot-Julia sets of the complex C-K Map. Based on the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing, we investigated the symmetry of the Mandelbrot-Julia set and studied the topological inflexibility of distribution of the periodic region in the Mandelbrot set, and found that the Mandelbrot set contains abundant information of the structure of Julia sets by finding the whole portray of Julia sets based on Mandelbrot set qualitatively.

Discrete dynamical laser equation for the critical onset of bistability, entanglement and disappearance

NASA Astrophysics Data System (ADS)

Abdul, M.; Farooq, U.; Akbar, Jehan; Saif, F.

2018-06-01

We transform the semi-classical laser equation for single mode homogeneously broadened lasers to a one-dimensional nonlinear map by using the discrete dynamical approach. The obtained mapping, referred to as laser logistic mapping (LLM), characteristically exhibits convergent, cyclic and chaotic behavior depending on the control parameter. Thus, the so obtained LLM explains stable, bistable, multi-stable, and chaotic solutions for output field intensity. The onset of bistability takes place at a critical value of the effective gain coefficient. The obtained analytical results are confirmed through numerical calculations.

Attack to AN Image Encryption Based on Chaotic Logistic Map

NASA Astrophysics Data System (ADS)

Wang, Xing-Yuan; Chen, Feng; Wang, Tian; Xu, Dahai; Ma, Yutian

2013-10-01

This paper offers two different attacks on a freshly proposed image encryption based on chaotic logistic map. The cryptosystem under study first uses a secret key of 80-bit and employed two chaotic logistic maps. We derived the initial conditions of the logistic maps from using the secret key by providing different weights to all its bits. Additionally, in this paper eight different types of procedures are used to encrypt the pixels of an image in the proposed encryption process of which one of them will be used for a certain pixel which is determined by the product of the logistic map. The secret key is revised after encrypting each block which consisted of 16 pixels of the image. The encrypting process have weakness, worst of which is that every byte of plaintext is independent when substituted, so the cipher text of the byte will not change even the other bytes have changed. As a result of weakness, a chosen plaintext attack and a chosen cipher text attack can be completed without any knowledge of the key value to recuperate the ciphered image.

Coupled chaotic fluctuations in a model of international trade and innovation: Some preliminary results

NASA Astrophysics Data System (ADS)

Sushko, Iryna; Gardini, Laura; Matsuyama, Kiminori

2018-05-01

We consider a two-dimensional continuous noninvertible piecewise smooth map, which characterizes the dynamics of innovation activities in the two-country model of trade and product innovation proposed in [7]. This two-dimensional map can be viewed as a coupling of two one-dimensional skew tent maps, each of which characterizes the innovation dynamics in each country in the absence of trade, and the coupling parameter depends inversely on the trade cost between the two countries. Hence, this model offers a laboratory for studying how a decline in the trade cost, or globalization, might synchronize endogenous fluctuations of innovation activities in the two countries. In this paper, we focus on the bifurcation scenarios, how the phase portrait of the two-dimensional map changes with a gradual decline of the trade cost, leading to border collision, merging, expansion and final bifurcations of the coexisting chaotic attractors. An example of peculiar border collision bifurcation leading to an increase of dimension of the chaotic attractor is also presented.

A Novel Color Image Encryption Algorithm Based on Quantum Chaos Sequence

NASA Astrophysics Data System (ADS)

Liu, Hui; Jin, Cong

2017-03-01

In this paper, a novel algorithm of image encryption based on quantum chaotic is proposed. The keystreams are generated by the two-dimensional logistic map as initial conditions and parameters. And then general Arnold scrambling algorithm with keys is exploited to permute the pixels of color components. In diffusion process, a novel encryption algorithm, folding algorithm, is proposed to modify the value of diffused pixels. In order to get the high randomness and complexity, the two-dimensional logistic map and quantum chaotic map are coupled with nearest-neighboring coupled-map lattices. Theoretical analyses and computer simulations confirm that the proposed algorithm has high level of security.

A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata

NASA Astrophysics Data System (ADS)

Enayatifar, Rasul; Sadaei, Hossein Javedani; Abdullah, Abdul Hanan; Lee, Malrey; Isnin, Ismail Fauzi

2015-08-01

Currently, there are many studies have conducted on developing security of the digital image in order to protect such data while they are sending on the internet. This work aims to propose a new approach based on a hybrid model of the Tinkerbell chaotic map, deoxyribonucleic acid (DNA) and cellular automata (CA). DNA rules, DNA sequence XOR operator and CA rules are used simultaneously to encrypt the plain-image pixels. To determine rule number in DNA sequence and also CA, a 2-dimension Tinkerbell chaotic map is employed. Experimental results and computer simulations, both confirm that the proposed scheme not only demonstrates outstanding encryption, but also resists various typical attacks.

Implementation of efficient trajectories for an ultrasonic scanner using chaotic maps

NASA Astrophysics Data System (ADS)

Almeda, A.; Baltazar, A.; Treesatayapun, C.; Mijarez, R.

2012-05-01

Typical ultrasonic methodology for nondestructive scanning evaluation uses systematic scanning paths. In many cases, this approach is time inefficient and also energy and computational power consuming. Here, a methodology for the scanning of defects using an ultrasonic echo-pulse scanning technique combined with chaotic trajectory generation is proposed. This is implemented in a Cartesian coordinate robotic system developed in our lab. To cover the entire search area, a chaotic function and a proposed mirror mapping were incorporated. To improve detection probability, our proposed scanning methodology is complemented with a probabilistic approach of discontinuity detection. The developed methodology was found to be more efficient than traditional ones used to localize and characterize hidden flaws.

An image encryption algorithm based on 3D cellular automata and chaotic maps

NASA Astrophysics Data System (ADS)

Del Rey, A. Martín; Sánchez, G. Rodríguez

2015-05-01

A novel encryption algorithm to cipher digital images is presented in this work. The digital image is rendering into a three-dimensional (3D) lattice and the protocol consists of two phases: the confusion phase where 24 chaotic Cat maps are applied and the diffusion phase where a 3D cellular automata is evolved. The encryption method is shown to be secure against the most important cryptanalytic attacks.

A new chaotic multi-verse optimization algorithm for solving engineering optimization problems

NASA Astrophysics Data System (ADS)

Sayed, Gehad Ismail; Darwish, Ashraf; Hassanien, Aboul Ella

2018-03-01

Multi-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO's performance.

Symmetry restoring bifurcations and quasiperiodic chaos induced by a new intermittency in a vibro-impact system.

PubMed

Yue, Yuan; Miao, Pengcheng; Xie, Jianhua; Celso, Grebogi

2016-11-01

Quasiperiodic chaos (QC), which is a combination of quasiperiodic sets and a chaotic set, is uncovered in the six dimensional Poincaré map of a symmetric three-degree of freedom vibro-impact system. Accompanied by symmetry restoring bifurcation, this QC is the consequence of a novel intermittency that occurs between two conjugate quasiperiodic sets and a chaotic set. The six dimensional Poincaré map P is the 2-fold composition of another virtual implicit map Q, yielding the symmetry of the system. Map Q can capture two conjugate attractors, which is at the core of the dynamics of the vibro-impact system. Three types of symmetry restoring bifurcations are analyzed in detail. First, if two conjugate chaotic attractors join together, the chaos-chaos intermittency induced by attractor-merging crisis takes place. Second, if two conjugate quasiperiodic sets are suddenly embedded in a chaotic one, QC is induced by a new intermittency between the three attractors. Third, if two conjugate quasiperiodic attractors connect with each other directly, they merge to form a single symmetric quasiperiodic one. For the second case, the new intermittency is caused by the collision of two conjugate quasiperiodic attractors with an unstable symmetric limit set. As the iteration number is increased, the largest finite-time Lyapunov exponent of the QC does not converge to a constant, but fluctuates in the positive region.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-06-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-03-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Localization of Stable and Chaotic Nonpropagating Structures in Nonlinear Mesoscopic Lattices.

NASA Astrophysics Data System (ADS)

Greenfield, Alan Barry

Recent developments in the study of non-linear localized states, especially non-propagating ones, are outlined. Theoretical models of linear and nonlinear states in a lattice of coupled pendulums and related systems are reviewed. Particular attention is paid to those states which can be described by the Nonlinear Schrodinger equation as well as states where two modes can coexist and states exhibiting chaos. Measurement of localized stable and chaotic states in a 35 site physical pendulum lattice is reported. Various measurement techniques that were used are explained. States that were measured include the tanh profile or kink soliton, and the corresponding uniform state in the wavelength 2 mode, a similar soliton and uniform state in the wavelength 4 mode, a domain wall between the wavelength 2 and 4 modes and a domain wall between a chaotic state and the wavelength 2 mode. Amplitude profiles were measured for the stable kink and domain wall states and smooth curves were obtained by dividing the kink states by the corresponding uniform states. Return maps were measured for two sites in the chaotic domain wall. Simulation of a chaotic domain wall in a 50 site numerical lattice is reported. This system has the advantage that its parameters can be modified much more easily than those of the physical lattice. An attempt is made at quantifying the level of chaos as a function of lattice site with fractal dimension calculations on return maps embedded in a three dimensional space. The drive plane of the chaotic domain wall is mapped out in the drive amplitude - drive frequency plane. Transitions to various stable and quasiperiodic domain walls are noted.

Visibility graphlet approach to chaotic time series

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mutua, Stephen; Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega; Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn

Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems.more » Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.« less

Effect of randomness in logistic maps

NASA Astrophysics Data System (ADS)

Khaleque, Abdul; Sen, Parongama

2015-01-01

We study a random logistic map xt+1 = atxt[1 - xt] where at are bounded (q1 ≤ at ≤ q2), random variables independently drawn from a distribution. xt does not show any regular behavior in time. We find that xt shows fully ergodic behavior when the maximum allowed value of at is 4. However , averaged over different realizations reaches a fixed point. For 1 ≤ at ≤ 4, the system shows nonchaotic behavior and the Lyapunov exponent is strongly dependent on the asymmetry of the distribution from which at is drawn. Chaotic behavior is seen to occur beyond a threshold value of q1(q2) when q2(q1) is varied. The most striking result is that the random map is chaotic even when q2 is less than the threshold value 3.5699⋯ at which chaos occurs in the nonrandom map. We also employ a different method in which a different set of random variables are used for the evolution of two initially identical x values, here the chaotic regime exists for all q1 ≠ q2 values.

Chaos in a chemical system

NASA Astrophysics Data System (ADS)

Srivastava, R.; Srivastava, P. K.; Chattopadhyay, J.

2013-07-01

Chaotic oscillations have been observed experimentally in dual-frequency oscillator OAP - Ce+4-BrO- 3-H2SO4 in CSTR. The system shows variation of oscillating potential and frequencies when it moves from low frequency to high frequency region and vice-versa. It was observed that system bifurcate from low frequency to chaotic regime through periode-2 and period-3 on the other hand system bifurcate from chaotic regime to high frequency oscillation through period-2. It was established that the observed oscillations are chaotic in nature on the basis of next amplitude map and bifurcation sequences.

Fast and secure encryption-decryption method based on chaotic dynamics

DOEpatents

Protopopescu, Vladimir A.; Santoro, Robert T.; Tolliver, Johnny S.

1995-01-01

A method and system for the secure encryption of information. The method comprises the steps of dividing a message of length L into its character components; generating m chaotic iterates from m independent chaotic maps; producing an "initial" value based upon the m chaotic iterates; transforming the "initial" value to create a pseudo-random integer; repeating the steps of generating, producing and transforming until a pseudo-random integer sequence of length L is created; and encrypting the message as ciphertext based upon the pseudo random integer sequence. A system for accomplishing the invention is also provided.

Pseudorandom number generation using chaotic true orbits of the Bernoulli map

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saito, Asaki, E-mail: saito@fun.ac.jp; Yamaguchi, Akihiro

We devise a pseudorandom number generator that exactly computes chaotic true orbits of the Bernoulli map on quadratic algebraic integers. Moreover, we describe a way to select the initial points (seeds) for generating multiple pseudorandom binary sequences. This selection method distributes the initial points almost uniformly (equidistantly) in the unit interval, and latter parts of the generated sequences are guaranteed not to coincide. We also demonstrate through statistical testing that the generated sequences possess good randomness properties.

Partially chaotic orbits in a perturbed cubic force model

NASA Astrophysics Data System (ADS)

Muzzio, J. C.

2017-11-01

Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincaré maps to show that partially chaotic orbits are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit.

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

NASA Astrophysics Data System (ADS)

Liu, Zeyu; Xia, Tiecheng; Wang, Jinbo

2018-03-01

We propose a new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes–Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms. Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

Chaos based encryption system for encrypting electroencephalogram signals.

PubMed

Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De

2014-05-01

In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.

On generic obstructions to recovering correct statistics from climate simulations: Homogenization for deterministic maps and multiplicative noise

NASA Astrophysics Data System (ADS)

Gottwald, Georg; Melbourne, Ian

2013-04-01

Whereas diffusion limits of stochastic multi-scale systems have a long and successful history, the case of constructing stochastic parametrizations of chaotic deterministic systems has been much less studied. We present rigorous results of convergence of a chaotic slow-fast system to a stochastic differential equation with multiplicative noise. Furthermore we present rigorous results for chaotic slow-fast maps, occurring as numerical discretizations of continuous time systems. This raises the issue of how to interpret certain stochastic integrals; surprisingly the resulting integrals of the stochastic limit system are generically neither of Stratonovich nor of Ito type in the case of maps. It is shown that the limit system of a numerical discretisation is different to the associated continuous time system. This has important consequences when interpreting the statistics of long time simulations of multi-scale systems - they may be very different to the one of the original continuous time system which we set out to study.

An efficient chaotic maps-based authentication and key agreement scheme using smartcards for telecare medicine information systems.

PubMed

Lee, Tian-Fu

2013-12-01

A smartcard-based authentication and key agreement scheme for telecare medicine information systems enables patients, doctors, nurses and health visitors to use smartcards for secure login to medical information systems. Authorized users can then efficiently access remote services provided by the medicine information systems through public networks. Guo and Chang recently improved the efficiency of a smartcard authentication and key agreement scheme by using chaotic maps. Later, Hao et al. reported that the scheme developed by Guo and Chang had two weaknesses: inability to provide anonymity and inefficient double secrets. Therefore, Hao et al. proposed an authentication scheme for telecare medicine information systems that solved these weaknesses and improved performance. However, a limitation in both schemes is their violation of the contributory property of key agreements. This investigation discusses these weaknesses and proposes a new smartcard-based authentication and key agreement scheme that uses chaotic maps for telecare medicine information systems. Compared to conventional schemes, the proposed scheme provides fewer weaknesses, better security, and more efficiency.

Scale invariance in chaotic time series: Classical and quantum examples

NASA Astrophysics Data System (ADS)

Landa, Emmanuel; Morales, Irving O.; Stránský, Pavel; Fossion, Rubén; Velázquez, Victor; López Vieyra, J. C.; Frank, Alejandro

Important aspects of chaotic behavior appear in systems of low dimension, as illustrated by the Map Module 1. It is indeed a remarkable fact that all systems tha make a transition from order to disorder display common properties, irrespective of their exacta functional form. We discuss evidence for 1/f power spectra in the chaotic time series associated in classical and quantum examples, the one-dimensional map module 1 and the spectrum of 48Ca. A Detrended Fluctuation Analysis (DFA) method is applied to investigate the scaling properties of the energy fluctuations in the spectrum of 48Ca obtained with a large realistic shell model calculation (ANTOINE code) and with a random shell model (TBRE) calculation also in the time series obtained with the map mod 1. We compare the scale invariant properties of the 48Ca nuclear spectrum sith similar analyses applied to the RMT ensambles GOE and GDE. A comparison with the corresponding power spectra is made in both cases. The possible consequences of the results are discussed.

Stability and Noise-induced Transitions in an Ensemble of Nonlocally Coupled Chaotic Maps

NASA Astrophysics Data System (ADS)

Bukh, Andrei V.; Slepnev, Andrei V.; Anishchenko, Vadim S.; Vadivasova, Tatiana E.

2018-05-01

The influence of noise on chimera states arising in ensembles of nonlocally coupled chaotic maps is studied. There are two types of chimera structures that can be obtained in such ensembles: phase and amplitude chimera states. In this work, a series of numerical experiments is carried out to uncover the impact of noise on both types of chimeras. The noise influence on a chimera state in the regime of periodic dynamics results in the transition to chaotic dynamics. At the same time, the transformation of incoherence clusters of the phase chimera to incoherence clusters of the amplitude chimera occurs. Moreover, it is established that the noise impact may result in the appearance of a cluster with incoherent behavior in the middle of a coherence cluster.

Image encryption algorithm based on multiple mixed hash functions and cyclic shift

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Zhu, Xiaoqiang; Wu, Xiangjun; Zhang, Yingqian

2018-08-01

This paper proposes a new one-time pad scheme for chaotic image encryption that is based on the multiple mixed hash functions and the cyclic-shift function. The initial value is generated using both information of the plaintext image and the chaotic sequences, which are calculated from the SHA1 and MD5 hash algorithms. The scrambling sequences are generated by the nonlinear equations and logistic map. This paper aims to improve the deficiencies of traditional Baptista algorithms and its improved algorithms. We employ the cyclic-shift function and piece-wise linear chaotic maps (PWLCM), which give each shift number the characteristics of chaos, to diffuse the image. Experimental results and security analysis show that the new scheme has better security and can resist common attacks.

Chaotic Behaviour of a Driven P-N Junction

NASA Astrophysics Data System (ADS)

Perez, Jose Maria

The chaotic behavior of a driven p-n junction is experimentally examined. Bifurcation diagrams for the system are measured, showing period doubling bifurcations up to f/32, onset of chaos, reverse bifurcations of chaotic bands, and periodic windows. Some of the measured bifurcation diagrams are similar to the bifurcation diagram of the logistic map x(,n+1) = (lamda)x(,n)(1 - x(,n)). A return map is also measured showing approximately a one-dimensional map with a single extremum at low driving voltages. The intermittency route to chaos is experimentally observed to occur near a tangent bifurcation as the system approaches a period 5 window at (lamda) = (lamda)(,5). Data are presented for the dependence of the average laminar length on (epsilon) = (lamda)(,5) - (lamda), and for the probability distribution P(l) vs. l. The effects of additive stochastic noise on period doubling, chaos, windows, and intermittency are examined and are found to agree with the logistic model and universal predictions. Three examples of crisis of the attractor are observed. The crises occur when an unstable orbit intersects the chaotic attractor. A period adding sequence is reported in which wide periodic windows of period 2, 3, 4, ... are observed for increasing driving voltage. The initial period doubling cascade and the period adding sequence are compared to two theoretical models, with reasonable success.

Alternative predictors in chaotic time series

NASA Astrophysics Data System (ADS)

Alves, P. R. L.; Duarte, L. G. S.; da Mota, L. A. C. P.

2017-06-01

In the scheme of reconstruction, non-polynomial predictors improve the forecast from chaotic time series. The algebraic manipulation in the Maple environment is the basis for obtaining of accurate predictors. Beyond the different times of prediction, the optional arguments of the computational routines optimize the running and the analysis of global mappings.

Route to broadband chaos in a chaotic laser diode subject to optical injection.

PubMed

Wang, An-Bang; Wang, Yun-Cai; Wang, Juan-Fen

2009-04-15

We experimentally and numerically demonstrate a route to bandwidth-enhanced chaos that is induced by an additional optical injection for a chaotic laser diode with optical feedback. The measured and calculated optical spectra consistently reveal that the mechanism of bandwidth enhancement is the interaction between the injection and chaotic laser field via beating. The bandwidth can be maximized only when the injected light is detuned into the edge of the optical spectrum of the chaotic laser field and the beating frequency exceeds the original bandwidth. The simulated dynamics maps indicate that 20 GHz broadband chaos can be obtained by commonly used laser diodes.

Timing variation in an analytically solvable chaotic system

NASA Astrophysics Data System (ADS)

Blakely, J. N.; Milosavljevic, M. S.; Corron, N. J.

2017-02-01

We present analytic solutions for a chaotic dynamical system that do not have the regular timing characteristic of recently reported solvable chaotic systems. The dynamical system can be viewed as a first order filter with binary feedback. The feedback state may be switched only at instants defined by an external clock signal. Generalizing from a period one clock, we show analytic solutions for period two and higher period clocks. We show that even when the clock 'ticks' randomly the chaotic system has an analytic solution. These solutions can be visualized in a stroboscopic map whose complexity increases with the complexity of the clock. We provide both analytic results as well as experimental data from an electronic circuit implementation of the system. Our findings bridge the gap between the irregular timing of well known chaotic systems such as Lorenz and Rossler and the well regulated oscillations of recently reported solvable chaotic systems.

Hash function based on chaotic map lattices.

PubMed

Wang, Shihong; Hu, Gang

2007-06-01

A new hash function system, based on coupled chaotic map dynamics, is suggested. By combining floating point computation of chaos and some simple algebraic operations, the system reaches very high bit confusion and diffusion rates, and this enables the system to have desired statistical properties and strong collision resistance. The chaos-based hash function has its advantages for high security and fast performance, and it serves as one of the most highly competitive candidates for practical applications of hash function for software realization and secure information communications in computer networks.

From globally coupled maps to complex-systems biology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaneko, Kunihiko, E-mail: kaneko@complex.c.u-tokyo.ac.jp

Studies of globally coupled maps, introduced as a network of chaotic dynamics, are briefly reviewed with an emphasis on novel concepts therein, which are universal in high-dimensional dynamical systems. They include clustering of synchronized oscillations, hierarchical clustering, chimera of synchronization and desynchronization, partition complexity, prevalence of Milnor attractors, chaotic itinerancy, and collective chaos. The degrees of freedom necessary for high dimensionality are proposed to equal the number in which the combinatorial exceeds the exponential. Future analysis of high-dimensional dynamical systems with regard to complex-systems biology is briefly discussed.

Hash function based on chaotic map lattices

NASA Astrophysics Data System (ADS)

Wang, Shihong; Hu, Gang

2007-06-01

A new hash function system, based on coupled chaotic map dynamics, is suggested. By combining floating point computation of chaos and some simple algebraic operations, the system reaches very high bit confusion and diffusion rates, and this enables the system to have desired statistical properties and strong collision resistance. The chaos-based hash function has its advantages for high security and fast performance, and it serves as one of the most highly competitive candidates for practical applications of hash function for software realization and secure information communications in computer networks.

A case study in bifurcation theory

NASA Astrophysics Data System (ADS)

Khmou, Youssef

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

A local chaotic quasi-attractor in a kicked rotator

NASA Astrophysics Data System (ADS)

Jiang, Yu-Mei; Lu, Yun-Qing; Zhao, Jin-Gang; Wang, Xu-Ming; Chen, He-Sheng; He, Da-Ren

2002-03-01

Recently, Hu et al. reported a diffusion in a special kind of stochastic web observed in a kicked rotator described by a discontinuous but invertible two-dimensional area-preserving map^1. We modified the function form of the system so that the period of the kicking force becomes different in two parts of the space, and the conservative map becomes both discontinuous and noninvertible. It is found that when the ratio between both periods becomes smaller or larger than (but near to) 1, the chaotic diffusion in the web transfers to chaotic transients, which are attracted to the elliptic islands those existed inside the holes of the web earlier when the ratio equals 1. As soon as reaching the islands, the iteration follows the conservative laws exactly. Therefore we address these elliptic islands as "regular quasi-attractor"^2. When the ratio increases further and becomes far from 1, all the elliptic islands disappear and a local chaotic quasi-attractor appears instead. It attracts the iterations starting from most initial points in the phase space. This behavior may be considered as a kind of "confinement" of chaotic motion of a particle. ^1B. Hu et al., Phys.Rev.Lett.,82(1999)4224. ^2J. Wang et al., Phys.Rev.E, 64(2001)026202.

Texture Analysis of Chaotic Coupled Map Lattices Based Image Encryption Algorithm

NASA Astrophysics Data System (ADS)

Khan, Majid; Shah, Tariq; Batool, Syeda Iram

2014-09-01

As of late, data security is key in different enclosures like web correspondence, media frameworks, therapeutic imaging, telemedicine and military correspondence. In any case, a large portion of them confronted with a few issues, for example, the absence of heartiness and security. In this letter, in the wake of exploring the fundamental purposes of the chaotic trigonometric maps and the coupled map lattices, we have presented the algorithm of chaos-based image encryption based on coupled map lattices. The proposed mechanism diminishes intermittent impact of the ergodic dynamical systems in the chaos-based image encryption. To assess the security of the encoded image of this scheme, the association of two nearby pixels and composition peculiarities were performed. This algorithm tries to minimize the problems arises in image encryption.

How to control chaotic behaviour and population size with proportional feedback

NASA Astrophysics Data System (ADS)

Liz, Eduardo

2010-01-01

We study the control of chaos in one-dimensional discrete maps as they often occur in modelling population dynamics. For managing the population, we seek to suppress any possible chaotic behavior, leading the system to a stable equilibrium. In this Letter, we make a rigorous analysis of the proportional feedback method under certain conditions fulfilled by a wide family of maps. We show that it is possible to stabilize the chaotic dynamics towards a globally stable positive equilibrium, that can be chosen among a broad range of possible values. In particular, the size of the population can be enhanced by control in form of population reduction. This paradoxical phenomenon is known as the hydra effect, and it has important implications in the design of strategies in such areas as fishing, pest management, and conservation biology.

Detecting chaos in particle accelerators through the frequency map analysis method.

PubMed

Papaphilippou, Yannis

2014-06-01

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

From Weakly Chaotic Dynamics to Deterministic Subdiffusion via Copula Modeling

NASA Astrophysics Data System (ADS)

Nazé, Pierre

2018-03-01

Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this technique to connect the statistical distributions of weakly chaotic dynamics and deterministic subdiffusion. More precisely, we decompose the jumps distribution of Geisel-Thomae map into a bivariate one and determine the marginal and copula distributions respectively by infinite ergodic theory and statistical inference techniques. We verify therefore that the characteristic tail distribution of subdiffusion is an extreme value copula coupling Mittag-Leffler distributions. We also present a method to calculate the exact copula and joint distributions in the case where weakly chaotic dynamics and deterministic subdiffusion statistical distributions are already known. Numerical simulations and consistency with the dynamical aspects of the map support our results.

Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Beşliu, C.; Jipa, Al.; Felea, D.; Grossu, I. V.

2008-05-01

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE. Program summaryProgram title: Chaos Catalogue identifier: AEAP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 885 No. of bytes in distributed program, including test data, etc.: 5925 Distribution format: tar.gz Programming language: Scilab 3.1.1 Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 100 Megabytes Classification: 6.2 Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem. Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.

"Coherence-incoherence" transition in ensembles of nonlocally coupled chaotic oscillators with nonhyperbolic and hyperbolic attractors

NASA Astrophysics Data System (ADS)

Semenova, Nadezhda I.; Rybalova, Elena V.; Strelkova, Galina I.; Anishchenko, Vadim S.

2017-03-01

We consider in detail similarities and differences of the "coherence-incoherence" transition in ensembles of nonlocally coupled chaotic discrete-time systems with nonhyperbolic and hyperbolic attractors. As basic models we employ the Hénon map and the Lozi map. We show that phase and amplitude chimera states appear in a ring of coupled Hénon maps, while no chimeras are observed in an ensemble of coupled Lozi maps. In the latter, the transition to spatio-temporal chaos occurs via solitary states. We present numerical results for the coupling function which describes the impact of neighboring oscillators on each partial element of an ensemble with nonlocal coupling. Varying the coupling strength we analyze the evolution of the coupling function and discuss in detail its role in the "coherence-incoherence" transition in the ensembles of Hénon and Lozi maps.

A Novel Image Encryption Scheme Based on Intertwining Chaotic Maps and RC4 Stream Cipher

NASA Astrophysics Data System (ADS)

Kumari, Manju; Gupta, Shailender

2018-03-01

As the systems are enabling us to transmit large chunks of data, both in the form of texts and images, there is a need to explore algorithms which can provide a higher security without increasing the time complexity significantly. This paper proposes an image encryption scheme which uses intertwining chaotic maps and RC4 stream cipher to encrypt/decrypt the images. The scheme employs chaotic map for the confusion stage and for generation of key for the RC4 cipher. The RC4 cipher uses this key to generate random sequences which are used to implement an efficient diffusion process. The algorithm is implemented in MATLAB-2016b and various performance metrics are used to evaluate its efficacy. The proposed scheme provides highly scrambled encrypted images and can resist statistical, differential and brute-force search attacks. The peak signal-to-noise ratio values are quite similar to other schemes, the entropy values are close to ideal. In addition, the scheme is very much practical since having lowest time complexity then its counterparts.

Experiments of reconstructing discrete atmospheric dynamic models from data (I)

NASA Astrophysics Data System (ADS)

Lin, Zhenshan; Zhu, Yanyu; Deng, Ziwang

1995-03-01

In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, x n + 1 = 1- μx {2/n}, could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.

Improved numerical solutions for chaotic-cancer-model

NASA Astrophysics Data System (ADS)

Yasir, Muhammad; Ahmad, Salman; Ahmed, Faizan; Aqeel, Muhammad; Akbar, Muhammad Zubair

2017-01-01

In biological sciences, dynamical system of cancer model is well known due to its sensitivity and chaoticity. Present work provides detailed computational study of cancer model by counterbalancing its sensitive dependency on initial conditions and parameter values. Cancer chaotic model is discretized into a system of nonlinear equations that are solved using the well-known Successive-Over-Relaxation (SOR) method with a proven convergence. This technique enables to solve large systems and provides more accurate approximation which is illustrated through tables, time history maps and phase portraits with detailed analysis.

Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication.

PubMed

Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang

2013-03-01

Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.

Quantitative Universality for a Class of Weakly Chaotic Systems

NASA Astrophysics Data System (ADS)

Venegeroles, Roberto

2014-02-01

We consider a general class of intermittent maps designed to be weakly chaotic, i.e., for which the separation of trajectories of nearby initial conditions is weaker than exponential. We show that all its spatio and temporal properties, hitherto regarded independently in the literature, can be represented by a single characteristic function ϕ. A universal criterion for the choice of ϕ is obtained within the Feigenbaum's renormalization-group approach. We find a general expression for the dispersion rate ζ( t) of initially nearby trajectories and we show that the instability scenario for weakly chaotic systems is more general than that originally proposed by Gaspard and Wang (Proc. Natl. Acad. Sci. USA 85:4591, 1988). We also consider a spatially extended version of such class of maps, which leads to anomalous diffusion, and we show that the mean squared displacement satisfies σ 2( t)˜ ζ( t). To illustrate our results, some examples are discussed in detail.

Image secure transmission for optical orthogonal frequency-division multiplexing visible light communication systems using chaotic discrete cosine transform

NASA Astrophysics Data System (ADS)

Wang, Zhongpeng; Zhang, Shaozhong; Chen, Fangni; Wu, Ming-Wei; Qiu, Weiwei

2017-11-01

A physical encryption scheme for orthogonal frequency-division multiplexing (OFDM) visible light communication (VLC) systems using chaotic discrete cosine transform (DCT) is proposed. In the scheme, the row of the DCT matrix is permutated by a scrambling sequence generated by a three-dimensional (3-D) Arnold chaos map. Furthermore, two scrambling sequences, which are also generated from a 3-D Arnold map, are employed to encrypt the real and imaginary parts of the transmitted OFDM signal before the chaotic DCT operation. The proposed scheme enhances the physical layer security and improves the bit error rate (BER) performance for OFDM-based VLC. The simulation results prove the efficiency of the proposed encryption method. The experimental results show that the proposed security scheme not only protects image data from eavesdroppers but also keeps the good BER and peak-to-average power ratio performances for image-based OFDM-VLC systems.

A family of chaotic pure analog coding schemes based on baker's map function

NASA Astrophysics Data System (ADS)

Liu, Yang; Li, Jing; Lu, Xuanxuan; Yuen, Chau; Wu, Jun

2015-12-01

This paper considers a family of pure analog coding schemes constructed from dynamic systems which are governed by chaotic functions—baker's map function and its variants. Various decoding methods, including maximum likelihood (ML), minimum mean square error (MMSE), and mixed ML-MMSE decoding algorithms, have been developed for these novel encoding schemes. The proposed mirrored baker's and single-input baker's analog codes perform a balanced protection against the fold error (large distortion) and weak distortion and outperform the classical chaotic analog coding and analog joint source-channel coding schemes in literature. Compared to the conventional digital communication system, where quantization and digital error correction codes are used, the proposed analog coding system has graceful performance evolution, low decoding latency, and no quantization noise. Numerical results show that under the same bandwidth expansion, the proposed analog system outperforms the digital ones over a wide signal-to-noise (SNR) range.

A quasi-crisis

NASA Astrophysics Data System (ADS)

Wang, Ying-Mei; Wang, Wen-Xiu; Chen, He-Sheng; Zhang, Kai; Jiang, Yu-Mei; Wang, Xu-Ming; He, Da-Ren

2002-03-01

A system concatenated by two area-preserving maps may be addressed as "quasi- dissipative," since such a system can display dissipative behaviors^1. This is due to noninvertibility induced by discontinuity in the system function. In such a system, the image set of the discontinuous border forms a chaotic quasi-attractor. At a critical control parameter value the quasi-attractor suddenly vanishes. The chaotic iterations escape, via a leaking hole, to an emergent period-8 elliptic island. The hole is the intersection of the chaotic quasi-attractor and the period-8 island. The chaotic quasi-attractor thus changes to chaotic quasi-transients. The scaling behavior that drives the quasi-crisis has been investigated numerically. It reads: ∝ (p-p_c)^-ν , where is defined as the averaged length of quasi-transients. The scaling exponent ν=1.66 ± 0.04. The critical parameter value equals p_c=-1.0069799. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

An efficient and secure partial image encryption for wireless multimedia sensor networks using discrete wavelet transform, chaotic maps and substitution box

NASA Astrophysics Data System (ADS)

Khan, Muazzam A.; Ahmad, Jawad; Javaid, Qaisar; Saqib, Nazar A.

2017-03-01

Wireless Sensor Networks (WSN) is widely deployed in monitoring of some physical activity and/or environmental conditions. Data gathered from WSN is transmitted via network to a central location for further processing. Numerous applications of WSN can be found in smart homes, intelligent buildings, health care, energy efficient smart grids and industrial control systems. In recent years, computer scientists has focused towards findings more applications of WSN in multimedia technologies, i.e. audio, video and digital images. Due to bulky nature of multimedia data, WSN process a large volume of multimedia data which significantly increases computational complexity and hence reduces battery time. With respect to battery life constraints, image compression in addition with secure transmission over a wide ranged sensor network is an emerging and challenging task in Wireless Multimedia Sensor Networks. Due to the open nature of the Internet, transmission of data must be secure through a process known as encryption. As a result, there is an intensive demand for such schemes that is energy efficient as well as highly secure since decades. In this paper, discrete wavelet-based partial image encryption scheme using hashing algorithm, chaotic maps and Hussain's S-Box is reported. The plaintext image is compressed via discrete wavelet transform and then the image is shuffled column-wise and row wise-wise via Piece-wise Linear Chaotic Map (PWLCM) and Nonlinear Chaotic Algorithm, respectively. To get higher security, initial conditions for PWLCM are made dependent on hash function. The permuted image is bitwise XORed with random matrix generated from Intertwining Logistic map. To enhance the security further, final ciphertext is obtained after substituting all elements with Hussain's substitution box. Experimental and statistical results confirm the strength of the anticipated scheme.

Chaotic Traversal (CHAT): Very Large Graphs Traversal Using Chaotic Dynamics

NASA Astrophysics Data System (ADS)

Changaival, Boonyarit; Rosalie, Martin; Danoy, Grégoire; Lavangnananda, Kittichai; Bouvry, Pascal

2017-12-01

Graph Traversal algorithms can find their applications in various fields such as routing problems, natural language processing or even database querying. The exploration can be considered as a first stepping stone into knowledge extraction from the graph which is now a popular topic. Classical solutions such as Breadth First Search (BFS) and Depth First Search (DFS) require huge amounts of memory for exploring very large graphs. In this research, we present a novel memoryless graph traversal algorithm, Chaotic Traversal (CHAT) which integrates chaotic dynamics to traverse large unknown graphs via the Lozi map and the Rössler system. To compare various dynamics effects on our algorithm, we present an original way to perform the exploration of a parameter space using a bifurcation diagram with respect to the topological structure of attractors. The resulting algorithm is an efficient and nonresource demanding algorithm, and is therefore very suitable for partial traversal of very large and/or unknown environment graphs. CHAT performance using Lozi map is proven superior than the, commonly known, Random Walk, in terms of number of nodes visited (coverage percentage) and computation time where the environment is unknown and memory usage is restricted.

Chaos-based partial image encryption scheme based on linear fractional and lifting wavelet transforms

NASA Astrophysics Data System (ADS)

Belazi, Akram; Abd El-Latif, Ahmed A.; Diaconu, Adrian-Viorel; Rhouma, Rhouma; Belghith, Safya

2017-01-01

In this paper, a new chaos-based partial image encryption scheme based on Substitution-boxes (S-box) constructed by chaotic system and Linear Fractional Transform (LFT) is proposed. It encrypts only the requisite parts of the sensitive information in Lifting-Wavelet Transform (LWT) frequency domain based on hybrid of chaotic maps and a new S-box. In the proposed encryption scheme, the characteristics of confusion and diffusion are accomplished in three phases: block permutation, substitution, and diffusion. Then, we used dynamic keys instead of fixed keys used in other approaches, to control the encryption process and make any attack impossible. The new S-box was constructed by mixing of chaotic map and LFT to insure the high confidentiality in the inner encryption of the proposed approach. In addition, the hybrid compound of S-box and chaotic systems strengthened the whole encryption performance and enlarged the key space required to resist the brute force attacks. Extensive experiments were conducted to evaluate the security and efficiency of the proposed approach. In comparison with previous schemes, the proposed cryptosystem scheme showed high performances and great potential for prominent prevalence in cryptographic applications.

Chaotic structure of oil prices

NASA Astrophysics Data System (ADS)

Bildirici, Melike; Sonustun, Fulya Ozaksoy

2018-01-01

The fluctuations in oil prices are very complicated and therefore, it is unable to predict its effects on economies. For modelling complex system of oil prices, linear economic models are not sufficient and efficient tools. Thus, in recent years, economists attached great attention to non-linear structure of oil prices. For analyzing this relationship, GARCH types of models were used in some papers. Distinctively from the other papers, in this study, we aimed to analyze chaotic pattern of oil prices. Thus, it was used the Lyapunov Exponents and Hennon Map to determine chaotic behavior of oil prices for the selected time period.

Analysis of the time structure of synchronization in multidimensional chaotic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarenko, A. V., E-mail: avm.science@mail.ru

2015-05-15

A new approach is proposed to the integrated analysis of the time structure of synchronization of multidimensional chaotic systems. The method allows one to diagnose and quantitatively evaluate the intermittency characteristics during synchronization of chaotic oscillations in the T-synchronization mode. A system of two identical logistic mappings with unidirectional coupling that operate in the developed chaos regime is analyzed. It is shown that the widely used approach, in which only synchronization patterns are subjected to analysis while desynchronization areas are considered as a background signal and removed from analysis, should be regarded as methodologically incomplete.

Detection and Alert of muscle fatigue considering a Surface Electromyography Chaotic Model

NASA Astrophysics Data System (ADS)

Herrera, V.; Romero, J. F.; Amestegui, M.

2011-03-01

This work propose a detection and alert algorithm for muscle fatigue in paraplegic patients undergoing electro-therapy sessions. The procedure is based on a mathematical chaotic model emulating physiological signals and Continuous Wavelet Transform (CWT). The chaotic model developed is based on a logistic map that provides suitable data accomplishing some physiological signal class patterns. The CWT was applied to signals generated by the model and the resulting vector was obtained through Total Wavelet Entropy (TWE). In this sense, the presented work propose a viable and practical alert and detection algorithm for muscle fatigue.

Mechanisms of appearance of amplitude and phase chimera states in ensembles of nonlocally coupled chaotic systems

NASA Astrophysics Data System (ADS)

Bogomolov, Sergey A.; Slepnev, Andrei V.; Strelkova, Galina I.; Schöll, Eckehard; Anishchenko, Vadim S.

2017-02-01

We explore the bifurcation transition from coherence to incoherence in ensembles of nonlocally coupled chaotic systems. It is firstly shown that two types of chimera states, namely, amplitude and phase, can be found in a network of coupled logistic maps, while only amplitude chimera states can be observed in a ring of continuous-time chaotic systems. We reveal a bifurcation mechanism by analyzing the evolution of space-time profiles and the coupling function with varying coupling coefficient and formulate the necessary and sufficient conditions for realizing the chimera states in the ensembles.

Hiding message into DNA sequence through DNA coding and chaotic maps.

PubMed

Liu, Guoyan; Liu, Hongjun; Kadir, Abdurahman

2014-09-01

The paper proposes an improved reversible substitution method to hide data into deoxyribonucleic acid (DNA) sequence, and four measures have been taken to enhance the robustness and enlarge the hiding capacity, such as encode the secret message by DNA coding, encrypt it by pseudo-random sequence, generate the relative hiding locations by piecewise linear chaotic map, and embed the encoded and encrypted message into a randomly selected DNA sequence using the complementary rule. The key space and the hiding capacity are analyzed. Experimental results indicate that the proposed method has a better performance compared with the competing methods with respect to robustness and capacity.

Structure of chaotic magnetic field lines in IR-T1 tokamak due to ergodic magnetic limiter

NASA Astrophysics Data System (ADS)

Ahmadi, S.; Salar Elahi, A.; Ghorannevis, M.

2018-03-01

In this paper we have studied an Ergodic Magnetic Limiter (EML) based chaotic magnetic field for transport control in the edge plasma of IR-T1 tokamak. The resonance created by the EML causes perturbation of the equilibrium field line in tokamak and as a result, the field lines are chaotic in the vicinity of the dimerized island chains. Transport barriers are formed in the chaotic field line and actually observe in tokamak with reverse magnetic shear. We used area-preserving non-twist (and twist) Poincaré maps to describe the formation of transport barriers, which are actually features of Hamiltonian systems. This transport barrier is useful in reducing radial diffusion of the field line and thus improving the plasma confinement.

On the adaptivity and complexity embedded into differential evolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Senkerik, Roman; Pluhacek, Michal; Jasek, Roman

2016-06-08

This research deals with the comparison of the two modern approaches for evolutionary algorithms, which are the adaptivity and complex chaotic dynamics. This paper aims on the investigations on the chaos-driven Differential Evolution (DE) concept. This paper is aimed at the embedding of discrete dissipative chaotic systems in the form of chaotic pseudo random number generators for the DE and comparing the influence to the performance with the state of the art adaptive representative jDE. This research is focused mainly on the possible disadvantages and advantages of both compared approaches. Repeated simulations for Lozi map driving chaotic systems were performedmore » on the simple benchmark functions set, which are more close to the real optimization problems. Obtained results are compared with the canonical not-chaotic and not adaptive DE. Results show that with used simple test functions, the performance of ChaosDE is better in the most cases than jDE and Canonical DE, furthermore due to the unique sequencing in CPRNG given by the hidden chaotic dynamics, thus better and faster selection of unique individuals from population, ChaosDE is faster.« less

A Control Algorithm for Chaotic Physical Systems

DTIC Science & Technology

1991-10-01

revision expands the grid to cover the entire area of any attractor that is present. 5 Map Selection The final choices of the state- space mapping process...interval h?; overrange R0 ; control parameter interval AkO and range [kbro, khigh]; iteration depth. "* State- space mapping : 1. Set up grid by expanding

Parameter-dependent behaviour of periodic channels in a locus of boundary crisis

NASA Astrophysics Data System (ADS)

Rankin, James; Osinga, Hinke M.

2017-06-01

A boundary crisis occurs when a chaotic attractor outgrows its basin of attraction and suddenly disappears. As previously reported, the locus of a boundary crisis is organised by homo- or heteroclinic tangencies between the stable and unstable manifolds of saddle periodic orbits. In two parameters, such tangencies lead to curves, but the locus of boundary crisis along those curves exhibits gaps or channels, in which other non-chaotic attractors persist. These attractors are stable periodic orbits which themselves can undergo a cascade of period-doubling bifurcations culminating in multi-component chaotic attractors. The canonical diffeomorphic two-dimensional Hénon map exhibits such periodic channels, which are structured in a particular ordered way: each channel is bounded on one side by a saddle-node bifurcation and on the other by a period-doubling cascade to chaos; furthermore, all channels seem to have the same orientation, with the saddle-node bifurcation always on the same side. We investigate the locus of boundary crisis in the Ikeda map, which models the dynamics of energy levels in a laser ring cavity. We find that the Ikeda map features periodic channels with a richer and more general organisation than for the Hénon map. Using numerical continuation, we investigate how the periodic channels depend on a third parameter and characterise how they split into multiple channels with different properties.

Generalized Smooth Transition Map Between Tent and Logistic Maps

NASA Astrophysics Data System (ADS)

Sayed, Wafaa S.; Fahmy, Hossam A. H.; Rezk, Ahmed A.; Radwan, Ahmed G.

There is a continuous demand on novel chaotic generators to be employed in various modeling and pseudo-random number generation applications. This paper proposes a new chaotic map which is a general form for one-dimensional discrete-time maps employing the power function with the tent and logistic maps as special cases. The proposed map uses extra parameters to provide responses that fit multiple applications for which conventional maps were not enough. The proposed generalization covers also maps whose iterative relations are not based on polynomials, i.e. with fractional powers. We introduce a framework for analyzing the proposed map mathematically and predicting its behavior for various combinations of its parameters. In addition, we present and explain the transition map which results in intermediate responses as the parameters vary from their values corresponding to tent map to those corresponding to logistic map case. We study the properties of the proposed map including graph of the map equation, general bifurcation diagram and its key-points, output sequences, and maximum Lyapunov exponent. We present further explorations such as effects of scaling, system response with respect to the new parameters, and operating ranges other than transition region. Finally, a stream cipher system based on the generalized transition map validates its utility for image encryption applications. The system allows the construction of more efficient encryption keys which enhances its sensitivity and other cryptographic properties.

Optical image cryptosystem using chaotic phase-amplitude masks encoding and least-data-driven decryption by compressive sensing

NASA Astrophysics Data System (ADS)

Lang, Jun; Zhang, Jing

2015-03-01

In our proposed optical image cryptosystem, two pairs of phase-amplitude masks are generated from the chaotic web map for image encryption in the 4f double random phase-amplitude encoding (DRPAE) system. Instead of transmitting the real keys and the enormous masks codes, only a few observed measurements intermittently chosen from the masks are delivered. Based on compressive sensing paradigm, we suitably refine the series expansions of web map equations to better reconstruct the underlying system. The parameters of the chaotic equations can be successfully calculated from observed measurements and then can be used to regenerate the correct random phase-amplitude masks for decrypting the encoded information. Numerical simulations have been performed to verify the proposed optical image cryptosystem. This cryptosystem can provide a new key management and distribution method. It has the advantages of sufficiently low occupation of the transmitted key codes and security improvement of information transmission without sending the real keys.

The Arnol'd cat: Failure of the correspondence principle

NASA Astrophysics Data System (ADS)

Ford, Joseph; Mantica, Giorgio; Ristow, Gerald H.

1991-07-01

The classical Hamiltonian H = p2/2 m + ɛ( q2/2) Σδ[ s-( t/ T)] has an integrable mapping of the plane, [ qn+1 , pn+1 ]= [ qn+1 + pn, qn+2 pn], as its equations of motion. But then by introducing periodic boundary conditions via (mod 1) applied to both q and p variables, the equations of motion become the Arnol'd cat map, [ qn+1 , pn+1 ] = [ qn + pn, qn + 2 pn], (mod 1), revealing it to be one of the simplest fully chaotic systems which can be derived from a Hamiltonian and analyzed. Consequently, we here quantize the Arnol'd cat and examine its quantum motion for signs of chaos using algorithmic complexity as the litmus. Our analysis reveals that the quantum cat is not chaotic in the deep quantum domain nor does it become chaotic in the classical limit as required by the correspondence principle. We therefore conclude that the correspondence principle, as defined herein, fails for the quantum Arnol'd cat.

A noise resistant symmetric key cryptosystem based on S8 S-boxes and chaotic maps

NASA Astrophysics Data System (ADS)

Hussain, Iqtadar; Anees, Amir; Aslam, Muhammad; Ahmed, Rehan; Siddiqui, Nasir

2018-04-01

In this manuscript, we have proposed an encryption algorithm to encrypt any digital data. The proposed algorithm is primarily based on the substitution-permutation in which the substitution process is performed by the S 8 Substitution boxes. The proposed algorithm incorporates three different chaotic maps. We have analysed the behaviour of chaos by secure communication in great length, and accordingly, we have applied those chaotic sequences in the proposed encryption algorithm. The simulation and statistical results revealed that the proposed encryption scheme is secure against different attacks. Moreover, the encryption scheme can tolerate the channel noise as well; if the encrypted data is corrupted by the unauthenticated user or by the channel noise, the decryption can still be successfully done with some distortion. The overall results confirmed that the presented work has good cryptographic features, low computational complexity and resistant to the channel noise which makes it suitable for low profile mobile applications.

Generalized Lorenz equations on a three-sphere

NASA Astrophysics Data System (ADS)

Saiki, Yoshitaka; Sander, Evelyn; Yorke, James A.

2017-06-01

Edward Lorenz is best known for one specific three-dimensional differential equation, but he actually created a variety of related N-dimensional models. In this paper, we discuss a unifying principle for these models and put them into an overall mathematical framework. Because this family of models is so large, we are forced to choose. We sample the variety of dynamics seen in these models, by concentrating on a four-dimensional version of the Lorenz models for which there are three parameters and the norm of the solution vector is preserved. We can therefore restrict our focus to trajectories on the unit sphere S 3 in ℝ4. Furthermore, we create a type of Poincaré return map. We choose the Poincaré surface to be the set where one of the variables is 0, i.e., the Poincaré surface is a two-sphere S 2 in ℝ3. Examining different choices of our three parameters, we illustrate the wide variety of dynamical behaviors, including chaotic attractors, period doubling cascades, Standard-Map-like structures, and quasiperiodic trajectories. Note that neither Standard-Map-like structure nor quasiperiodicity has previously been reported for Lorenz models.

A Double Chaotic Layer Encryption Algorithm for Clinical Signals in Telemedicine.

PubMed

Murillo-Escobar, M A; Cardoza-Avendaño, L; López-Gutiérrez, R M; Cruz-Hernández, C

2017-04-01

Recently, telemedicine offers medical services remotely via telecommunications systems and physiological monitoring devices. This scheme provides healthcare delivery services between physicians and patients conveniently, since some patients can not attend the hospital due to any reason. However, transmission of information over an insecure channel such as internet or private data storing generates a security problem. Therefore, authentication, confidentiality, and privacy are important challenges in telemedicine, where only authorized users should have access to medical or clinical records. On the other hand, chaotic systems have been implemented efficiently in cryptographic systems to provide confidential and privacy. In this work, we propose a novel symmetric encryption algorithm based on logistic map with double chaotic layer encryption (DCLE) in diffusion process and just one round of confusion-diffusion for the confidentiality and privacy of clinical information such as electrocardiograms (ECG), electroencephalograms (EEG), and blood pressure (BP) for applications in telemedicine. The clinical signals are acquired from PhysioBank data base for encryption proposes and analysis. In contrast with recent schemes in literature, we present a secure cryptographic algorithm based on chaos validated with the most complete security analysis until this time. In addition, the cryptograms are validated with the most complete pseudorandomness tests based on National Institute of Standards and Technology (NIST) 800-22 suite. All results are at MATLAB simulations and all them show the effectiveness, security, robustness, and the potential use of the proposed scheme in telemedicine.

Hierarchical collapse of regular islands via dissipation

NASA Astrophysics Data System (ADS)

Jousseph, C. A. C.; Abdulack, S. A.; Manchein, C.; Beims, M. W.

2018-03-01

In this work we investigate how regular islands localized in a mixed phase-space of generic area-preserving Hamiltonian systems are affected by a small amount of dissipation. Mainly we search for a universality (hierarchy) in the convergence of higher-order resonances and their periods when dissipation increases. One very simple scenario is already known: when subjected to small dissipation, stable periodic points become sinks attracting almost all the surrounding orbits, destroying all invariant curves which divide the phase-space in chaotic and regular domains. However, performing numerical experiments with the paradigmatic Chirikov-Taylor standard mapping we show that this presumably simple scenario can be rather complicated. The first, not trivial, scenario is what happens to chaotic trajectories, since they can be attracted by the sinks or by chaotic attractors, in cases when they exist. We show that this depends very much on how basins of attraction are formed as dissipation increases. In addition, we demonstrate that higher-order resonances are usually first affected by small dissipation when compared to lower-order resonances from the conservative case. Nevertheless, this is not a generic behaviour. We show that a local hierarchical collapse of resonances, as dissipation increases, is related to the area of the islands from the conservative case surrounding the periodic orbits. All observed resonance destructions occur via the bifurcation phenomena and are quantified here by determining the largest finite-time Lyapunov exponent.

Exact folded-band chaotic oscillator.

PubMed

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Adaptive synchronisation of memristor-based neural networks with leakage delays and applications in chaotic masking secure communication

NASA Astrophysics Data System (ADS)

Liu, Jian; Xu, Rui

2018-04-01

Chaotic synchronisation has caused extensive attention due to its potential application in secure communication. This paper is concerned with the problem of adaptive synchronisation for two different kinds of memristor-based neural networks with time delays in leakage terms. By applying set-valued maps and differential inclusions theories, synchronisation criteria are obtained via linear matrix inequalities technique, which guarantee drive system being synchronised with response system under adaptive control laws. Finally, a numerical example is given to illustrate the feasibility of our theoretical results, and two schemes for secure communication are introduced based on chaotic masking method.

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

Ulam method and fractal Weyl law for Perron-Frobenius operators

NASA Astrophysics Data System (ADS)

Ermann, L.; Shepelyansky, D. L.

2010-06-01

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

Dynamical phases of the Hindmarsh-Rose neuronal model: studies of the transition from bursting to spiking chaos.

PubMed

Innocenti, Giacomo; Morelli, Alice; Genesio, Roberto; Torcini, Alessandro

2007-12-01

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts.

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1990-01-01

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

A Scheme for Obtaining Secure S-Boxes Based on Chaotic Baker's Map

NASA Astrophysics Data System (ADS)

Gondal, Muhammad Asif; Abdul Raheem; Hussain, Iqtadar

2014-09-01

In this paper, a method for obtaining cryptographically strong 8 × 8 substitution boxes (S-boxes) is presented. The method is based on chaotic baker's map and a "mini version" of a new block cipher with block size 8 bits and can be easily and efficiently performed on a computer. The cryptographic strength of some 8 × 8 S-boxes randomly produced by the method is analyzed. The results show (1) all of them are bijective; (2) the nonlinearity of each output bit of them is usually about 100; (3) all of them approximately satisfy the strict avalanche criterion and output bits independence criterion; (4) they all have an almost equiprobable input/output XOR distribution.

The Wigner distribution and 2D classical maps

NASA Astrophysics Data System (ADS)

Sakhr, Jamal

2017-07-01

The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics is introduced. Based on a well-known correspondence between the Wigner distribution and the 2D Poisson point process, the hypothesis that typical pseudo-trajectories of a 2D ergodic map have a Wignerian nearest-neighbor spacing distribution (NNSD) is put forward and numerically tested. The standard Euclidean metric is used to compute the interpoint spacings. In all test cases, the hypothesis is upheld, and the range of validity of the hypothesis appears to be robust in the sense that it is not affected by the presence or absence of: (i) mixing; (ii) time-reversal symmetry; and/or (iii) dissipation.

A chaotic cryptosystem for images based on Henon and Arnold cat map.

PubMed

Soleymani, Ali; Nordin, Md Jan; Sundararajan, Elankovan

2014-01-01

The rapid evolution of imaging and communication technologies has transformed images into a widespread data type. Different types of data, such as personal medical information, official correspondence, or governmental and military documents, are saved and transmitted in the form of images over public networks. Hence, a fast and secure cryptosystem is needed for high-resolution images. In this paper, a novel encryption scheme is presented for securing images based on Arnold cat and Henon chaotic maps. The scheme uses Arnold cat map for bit- and pixel-level permutations on plain and secret images, while Henon map creates secret images and specific parameters for the permutations. Both the encryption and decryption processes are explained, formulated, and graphically presented. The results of security analysis of five different images demonstrate the strength of the proposed cryptosystem against statistical, brute force and differential attacks. The evaluated running time for both encryption and decryption processes guarantee that the cryptosystem can work effectively in real-time applications.

Image encryption with chaotic map and Arnold transform in the gyrator transform domains

NASA Astrophysics Data System (ADS)

Sang, Jun; Luo, Hongling; Zhao, Jun; Alam, Mohammad S.; Cai, Bin

2017-05-01

An image encryption method combing chaotic map and Arnold transform in the gyrator transform domains was proposed. Firstly, the original secret image is XOR-ed with a random binary sequence generated by a logistic map. Then, the gyrator transform is performed. Finally, the amplitude and phase of the gyrator transform are permutated by Arnold transform. The decryption procedure is the inverse operation of encryption. The secret keys used in the proposed method include the control parameter and the initial value of the logistic map, the rotation angle of the gyrator transform, and the transform number of the Arnold transform. Therefore, the key space is large, while the key data volume is small. The numerical simulation was conducted to demonstrate the effectiveness of the proposed method and the security analysis was performed in terms of the histogram of the encrypted image, the sensitiveness to the secret keys, decryption upon ciphertext loss, and resistance to the chosen-plaintext attack.

A Chaotic Cryptosystem for Images Based on Henon and Arnold Cat Map

PubMed Central

Sundararajan, Elankovan

2014-01-01

The rapid evolution of imaging and communication technologies has transformed images into a widespread data type. Different types of data, such as personal medical information, official correspondence, or governmental and military documents, are saved and transmitted in the form of images over public networks. Hence, a fast and secure cryptosystem is needed for high-resolution images. In this paper, a novel encryption scheme is presented for securing images based on Arnold cat and Henon chaotic maps. The scheme uses Arnold cat map for bit- and pixel-level permutations on plain and secret images, while Henon map creates secret images and specific parameters for the permutations. Both the encryption and decryption processes are explained, formulated, and graphically presented. The results of security analysis of five different images demonstrate the strength of the proposed cryptosystem against statistical, brute force and differential attacks. The evaluated running time for both encryption and decryption processes guarantee that the cryptosystem can work effectively in real-time applications. PMID:25258724

Chaotic maps and biometrics-based anonymous three-party authenticated key exchange protocol without using passwords

NASA Astrophysics Data System (ADS)

Xie, Qi; Hu, Bin; Chen, Ke-Fei; Liu, Wen-Hao; Tan, Xiao

2015-11-01

In three-party password authenticated key exchange (AKE) protocol, since two users use their passwords to establish a secure session key over an insecure communication channel with the help of the trusted server, such a protocol may suffer the password guessing attacks and the server has to maintain the password table. To eliminate the shortages of password-based AKE protocol, very recently, according to chaotic maps, Lee et al. [2015 Nonlinear Dyn. 79 2485] proposed a first three-party-authenticated key exchange scheme without using passwords, and claimed its security by providing a well-organized BAN logic test. Unfortunately, their protocol cannot resist impersonation attack, which is demonstrated in the present paper. To overcome their security weakness, by using chaotic maps, we propose a biometrics-based anonymous three-party AKE protocol with the same advantages. Further, we use the pi calculus-based formal verification tool ProVerif to show that our AKE protocol achieves authentication, security and anonymity, and an acceptable efficiency. Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LZ12F02005), the Major State Basic Research Development Program of China (Grant No. 2013CB834205), and the National Natural Science Foundation of China (Grant No. 61070153).

Chaotic CDMA watermarking algorithm for digital image in FRFT domain

NASA Astrophysics Data System (ADS)

Liu, Weizhong; Yang, Wentao; Feng, Zhuoming; Zou, Xuecheng

2007-11-01

A digital image-watermarking algorithm based on fractional Fourier transform (FRFT) domain is presented by utilizing chaotic CDMA technique in this paper. As a popular and typical transmission technique, CDMA has many advantages such as privacy, anti-jamming and low power spectral density, which can provide robustness against image distortions and malicious attempts to remove or tamper with the watermark. A super-hybrid chaotic map, with good auto-correlation and cross-correlation characteristics, is adopted to produce many quasi-orthogonal codes (QOC) that can replace the periodic PN-code used in traditional CDAM system. The watermarking data is divided into a lot of segments that correspond to different chaotic QOC respectively and are modulated into the CDMA watermarking data embedded into low-frequency amplitude coefficients of FRFT domain of the cover image. During watermark detection, each chaotic QOC extracts its corresponding watermarking segment by calculating correlation coefficients between chaotic QOC and watermarked data of the detected image. The CDMA technique not only can enhance the robustness of watermark but also can compress the data of the modulated watermark. Experimental results show that the watermarking algorithm has good performances in three aspects: better imperceptibility, anti-attack robustness and security.

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

NASA Astrophysics Data System (ADS)

Giordano, C. M.; Cincotta, P. M.

2018-05-01

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

Statistical characterization of the standard map

NASA Astrophysics Data System (ADS)

Ruiz, Guiomar; Tirnakli, Ugur; Borges, Ernesto P.; Tsallis, Constantino

2017-06-01

The standard map, paradigmatic conservative system in the (x, p) phase space, has been recently shown (Tirnakli and Borges (2016 Sci. Rep. 6 23644)) to exhibit interesting statistical behaviors directly related to the value of the standard map external parameter K. A comprehensive statistical numerical description is achieved in the present paper. More precisely, for large values of K (e.g. K  =  10) where the Lyapunov exponents are neatly positive over virtually the entire phase space consistently with Boltzmann-Gibbs (BG) statistics, we verify that the q-generalized indices related to the entropy production q{ent} , the sensitivity to initial conditions q{sen} , the distribution of a time-averaged (over successive iterations) phase-space coordinate q{stat} , and the relaxation to the equilibrium final state q{rel} , collapse onto a fixed point, i.e. q{ent}=q{sen}=q{stat}=q{rel}=1 . In remarkable contrast, for small values of K (e.g. K  =  0.2) where the Lyapunov exponents are virtually zero over the entire phase space, we verify q{ent}=q{sen}=0 , q{stat} ≃ 1.935 , and q{rel} ≃1.4 . The situation corresponding to intermediate values of K, where both stable orbits and a chaotic sea are present, is discussed as well. The present results transparently illustrate when BG behavior and/or q-statistical behavior are observed.

Secure multiple access for indoor optical wireless communications with time-slot coding and chaotic phase.

PubMed

Liang, Tian; Wang, Ke; Lim, Christina; Wong, Elaine; Song, Tingting; Nirmalathas, Ampalavanapillai

2017-09-04

In this paper, we report a novel mechanism to simultaneously provide secure connections for multiple users in indoor optical wireless communication systems by employing the time-slot coding scheme together with chaotic phase sequence. The chaotic phase sequence is generated according to the logistic map and applied to each symbol to secure the transmission. Proof-of-concept experiments are carried out for multiple system capacities based on both 4-QAM and 16-QAM modulation formats, i.e. 1.25 Gb/s, 2 Gb/s and 2.5 Gb/s for 4-QAM, and 2.5 Gb/s, 3.33 Gb/s and 4 Gb/s for 16-QAM. Experimental results show that in all cases the added chaotic phase does not degrade the legitimate user's signal quality while the illegal user cannot detect the signal without the key.

Open quantum maps from complex scaling of kicked scattering systems

NASA Astrophysics Data System (ADS)

Mertig, Normann; Shudo, Akira

2018-04-01

We derive open quantum maps from periodically kicked scattering systems and discuss the computation of their resonance spectra in terms of theoretically grounded methods, such as complex scaling and sufficiently weak absorbing potentials. In contrast, we also show that current implementations of open quantum maps, based on strong absorptive or even projective openings, fail to produce the resonance spectra of kicked scattering systems. This comparison pinpoints flaws in current implementations of open quantum maps, namely, the inability to separate resonance eigenvalues from the continuum as well as the presence of diffraction effects due to strong absorption. The reported deviations from the true resonance spectra appear, even if the openings do not affect the classical trapped set, and become appreciable for shorter-lived resonances, e.g., those associated with chaotic orbits. This makes the open quantum maps, which we derive in this paper, a valuable alternative for future explorations of quantum-chaotic scattering systems, for example, in the context of the fractal Weyl law. The results are illustrated for a quantum map model whose classical dynamics exhibits key features of ionization and a trapped set which is organized by a topological horseshoe.

Chaotic Dynamics of Linguistic-Like Processes at the Syntactical and Semantic Levels: in the Pursuit of a Multifractal Attractor

NASA Astrophysics Data System (ADS)

Nicolis, John S.; Katsikas, Anastassis A.

Collective parameters such as the Zipf's law-like statistics, the Transinformation, the Block Entropy and the Markovian character are compared for natural, genetic, musical and artificially generated long texts from generating partitions (alphabets) on homogeneous as well as on multifractal chaotic maps. It appears that minimal requirements for a language at the syntactical level such as memory, selectivity of few keywords and broken symmetry in one dimension (polarity) are more or less met by dynamically iterating simple maps or flows e.g. very simple chaotic hardware. The same selectivity is observed at the semantic level where the aim refers to partitioning a set of enviromental impinging stimuli onto coexisting attractors-categories. Under the regime of pattern recognition and classification, few key features of a pattern or few categories claim the lion's share of the information stored in this pattern and practically, only these key features are persistently scanned by the cognitive processor. A multifractal attractor model can in principle explain this high selectivity, both at the syntactical and the semantic levels.

Perception-action map learning in controlled multiscroll systems applied to robot navigation.

PubMed

Arena, Paolo; De Fiore, Sebastiano; Fortuna, Luigi; Patané, Luca

2008-12-01

In this paper a new technique for action-oriented perception in robots is presented. The paper starts from exploiting the successful implementation of the basic idea that perceptual states can be embedded into chaotic attractors whose dynamical evolution can be associated with sensorial stimuli. In this way, it can be possible to encode, into the chaotic dynamics, environment-dependent patterns. These have to be suitably linked to an action, executed by the robot, to fulfill an assigned mission. This task is addressed here: the action-oriented perception loop is closed by introducing a simple unsupervised learning stage, implemented via a bio-inspired structure based on the motor map paradigm. In this way, perceptual meanings, useful for solving a given task, can be autonomously learned, based on the environment-dependent patterns embedded into the controlled chaotic dynamics. The presented framework has been tested on a simulated robot and the performance have been successfully compared with other traditional navigation control paradigms. Moreover an implementation of the proposed architecture on a Field Programmable Gate Array is briefly outlined and preliminary experimental results on a roving robot are also reported.

Hierarchical structure in sharply divided phase space for the piecewise linear map

NASA Astrophysics Data System (ADS)

Akaishi, Akira; Aoki, Kazuki; Shudo, Akira

2017-05-01

We have studied a two-dimensional piecewise linear map to examine how the hierarchical structure of stable regions affects the slow dynamics in Hamiltonian systems. In the phase space there are infinitely many stable regions, each of which is polygonal-shaped, and the rest is occupied by chaotic orbits. By using symbolic representation of stable regions, a procedure to compute the edges of the polygons is presented. The stable regions are hierarchically distributed in phase space and the edges of the stable regions show the marginal instability. The cumulative distribution of the recurrence time obeys a power law as ˜t-2 , the same as the one for the system with phase space, which is composed of a single stable region and chaotic components. By studying the symbol sequence of recurrence trajectories, we show that the hierarchical structure of stable regions has no significant effect on the power-law exponent and that only the marginal instability on the boundary of stable regions is responsible for determining the exponent. We also discuss the relevance of the hierarchical structure to those in more generic chaotic systems.

Using chaos to generate variations on movement sequences

NASA Astrophysics Data System (ADS)

Bradley, Elizabeth; Stuart, Joshua

1998-12-01

We describe a method for introducing variations into predefined motion sequences using a chaotic symbol-sequence reordering technique. A progression of symbols representing the body positions in a dance piece, martial arts form, or other motion sequence is mapped onto a chaotic trajectory, establishing a symbolic dynamics that links the movement sequence and the attractor structure. A variation on the original piece is created by generating a trajectory with slightly different initial conditions, inverting the mapping, and using special corpus-based graph-theoretic interpolation schemes to smooth any abrupt transitions. Sensitive dependence guarantees that the variation is different from the original; the attractor structure and the symbolic dynamics guarantee that the two resemble one another in both aesthetic and mathematical senses.

Correlation characteristics of phase and amplitude chimeras in an ensemble of nonlocally coupled maps

NASA Astrophysics Data System (ADS)

Vadivasova, T. E.; Strelkova, G. I.; Bogomolov, S. A.; Anishchenko, V. S.

2017-01-01

Correlation characteristics of chimera states have been calculated using the coefficient of mutual correlation of elements in a closed-ring ensemble of nonlocally coupled chaotic maps. Quantitative differences between the coefficients of mutual correlation for phase and amplitude chimeras are established for the first time.

Chaotic behavior in Casimir oscillators: A case study for phase-change materials.

PubMed

Tajik, Fatemeh; Sedighi, Mehdi; Khorrami, Mohammad; Masoudi, Amir Ali; Palasantzas, George

2017-10-01

Casimir forces between material surfaces at close proximity of less than 200 nm can lead to increased chaotic behavior of actuating devices depending on the strength of the Casimir interaction. We investigate these phenomena for phase-change materials in torsional oscillators, where the amorphous to crystalline phase transitions lead to transitions between high and low Casimir force and torque states, respectively, without material compositions. For a conservative system bifurcation curve and Poincare maps analysis show the absence of chaotic behavior but with the crystalline phase (high force-torque state) favoring more unstable behavior and stiction. However, for a nonconservative system chaotic behavior can take place introducing significant risk for stiction, which is again more pronounced for the crystalline phase. The latter illustrates the more general scenario that stronger Casimir forces and torques increase the possibility for chaotic behavior. The latter is making it impossible to predict whether stiction or stable actuation will occur on a long-term basis, and it is setting limitations in the design of micronano devices operating at short-range nanoscale separations.

Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems

NASA Astrophysics Data System (ADS)

Bäcker, A.

Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.

Invariants, Attractors and Bifurcation in Two Dimensional Maps with Polynomial Interaction

NASA Astrophysics Data System (ADS)

Hacinliyan, Avadis Simon; Aybar, Orhan Ozgur; Aybar, Ilknur Kusbeyzi

This work will present an extended discrete-time analysis on maps and their generalizations including iteration in order to better understand the resulting enrichment of the bifurcation properties. The standard concepts of stability analysis and bifurcation theory for maps will be used. Both iterated maps and flows are used as models for chaotic behavior. It is well known that when flows are converted to maps by discretization, the equilibrium points remain the same but a richer bifurcation scheme is observed. For example, the logistic map has a very simple behavior as a differential equation but as a map fold and period doubling bifurcations are observed. A way to gain information about the global structure of the state space of a dynamical system is investigating invariant manifolds of saddle equilibrium points. Studying the intersections of the stable and unstable manifolds are essential for understanding the structure of a dynamical system. It has been known that the Lotka-Volterra map and systems that can be reduced to it or its generalizations in special cases involving local and polynomial interactions admit invariant manifolds. Bifurcation analysis of this map and its higher iterates can be done to understand the global structure of the system and the artifacts of the discretization by comparing with the corresponding results from the differential equation on which they are based.

Desynchronization of chaos in coupled logistic maps.

PubMed

Maistrenko, Y L; Maistrenko, V L; Popovych, O; Mosekilde, E

1999-09-01

When identical chaotic oscillators interact, a state of complete or partial synchronization may be attained in which the motion is restricted to an invariant manifold of lower dimension than the full phase space. Riddling of the basin of attraction arises when particular orbits embedded in the synchronized chaotic state become transversely unstable while the state remains attracting on the average. Considering a system of two coupled logistic maps, we show that the transition to riddling will be soft or hard, depending on whether the first orbit to lose its transverse stability undergoes a supercritical or subcritical bifurcation. A subcritical bifurcation can lead directly to global riddling of the basin of attraction for the synchronized chaotic state. A supercritical bifurcation, on the other hand, is associated with the formation of a so-called mixed absorbing area that stretches along the synchronized chaotic state, and from which trajectories cannot escape. This gives rise to locally riddled basins of attraction. We present three different scenarios for the onset of riddling and for the subsequent transformations of the basins of attraction. Each scenario is described by following the type and location of the relevant asynchronous cycles, and determining their stable and unstable invariant manifolds. One scenario involves a contact bifurcation between the boundary of the basin of attraction and the absorbing area. Another scenario involves a long and interesting series of bifurcations starting with the stabilization of the asynchronous cycle produced in the riddling bifurcation and ending in a boundary crisis where the stability of an asynchronous chaotic state is destroyed. Finally, a phase diagram is presented to illustrate the parameter values at which the various transitions occur.

Bit-level plane image encryption based on coupled map lattice with time-varying delay

NASA Astrophysics Data System (ADS)

Lv, Xiupin; Liao, Xiaofeng; Yang, Bo

2018-04-01

Most of the existing image encryption algorithms had two basic properties: confusion and diffusion in a pixel-level plane based on various chaotic systems. Actually, permutation in a pixel-level plane could not change the statistical characteristics of an image, and many of the existing color image encryption schemes utilized the same method to encrypt R, G and B components, which means that the three color components of a color image are processed three times independently. Additionally, dynamical performance of a single chaotic system degrades greatly with finite precisions in computer simulations. In this paper, a novel coupled map lattice with time-varying delay therefore is applied in color images bit-level plane encryption to solve the above issues. Spatiotemporal chaotic system with both much longer period in digitalization and much excellent performances in cryptography is recommended. Time-varying delay embedded in coupled map lattice enhances dynamical behaviors of the system. Bit-level plane image encryption algorithm has greatly reduced the statistical characteristics of an image through the scrambling processing. The R, G and B components cross and mix with one another, which reduces the correlation among the three components. Finally, simulations are carried out and all the experimental results illustrate that the proposed image encryption algorithm is highly secure, and at the same time, also demonstrates superior performance.

A Round-Efficient Authenticated Key Agreement Scheme Based on Extended Chaotic Maps for Group Cloud Meeting.

PubMed

Lin, Tsung-Hung; Tsung, Chen-Kun; Lee, Tian-Fu; Wang, Zeng-Bo

2017-12-03

The security is a critical issue for business purposes. For example, the cloud meeting must consider strong security to maintain the communication privacy. Considering the scenario with cloud meeting, we apply extended chaotic map to present passwordless group authentication key agreement, termed as Passwordless Group Authentication Key Agreement (PL-GAKA). PL-GAKA improves the computation efficiency for the simple group password-based authenticated key agreement (SGPAKE) proposed by Lee et al. in terms of computing the session key. Since the extended chaotic map has equivalent security level to the Diffie-Hellman key exchange scheme applied by SGPAKE, the security of PL-GAKA is not sacrificed when improving the computation efficiency. Moreover, PL-GAKA is a passwordless scheme, so the password maintenance is not necessary. Short-term authentication is considered, hence the communication security is stronger than other protocols by dynamically generating session key in each cloud meeting. In our analysis, we first prove that each meeting member can get the correct information during the meeting. We analyze common security issues for the proposed PL-GAKA in terms of session key security, mutual authentication, perfect forward security, and data integrity. Moreover, we also demonstrate that communicating in PL-GAKA is secure when suffering replay attacks, impersonation attacks, privileged insider attacks, and stolen-verifier attacks. Eventually, an overall comparison is given to show the performance between PL-GAKA, SGPAKE and related solutions.

Temporal intermittency and the lifetime of chimera states in ensembles of nonlocally coupled chaotic oscillators

NASA Astrophysics Data System (ADS)

Semenova, N. I.; Strelkova, G. I.; Anishchenko, V. S.; Zakharova, A.

2017-06-01

We describe numerical results for the dynamics of networks of nonlocally coupled chaotic maps. Switchings in time between amplitude and phase chimera states have been first established and studied. It has been shown that in autonomous ensembles, a nonstationary regime of switchings has a finite lifetime and represents a transient process towards a stationary regime of phase chimera. The lifetime of the nonstationary switching regime can be increased to infinity by applying short-term noise perturbations.

Chaotic motion of comets in near-parabolic orbit: Mapping aproaches

NASA Astrophysics Data System (ADS)

Liu, Jie; Sun, Yi-Sui

1994-09-01

There exist many comets with near-parabolic orbits in the solar system. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable. The theory assumes that there is a cometary cloud at a distance 103 to 107 from the sun and that perturbing forces from planets or stars make orbits of some of these comets become the near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the solar system forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighborhood of any separatrix i.e. the trajectory with zero frequency of the uperturbed motion of a Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two-body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study of near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion. In this paper we derive a similar mapping directly and discuss its dynamical characters.

Studies of Nonlinear Phenomena in Plasmas.

DTIC Science & Technology

1980-03-01

Nonperiodic Oscillations of Langmuir Waves, UCLA Engr. Rpt. No. ENG- 7879 , Nov. 1978. .--- j, - :- -- ... . ___________ - - 8 V. PUBLICATIONS, REPORTS AND...OF CHAOTIC OSCILLATIONS ...... ............ 9 V. POINCARE MAPS ......... ...................... . 13 VI . CONCLUDING REMARKS...But the graphs of the Poincare maps in terms of some curve parameter are not readily obtainable. VI . CONCLUDING REMARKS The results of this study

Security scheme in IMDD-OFDM-PON system with the chaotic pilot interval and scrambling

NASA Astrophysics Data System (ADS)

Chen, Qianghua; Bi, Meihua; Fu, Xiaosong; Lu, Yang; Zeng, Ran; Yang, Guowei; Yang, Xuelin; Xiao, Shilin

2018-01-01

In this paper, a random chaotic pilot interval and permutations scheme without any requirement of redundant sideband information is firstly proposed for the physical layer security-enhanced intensity modulation direct detection orthogonal frequency division multiplexing passive optical network (IMDD-OFDM-PON) system. With the help of the position feature of inserting the pilot, a simple logistic chaos map is used to generate the random pilot interval and scramble the chaotic subcarrier allocation of each column pilot data for improving the physical layer confidentiality. Due to the dynamic chaotic permutations of pilot data, the enhanced key space of ∼103303 is achieved in OFDM-PON. Moreover, the transmission experiment of 10-Gb/s 16-QAM encrypted OFDM data is successfully demonstrated over 20-km single-mode fiber, which indicates that the proposed scheme not only improves the system security, but also can achieve the same performance as in the common IMDD-OFDM-PON system without encryption scheme.

Electric fields yield chaos in microflows

PubMed Central

Posner, Jonathan D.; Pérez, Carlos L.; Santiago, Juan G.

2012-01-01

We present an investigation of chaotic dynamics of a low Reynolds number electrokinetic flow. Electrokinetic flows arise due to couplings of electric fields and electric double layers. In these flows, applied (steady) electric fields can couple with ionic conductivity gradients outside electric double layers to produce flow instabilities. The threshold of these instabilities is controlled by an electric Rayleigh number, Rae. As Rae increases monotonically, we show here flow dynamics can transition from steady state to a time-dependent periodic state and then to an aperiodic, chaotic state. Interestingly, further monotonic increase of Rae shows a transition back to a well-ordered state, followed by a second transition to a chaotic state. Temporal power spectra and time-delay phase maps of low dimensional attractors graphically depict the sequence between periodic and chaotic states. To our knowledge, this is a unique report of a low Reynolds number flow with such a sequence of periodic-to-aperiodic transitions. Also unique is a report of strange attractors triggered and sustained through electric fluid body forces. PMID:22908251

Characterizing the chaotic nature of ocean ventilation

NASA Astrophysics Data System (ADS)

MacGilchrist, Graeme A.; Marshall, David P.; Johnson, Helen L.; Lique, Camille; Thomas, Matthew

2017-09-01

Ventilation of the upper ocean plays an important role in climate variability on interannual to decadal timescales by influencing the exchange of heat and carbon dioxide between the atmosphere and ocean. The turbulent nature of ocean circulation, manifest in a vigorous mesoscale eddy field, means that pathways of ventilation, once thought to be quasi-laminar, are in fact highly chaotic. We characterize the chaotic nature of ventilation pathways according to a nondimensional "filamentation number," which estimates the reduction in filament width of a ventilated fluid parcel due to mesoscale strain. In the subtropical North Atlantic of an eddy-permitting ocean model, the filamentation number is large everywhere across three upper ocean density surfaces—implying highly chaotic ventilation pathways—and increases with depth. By mapping surface ocean properties onto these density surfaces, we directly resolve the highly filamented structure and confirm that the filamentation number captures its spatial variability. These results have implications for the spreading of atmospherically-derived tracers into the ocean interior.

Secure chaotic map based block cryptosystem with application to camera sensor networks.

PubMed

Guo, Xianfeng; Zhang, Jiashu; Khan, Muhammad Khurram; Alghathbar, Khaled

2011-01-01

Recently, Wang et al. presented an efficient logistic map based block encryption system. The encryption system employs feedback ciphertext to achieve plaintext dependence of sub-keys. Unfortunately, we discovered that their scheme is unable to withstand key stream attack. To improve its security, this paper proposes a novel chaotic map based block cryptosystem. At the same time, a secure architecture for camera sensor network is constructed. The network comprises a set of inexpensive camera sensors to capture the images, a sink node equipped with sufficient computation and storage capabilities and a data processing server. The transmission security between the sink node and the server is gained by utilizing the improved cipher. Both theoretical analysis and simulation results indicate that the improved algorithm can overcome the flaws and maintain all the merits of the original cryptosystem. In addition, computational costs and efficiency of the proposed scheme are encouraging for the practical implementation in the real environment as well as camera sensor network.

An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers.

PubMed

Zapateiro De la Hoz, Mauricio; Acho, Leonardo; Vidal, Yolanda

2015-01-01

Security and secrecy are some of the important concerns in the communications world. In the last years, several encryption techniques have been proposed in order to improve the secrecy of the information transmitted. Chaos-based encryption techniques are being widely studied as part of the problem because of the highly unpredictable and random-look nature of the chaotic signals. In this paper we propose a digital-based communication system that uses the logistic map which is a mathematically simple model that is chaotic under certain conditions. The input message signal is modulated using a simple Delta modulator and encrypted using a logistic map. The key signal is also encrypted using the same logistic map with different initial conditions. In the receiver side, the binary-coded message is decrypted using the encrypted key signal that is sent through one of the communication channels. The proposed scheme is experimentally tested using Arduino shields which are simple yet powerful development kits that allows for the implementation of the communication system for testing purposes.

Secure Chaotic Map Based Block Cryptosystem with Application to Camera Sensor Networks

PubMed Central

Guo, Xianfeng; Zhang, Jiashu; Khan, Muhammad Khurram; Alghathbar, Khaled

2011-01-01

Recently, Wang et al. presented an efficient logistic map based block encryption system. The encryption system employs feedback ciphertext to achieve plaintext dependence of sub-keys. Unfortunately, we discovered that their scheme is unable to withstand key stream attack. To improve its security, this paper proposes a novel chaotic map based block cryptosystem. At the same time, a secure architecture for camera sensor network is constructed. The network comprises a set of inexpensive camera sensors to capture the images, a sink node equipped with sufficient computation and storage capabilities and a data processing server. The transmission security between the sink node and the server is gained by utilizing the improved cipher. Both theoretical analysis and simulation results indicate that the improved algorithm can overcome the flaws and maintain all the merits of the original cryptosystem. In addition, computational costs and efficiency of the proposed scheme are encouraging for the practical implementation in the real environment as well as camera sensor network. PMID:22319371

Probing the statistics of transport in the Hénon Map

NASA Astrophysics Data System (ADS)

Alus, O.; Fishman, S.; Meiss, J. D.

2016-09-01

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant "boundary circles." We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.

Exploration of the Chaotic Behaviour in a Buck-Boost Converter Depending on the Converter and Load Elements

NASA Astrophysics Data System (ADS)

Demirbaş, Şevki; Fidanboy, Hikmet; Kurt, Erol

2016-08-01

In this paper, detailed analyses of the chaotic behavior observed in a buck-boost converter are presented. Although this basic converter system is already known world-wide for the purpose of dc-dc conversion of the output of renewable energy systems, it indicates certain chaotic regimes where both the output amplitude and frequency change randomly. This chaotic regime can yield an unstable output over the resistive or resistive/inductive electrical loads. This study presents a detailed map for the regular and chaotic regions in terms of material parameters, such as converter capacitance C, resistive load R, and inductive load L. Thus, the stable area of operation for efficient and renewable electricity production will be ascertained for the studied converter system. We emphasize that the material parameters C, R, and L play important roles in generating energy from the solar cell; indeed, the stability increases with higher values of the converter capacitor and load inductance, whereas it decreases according to the resistive load. A number of periodic windows have been observed and the output frequency gives a broad-band spectrum of up to 50 kHz.

An Investigation of Traveling-Wave Electrophoresis using a Trigonometric Potential

NASA Astrophysics Data System (ADS)

Vopal, James

Traveling-wave electrophoresis, a technique for microfluidic separations in lab-on-achip devices, is investigated using a trigonometric model that naturally incorporates the spatial periodicity of the device. Traveling-wave electrophoresis can be used to separate high-mobility ions from low-mobility ions in forensic and medical applications, with a separation threshold that can be tuned for specific applications by simply choosing the traveling wave frequency. Our simulations predict plateaus in the average ion velocity verses the mobility, plateaus that correspond to Farey fractions and yield Devil's staircases for non-zero discreteness values. The plateaus indicate that ions with different mobilities can travel with the same average velocity. To determine the conditions for chaos, Lyapunov exponents and contact maps are employed. Through the use of contact maps, the chaotic trajectories are determined to be either narrowband or broadband. Narrowband chaotic trajectories are exhibited in the plateaus of the average velocity, while broadband chaotic trajectories are exhibited where the average velocity varies nonmonotonically with the mobility. Narrowband chaos will be investigated in future work incorporating the role of diffusion. The results of this and future work can be used to develop new tools for electrophoretic separation.

Innovative hyperchaotic encryption algorithm for compressed video

NASA Astrophysics Data System (ADS)

Yuan, Chun; Zhong, Yuzhuo; Yang, Shiqiang

2002-12-01

It is accepted that stream cryptosystem can achieve good real-time performance and flexibility which implements encryption by selecting few parts of the block data and header information of the compressed video stream. Chaotic random number generator, for example Logistics Map, is a comparatively promising substitute, but it is easily attacked by nonlinear dynamic forecasting and geometric information extracting. In this paper, we present a hyperchaotic cryptography scheme to encrypt the compressed video, which integrates Logistics Map with Z(232 - 1) field linear congruential algorithm to strengthen the security of the mono-chaotic cryptography, meanwhile, the real-time performance and flexibility of the chaotic sequence cryptography are maintained. It also integrates with the dissymmetrical public-key cryptography and implements encryption and identity authentification on control parameters at initialization phase. In accord with the importance of data in compressed video stream, encryption is performed in layered scheme. In the innovative hyperchaotic cryptography, the value and the updating frequency of control parameters can be changed online to satisfy the requirement of the network quality, processor capability and security requirement. The innovative hyperchaotic cryprography proves robust security by cryptoanalysis, shows good real-time performance and flexible implement capability through the arithmetic evaluating and test.

Granular chaos and mixing: Whirled in a grain of sand.

PubMed

Shinbrot, Troy

2015-09-01

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combines micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.

Granular chaos and mixing: Whirled in a grain of sand

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shinbrot, Troy, E-mail: shinbrot@rutgers.edu

2015-09-15

In this paper, we overview examples of chaos in granular flows. We begin by reviewing several remarkable behaviors that have intrigued researchers over the past few decades, and we then focus on three areas in which chaos plays an intrinsic role in granular behavior. First, we discuss pattern formation in vibrated beds, which we show is a direct result of chaotic scattering combined with dynamical dissipation. Next, we consider stick-slip motion, which involves chaotic scattering on the micro-scale, and which results in complex and as yet unexplained peculiarities on the macro-scale. Finally, we examine granular mixing, which we show combinesmore » micro-scale chaotic scattering and macro-scale stick-slip motion into behaviors that are well described by dynamical systems tools, such as iterative mappings.« less

Chaos and Correlated Avalanches in Excitatory Neural Networks with Synaptic Plasticity

NASA Astrophysics Data System (ADS)

Pittorino, Fabrizio; Ibáñez-Berganza, Miguel; di Volo, Matteo; Vezzani, Alessandro; Burioni, Raffaella

2017-03-01

A collective chaotic phase with power law scaling of activity events is observed in a disordered mean field network of purely excitatory leaky integrate-and-fire neurons with short-term synaptic plasticity. The dynamical phase diagram exhibits two transitions from quasisynchronous and asynchronous regimes to the nontrivial, collective, bursty regime with avalanches. In the homogeneous case without disorder, the system synchronizes and the bursty behavior is reflected into a period doubling transition to chaos for a two dimensional discrete map. Numerical simulations show that the bursty chaotic phase with avalanches exhibits a spontaneous emergence of persistent time correlations and enhanced Kolmogorov complexity. Our analysis reveals a mechanism for the generation of irregular avalanches that emerges from the combination of disorder and deterministic underlying chaotic dynamics.

Three-dimensional information hierarchical encryption based on computer-generated holograms

NASA Astrophysics Data System (ADS)

Kong, Dezhao; Shen, Xueju; Cao, Liangcai; Zhang, Hao; Zong, Song; Jin, Guofan

2016-12-01

A novel approach for encrypting three-dimensional (3-D) scene information hierarchically based on computer-generated holograms (CGHs) is proposed. The CGHs of the layer-oriented 3-D scene information are produced by angular-spectrum propagation algorithm at different depths. All the CGHs are then modulated by different chaotic random phase masks generated by the logistic map. Hierarchical encryption encoding is applied when all the CGHs are accumulated one by one, and the reconstructed volume of the 3-D scene information depends on permissions of different users. The chaotic random phase masks could be encoded into several parameters of the chaotic sequences to simplify the transmission and preservation of the keys. Optical experiments verify the proposed method and numerical simulations show the high key sensitivity, high security, and application flexibility of the method.

A Double-function Digital Watermarking Algorithm Based on Chaotic System and LWT

NASA Astrophysics Data System (ADS)

Yuxia, Zhao; Jingbo, Fan

A double- function digital watermarking technology is studied and a double-function digital watermarking algorithm of colored image is presented based on chaotic system and the lifting wavelet transformation (LWT).The algorithm has realized the double aims of the copyright protection and the integrity authentication of image content. Making use of feature of human visual system (HVS), the watermark image is embedded into the color image's low frequency component and middle frequency components by different means. The algorithm has great security by using two kinds chaotic mappings and Arnold to scramble the watermark image at the same time. The algorithm has good efficiency by using LWT. The emulation experiment indicates the algorithm has great efficiency and security, and the effect of concealing is really good.

The chaotic regime of D-term inflation

NASA Astrophysics Data System (ADS)

Buchmüller, W.; Domcke, V.; Schmitz, K.

2014-11-01

We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of `chaotic inflation'.

Chaos in War: Is It Present and What Does It Mean?

DTIC Science & Technology

1994-06-01

the Poincare map. The results of this work indicated that chaos is, in fact, present in warfare. The implications of this result include IV...confirmed the validity of our software and provided us with the Poincare maps and the power spectrum. LTC Pentland of the School for Advanced...nearly identical initial conditions for the logistics equation 20 8 . Poincare map 22 9. Phase-space trajectories of chaotic systems 23 10

Genetic training of network using chaos concept: application to QSAR studies of vibration modes of tetrahedral halides.

PubMed

Lu, Qingzhang; Shen, Guoli; Yu, Ruqin

2002-11-15

The chaotic dynamical system is introduced in genetic algorithm to train ANN to formulate the CGANN algorithm. Logistic mapping as one of the most important chaotic dynamic mappings provides each new generation a high chance to hold GA's population diversity. This enhances the ability to overcome overfitting in training an ANN. The proposed CGANN has been used for QSAR studies to predict the tetrahedral modes (nu(1)(A1) and nu(2)(E)) of halides [MX(4)](epsilon). The frequencies predicted by QSAR were compared with those calculated by quantum chemistry methods including PM3, AM1, and MNDO/d. The possibility of improving the predictive ability of QSAR by including quantum chemistry parameters as feature variables has been investigated using tetrahedral tetrahalide examples. Copyright 2002 Wiley Periodicals, Inc.

A Round-Efficient Authenticated Key Agreement Scheme Based on Extended Chaotic Maps for Group Cloud Meeting

PubMed Central

Lee, Tian-Fu; Wang, Zeng-Bo

2017-01-01

The security is a critical issue for business purposes. For example, the cloud meeting must consider strong security to maintain the communication privacy. Considering the scenario with cloud meeting, we apply extended chaotic map to present passwordless group authentication key agreement, termed as Passwordless Group Authentication Key Agreement (PL-GAKA). PL-GAKA improves the computation efficiency for the simple group password-based authenticated key agreement (SGPAKE) proposed by Lee et al. in terms of computing the session key. Since the extended chaotic map has equivalent security level to the Diffie–Hellman key exchange scheme applied by SGPAKE, the security of PL-GAKA is not sacrificed when improving the computation efficiency. Moreover, PL-GAKA is a passwordless scheme, so the password maintenance is not necessary. Short-term authentication is considered, hence the communication security is stronger than other protocols by dynamically generating session key in each cloud meeting. In our analysis, we first prove that each meeting member can get the correct information during the meeting. We analyze common security issues for the proposed PL-GAKA in terms of session key security, mutual authentication, perfect forward security, and data integrity. Moreover, we also demonstrate that communicating in PL-GAKA is secure when suffering replay attacks, impersonation attacks, privileged insider attacks, and stolen-verifier attacks. Eventually, an overall comparison is given to show the performance between PL-GAKA, SGPAKE and related solutions. PMID:29207509

Understanding the Chaotic Behavior of Field Lines using the Simple Map

NASA Astrophysics Data System (ADS)

Saralkar, R.; White, C.; Ali, H.; Punjabi, A.

1998-11-01

The Simple Map is given by x_n+1=x_n-ky_n(1-y_n), y_n+1=y_n+kx_n+1. Different initial values of x and y create different surfaces. We can see at what point the order begins to fade, at what point the surface breaks up and islands form, and at what point chaos occurs. The outer surfaces are chaotic as expected because the plasma is nearing the X-point in the tokamak, where the order begins to break up. We are specifically investigating two areas of the Simple Map. First we want to see what ther surfaces look like if they are magnified near the X-point. We are looking for self-similar structures in which order can be found in chaos, and chaos can be found in order. Our second investigation deals with how neighboring field lines separate in the chaotic region. We are expecting to see the distance between two close points drastically increase as we near the X-point. Reshama Saralkar and Cedric White are HU CFRT 1998 Summer Fusion High School Workshop Participants from the NASA SHARP PLUS Program. RS attends Watkins Mill High School in Gaithersburg, MD. CW attends Gwynn Park High School in Brandywine,MD. They are mentored by Dr. Ali and Dr. Punjabi of HU CFRT. 1. Punjabi et al, Phys Rev Lett 69 3322 (1992) 2. Punjabi et al, J Plasma Phys 52 91 (1994)

A secure chaotic maps and smart cards based password authentication and key agreement scheme with user anonymity for telecare medicine information systems.

PubMed

Li, Chun-Ta; Lee, Cheng-Chi; Weng, Chi-Yao

2014-09-01

Telecare medicine information system (TMIS) is widely used for providing a convenient and efficient communicating platform between patients at home and physicians at medical centers or home health care (HHC) organizations. To ensure patient privacy, in 2013, Hao et al. proposed a chaotic map based authentication scheme with user anonymity for TMIS. Later, Lee showed that Hao et al.'s scheme is in no provision for providing fairness in session key establishment and gave an efficient user authentication and key agreement scheme using smart cards, in which only few hashing and Chebyshev chaotic map operations are required. In addition, Jiang et al. discussed that Hao et al.'s scheme can not resist stolen smart card attack and they further presented an improved scheme which attempts to repair the security pitfalls found in Hao et al.'s scheme. In this paper, we found that both Lee's and Jiang et al.'s authentication schemes have a serious security problem in that a registered user's secret parameters may be intentionally exposed to many non-registered users and this problem causing the service misuse attack. Therefore, we propose a slight modification on Lee's scheme to prevent the shortcomings. Compared with previous schemes, our improved scheme not only inherits the advantages of Lee's and Jiang et al.'s authentication schemes for TMIS but also remedies the serious security weakness of not being able to withstand service misuse attack.

Chaotic dynamics of Comet 1P/Halley: Lyapunov exponent and survival time expectancy

NASA Astrophysics Data System (ADS)

Muñoz-Gutiérrez, M. A.; Reyes-Ruiz, M.; Pichardo, B.

2015-03-01

The orbital elements of Comet Halley are known to a very high precision, suggesting that the calculation of its future dynamical evolution is straightforward. In this paper we seek to characterize the chaotic nature of the present day orbit of Comet Halley and to quantify the time-scale over which its motion can be predicted confidently. In addition, we attempt to determine the time-scale over which its present day orbit will remain stable. Numerical simulations of the dynamics of test particles in orbits similar to that of Comet Halley are carried out with the MERCURY 6.2 code. On the basis of these we construct survival time maps to assess the absolute stability of Halley's orbit, frequency analysis maps to study the variability of the orbit, and we calculate the Lyapunov exponent for the orbit for variations in initial conditions at the level of the present day uncertainties in our knowledge of its orbital parameters. On the basis of our calculations of the Lyapunov exponent for Comet Halley, the chaotic nature of its motion is demonstrated. The e-folding time-scale for the divergence of initially very similar orbits is approximately 70 yr. The sensitivity of the dynamics on initial conditions is also evident in the self-similarity character of the survival time and frequency analysis maps in the vicinity of Halley's orbit, which indicates that, on average, it is unstable on a time-scale of hundreds of thousands of years. The chaotic nature of Halley's present day orbit implies that a precise determination of its motion, at the level of the present-day observational uncertainty, is difficult to predict on a time-scale of approximately 100 yr. Furthermore, we also find that the ejection of Halley from the Solar system or its collision with another body could occur on a time-scale as short as 10 000 yr.

Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Solar system dynamics

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

The rotational dynamics of irregularly shaped satellites and the origin of Kirkwood Gaps are discussed. The chaotic tumbling of Hyperion and the anomalously low eccentricity of Deimos are examined. The Digital Orrery is used to explore the phase space of the ellipic restricted three body problem near the principal commensurabilities (2/1, 5/2, 3/1, and 3/2). The results for the 3/1 commensurability are in close agreement with those found earlier with the algebraic mapping method. Large chaotic zones are associated with the 3/1, 2/1 and 5/2 resonances, where there are gaps in the distribution of asteroids. The region near the 3/2 resonance, where the Hilda group of asteroids is located, is largely devoid of chaotic behavior. Thus, there is a qualitative agreement between the character of the motion and the distribution of asteroids.

Temporal chaos in Boussinesq magnetoconvection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bekki, Naoaki; Moriguchi, Hirofumi; Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495

2007-01-15

Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincare return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famousmore » Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point.« less

Bouncing ball problem: stability of the periodic modes.

PubMed

Barroso, Joaquim J; Carneiro, Marcus V; Macau, Elbert E N

2009-02-01

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip v=+/-Gamma(1-epsilon) , where Gamma is the nondimensionalized shaking acceleration and epsilon the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

Two-Layer Fragile Watermarking Method Secured with Chaotic Map for Authentication of Digital Holy Quran

PubMed Central

Khalil, Mohammed S.; Khan, Muhammad Khurram; Alginahi, Yasser M.

2014-01-01

This paper presents a novel watermarking method to facilitate the authentication and detection of the image forgery on the Quran images. Two layers of embedding scheme on wavelet and spatial domain are introduced to enhance the sensitivity of fragile watermarking and defend the attacks. Discrete wavelet transforms are applied to decompose the host image into wavelet prior to embedding the watermark in the wavelet domain. The watermarked wavelet coefficient is inverted back to spatial domain then the least significant bits is utilized to hide another watermark. A chaotic map is utilized to blur the watermark to make it secure against the local attack. The proposed method allows high watermark payloads, while preserving good image quality. Experiment results confirm that the proposed methods are fragile and have superior tampering detection even though the tampered area is very small. PMID:25028681

Two-layer fragile watermarking method secured with chaotic map for authentication of digital Holy Quran.

PubMed

Khalil, Mohammed S; Kurniawan, Fajri; Khan, Muhammad Khurram; Alginahi, Yasser M

2014-01-01

This paper presents a novel watermarking method to facilitate the authentication and detection of the image forgery on the Quran images. Two layers of embedding scheme on wavelet and spatial domain are introduced to enhance the sensitivity of fragile watermarking and defend the attacks. Discrete wavelet transforms are applied to decompose the host image into wavelet prior to embedding the watermark in the wavelet domain. The watermarked wavelet coefficient is inverted back to spatial domain then the least significant bits is utilized to hide another watermark. A chaotic map is utilized to blur the watermark to make it secure against the local attack. The proposed method allows high watermark payloads, while preserving good image quality. Experiment results confirm that the proposed methods are fragile and have superior tampering detection even though the tampered area is very small.

Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding

NASA Astrophysics Data System (ADS)

Chen, Jun-Xin; Zhu, Zhi-Liang; Fu, Chong; Zhang, Li-Bo; Zhang, Yushu

2014-12-01

In this paper, we evaluate the security of an enhanced double random phase encoding (DRPE) image encryption scheme (2013 J. Lightwave Technol. 31 2533). The original system employs a chaotic Baker map prior to DRPE to provide more protection to the plain image and hence promote the security level of DRPE, as claimed. However, cryptanalysis shows that this scheme is vulnerable to a chosen-plaintext attack, and the ciphertext can be precisely recovered. The corresponding improvement is subsequently reported upon the basic premise that no extra equipment or computational complexity is required. The simulation results and security analyses prove its effectiveness and security. The proposed achievements are suitable for all cryptosystems under permutation and, following that, the DRPE architecture, and we hope that our work can motivate the further research on optical image encryption.

Efficient biometric authenticated key agreements based on extended chaotic maps for telecare medicine information systems.

PubMed

Lou, Der-Chyuan; Lee, Tian-Fu; Lin, Tsung-Hung

2015-05-01

Authenticated key agreements for telecare medicine information systems provide patients, doctors, nurses and health visitors with accessing medical information systems and getting remote services efficiently and conveniently through an open network. In order to have higher security, many authenticated key agreement schemes appended biometric keys to realize identification except for using passwords and smartcards. Due to too many transmissions and computational costs, these authenticated key agreement schemes are inefficient in communication and computation. This investigation develops two secure and efficient authenticated key agreement schemes for telecare medicine information systems by using biometric key and extended chaotic maps. One scheme is synchronization-based, while the other nonce-based. Compared to related approaches, the proposed schemes not only retain the same security properties with previous schemes, but also provide users with privacy protection and have fewer transmissions and lower computational cost.

Design of a fast echo matching algorithm to reduce crosstalk with Doppler shifts in ultrasonic ranging

NASA Astrophysics Data System (ADS)

Liu, Lei; Guo, Rui; Wu, Jun-an

2017-02-01

Crosstalk is a main factor for wrong distance measurement by ultrasonic sensors, and this problem becomes more difficult to deal with under Doppler effects. In this paper, crosstalk reduction with Doppler shifts on small platforms is focused on, and a fast echo matching algorithm (FEMA) is proposed on the basis of chaotic sequences and pulse coding technology, then verified through applying it to match practical echoes. Finally, we introduce how to select both better mapping methods for chaotic sequences, and algorithm parameters for higher achievable maximum of cross-correlation peaks. The results indicate the following: logistic mapping is preferred to generate good chaotic sequences, with high autocorrelation even when the length is very limited; FEMA can not only match echoes and calculate distance accurately with an error degree mostly below 5%, but also generates nearly the same calculation cost level for static or kinematic ranging, much lower than that by direct Doppler compensation (DDC) with the same frequency compensation step; The sensitivity to threshold value selection and performance of FEMA depend significantly on the achievable maximum of cross-correlation peaks, and a higher peak is preferred, which can be considered as a criterion for algorithm parameter optimization under practical conditions.

Color image encryption based on hybrid hyper-chaotic system and cellular automata

NASA Astrophysics Data System (ADS)

Yaghouti Niyat, Abolfazl; Moattar, Mohammad Hossein; Niazi Torshiz, Masood

2017-03-01

This paper proposes an image encryption scheme based on Cellular Automata (CA). CA is a self-organizing structure with a set of cells in which each cell is updated by certain rules that are dependent on a limited number of neighboring cells. The major disadvantages of cellular automata in cryptography include limited number of reversal rules and inability to produce long sequences of states by these rules. In this paper, a non-uniform cellular automata framework is proposed to solve this problem. This proposed scheme consists of confusion and diffusion steps. In confusion step, the positions of the original image pixels are replaced by chaos mapping. Key image is created using non-uniform cellular automata and then the hyper-chaotic mapping is used to select random numbers from the image key for encryption. The main contribution of the paper is the application of hyper chaotic functions and non-uniform CA for robust key image generation. Security analysis and experimental results show that the proposed method has a very large key space and is resistive against noise and attacks. The correlation between adjacent pixels in the encrypted image is reduced and the amount of entropy is equal to 7.9991 which is very close to 8 which is ideal.

An Experimental Realization of a Chaos-Based Secure Communication Using Arduino Microcontrollers

PubMed Central

Zapateiro De la Hoz, Mauricio; Vidal, Yolanda

2015-01-01

Security and secrecy are some of the important concerns in the communications world. In the last years, several encryption techniques have been proposed in order to improve the secrecy of the information transmitted. Chaos-based encryption techniques are being widely studied as part of the problem because of the highly unpredictable and random-look nature of the chaotic signals. In this paper we propose a digital-based communication system that uses the logistic map which is a mathematically simple model that is chaotic under certain conditions. The input message signal is modulated using a simple Delta modulator and encrypted using a logistic map. The key signal is also encrypted using the same logistic map with different initial conditions. In the receiver side, the binary-coded message is decrypted using the encrypted key signal that is sent through one of the communication channels. The proposed scheme is experimentally tested using Arduino shields which are simple yet powerful development kits that allows for the implementation of the communication system for testing purposes. PMID:26413563

The grief map

NASA Astrophysics Data System (ADS)

Monteiro, L. H. A.

2014-12-01

Grieving is a natural human reaction to a significant loss. According to a psychiatric model, this process is characterized by a typical sequence of psychological changes. Here, I propose a discrete-time dynamical system, called the grief map, in order to represent the grieving process. The corresponding bifurcation diagram, which exhibits stationary, periodic, and chaotic behavior, is related to the stages of this sorrowful journey occurring during about 12 months post-loss.

Dynamic Regimes of El Niño Southern Oscillation and Influenza Pandemic Timing

PubMed Central

Oluwole, Olusegun Steven Ayodele

2017-01-01

El Niño southern oscillation (ENSO) dynamics has been shown to drive seasonal influenza dynamics. Severe seasonal influenza epidemics and the 2009–2010 pandemic were coincident with chaotic regime of ENSO dynamics. ENSO dynamics from 1876 to 2016 were characterized to determine if influenza pandemics are coupled to chaotic regimes. Time-varying spectra of southern oscillation index (SOI) and sea surface temperature (SST) were compared. SOI and SST were decomposed to components using the algorithm of noise-assisted multivariate empirical mode decomposition. The components were Hilbert transformed to generate instantaneous amplitudes and phases. The trajectories and attractors of components were characterized in polar coordinates and state space. Influenza pandemics were mapped to dynamic regimes of SOI and SST joint recurrence of annual components. State space geometry of El Niños lagged by influenza pandemics were characterized and compared with other El Niños. Timescales of SOI and SST components ranged from sub-annual to multidecadal. The trajectories of SOI and SST components and the joint recurrence of annual components were dissipative toward chaotic attractors. Periodic, quasi-periodic, and chaotic regimes were present in the recurrence of trajectories, but chaos–chaos transitions dominated. Influenza pandemics occurred during chaotic regimes of significantly low transitivity dimension (p < 0.0001). El Niños lagged by influenza pandemics had distinct state space geometry (p < 0.0001). Chaotic dynamics explains the aperiodic timing, and varying duration and strength of El Niños. Coupling of all influenza pandemics of the past 140 years to chaotic regimes of low transitivity indicate that ENSO dynamics drives influenza pandemic dynamics. Forecasts models from ENSO dynamics should compliment surveillance for novel influenza viruses. PMID:29218303

The security energy encryption in wireless power transfer

NASA Astrophysics Data System (ADS)

Sadzali, M. N.; Ali, A.; Azizan, M. M.; Albreem, M. A. M.

2017-09-01

This paper presents a concept of security in wireless power transfer (WPT) by applying chaos theory. Chaos theory is applied as a security system in order to safeguard the transfer of energy from a transmitter to the intended receiver. The energy encryption of the wireless power transfer utilizes chaos theory to generate the possibility of a logistic map for the chaotic security key. The simulation for energy encryption wireless power transfer system was conducted by using MATLAB and Simulink. By employing chaos theory, the chaotic key ensures the transmission of energy from transmitter to its intended receiver.

Mapa MEGNO para satélites irregulares de Satuno

NASA Astrophysics Data System (ADS)

Moyano, M. M.; Leiva, A. M.

By implementing the elliptic restricted three-body model we obtain high resolution dynamical maps in the phase space region corresponding to that where Saturn's irregular satellites are currently found. The nature of the trajectories is characterized by the MEGNO chaos indicator (Cincotta P. and Simó C., 2000), which allows to identify regions of chaotic and quasi- periodic trajectories much faster than with other indicators (e.g. Lyapunov exponents). The results obtained allow to identify with great detail the boundaries of the regions of regular motion, chaotic motion, and substruc- tures associated to mean motion resonances. FULL TEXT IN SPANISH

Interesting examples of supervised continuous variable systems

NASA Technical Reports Server (NTRS)

Chase, Christopher; Serrano, Joe; Ramadge, Peter

1990-01-01

The authors analyze two simple deterministic flow models for multiple buffer servers which are examples of the supervision of continuous variable systems by a discrete controller. These systems exhibit what may be regarded as the two extremes of complexity of the closed loop behavior: one is eventually periodic, the other is chaotic. The first example exhibits chaotic behavior that could be characterized statistically. The dual system, the switched server system, exhibits very predictable behavior, which is modeled by a finite state automaton. This research has application to multimodal discrete time systems where the controller can choose from a set of transition maps to implement.

Controlling chaos faster.

PubMed

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-09-01

Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.

Double-well chimeras in 2D lattice of chaotic bistable elements

NASA Astrophysics Data System (ADS)

Shepelev, I. A.; Bukh, A. V.; Vadivasova, T. E.; Anishchenko, V. S.; Zakharova, A.

2018-01-01

We investigate spatio-temporal dynamics of a 2D ensemble of nonlocally coupled chaotic cubic maps in a bistability regime. In particular, we perform a detailed study on the transition ;coherence - incoherence; for varying coupling strength for a fixed interaction radius. For the 2D ensemble we show the appearance of amplitude and phase chimera states previously reported for 1D ensembles of nonlocally coupled chaotic systems. Moreover, we uncover a novel type of chimera state, double-well chimera, which occurs due to the interplay of the bistability of the local dynamics and the 2D ensemble structure. Additionally, we find double-well chimera behavior for steady states which we call double-well chimera death. A distinguishing feature of chimera patterns observed in the lattice is that they mainly combine clusters of different chimera types: phase, amplitude and double-well chimeras.

Quantification of chaotic strength and mixing in a micro fluidic system

NASA Astrophysics Data System (ADS)

Kim, Ho Jun; Beskok, Ali

2007-11-01

Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in micro fluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. The 'chaotic electroosmotic stirrer' of Qian and Bau (2002 Anal. Chem. 74 3616-25) is utilized as the benchmark case due to its well-defined flow kinematics. Lagrangian particle tracking methods are utilized to study particle dispersion in the conceptual device using spectral element and fourth-order Runge-Kutta discretizations in space and time, respectively. Stirring efficiency is predicted using the stirring index based on the box counting method, and Poincaré sections are utilized to identify the chaotic and regular regions under various actuation conditions. Finite time Lyapunov exponents are calculated to quantify the chaotic strength, while the probability density function of the stretching field is utilized as an alternative method to demonstrate the statistical analysis of chaotic and partially chaotic cases. Mixing index inverse, based on the standard deviation of scalar species distribution, is utilized as a metric to quantify the mixing efficiency. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing time (tm) is characterized as a function of the Pe number, and tm ~ ln(Pe) scaling is demonstrated for fully chaotic cases, while tm ~ Peα scaling with α ≈ 0.33 and α = 0.5 are observed for partially chaotic and regular cases, respectively. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified.

Ensemble of Chaotic and Naive Approaches for Performance Enhancement in Video Encryption.

PubMed

Chandrasekaran, Jeyamala; Thiruvengadam, S J

2015-01-01

Owing to the growth of high performance network technologies, multimedia applications over the Internet are increasing exponentially. Applications like video conferencing, video-on-demand, and pay-per-view depend upon encryption algorithms for providing confidentiality. Video communication is characterized by distinct features such as large volume, high redundancy between adjacent frames, video codec compliance, syntax compliance, and application specific requirements. Naive approaches for video encryption encrypt the entire video stream with conventional text based cryptographic algorithms. Although naive approaches are the most secure for video encryption, the computational cost associated with them is very high. This research work aims at enhancing the speed of naive approaches through chaos based S-box design. Chaotic equations are popularly known for randomness, extreme sensitivity to initial conditions, and ergodicity. The proposed methodology employs two-dimensional discrete Henon map for (i) generation of dynamic and key-dependent S-box that could be integrated with symmetric algorithms like Blowfish and Data Encryption Standard (DES) and (ii) generation of one-time keys for simple substitution ciphers. The proposed design is tested for randomness, nonlinearity, avalanche effect, bit independence criterion, and key sensitivity. Experimental results confirm that chaos based S-box design and key generation significantly reduce the computational cost of video encryption with no compromise in security.

Emergent scar lines in chaotic advection of passive directors

NASA Astrophysics Data System (ADS)

Hejazi, Bardia; Mehlig, Bernhard; Voth, Greg A.

2017-12-01

We examine the spatial field of orientations of slender fibers that are advected by a two-dimensional fluid flow. The orientation field of these passive directors are important in a wide range of industrial and geophysical flows. We introduce emergent scar lines as the dominant coherent structures in the orientation field of passive directors in chaotic flows. Previous work has identified the existence of scar lines where the orientation rotates by π over short distances, but the lines that were identified disappeared as time progressed. As a result, earlier work focused on topological singularities in the orientation field, which we find to play a negligible role at long times. We use the standard map as a simple time-periodic two-dimensional flow that produces Lagrangian chaos. This class of flows produces persistent patterns in passive scalar advection and we find that a different kind of persistent pattern develops in the passive director orientation field. We identify the mechanism by which emergent scar lines grow to dominate these patterns at long times in complex flows. Emergent scar lines form where the recent stretching of the fluid element is perpendicular to earlier stretching. Thus these scar lines can be labeled by their age, defined as the time since their stretching reached a maximum.

Ensemble of Chaotic and Naive Approaches for Performance Enhancement in Video Encryption

PubMed Central

Chandrasekaran, Jeyamala; Thiruvengadam, S. J.

2015-01-01

Owing to the growth of high performance network technologies, multimedia applications over the Internet are increasing exponentially. Applications like video conferencing, video-on-demand, and pay-per-view depend upon encryption algorithms for providing confidentiality. Video communication is characterized by distinct features such as large volume, high redundancy between adjacent frames, video codec compliance, syntax compliance, and application specific requirements. Naive approaches for video encryption encrypt the entire video stream with conventional text based cryptographic algorithms. Although naive approaches are the most secure for video encryption, the computational cost associated with them is very high. This research work aims at enhancing the speed of naive approaches through chaos based S-box design. Chaotic equations are popularly known for randomness, extreme sensitivity to initial conditions, and ergodicity. The proposed methodology employs two-dimensional discrete Henon map for (i) generation of dynamic and key-dependent S-box that could be integrated with symmetric algorithms like Blowfish and Data Encryption Standard (DES) and (ii) generation of one-time keys for simple substitution ciphers. The proposed design is tested for randomness, nonlinearity, avalanche effect, bit independence criterion, and key sensitivity. Experimental results confirm that chaos based S-box design and key generation significantly reduce the computational cost of video encryption with no compromise in security. PMID:26550603

Experimental chaotic quantification in bistable vortex induced vibration systems

NASA Astrophysics Data System (ADS)

Huynh, B. H.; Tjahjowidodo, T.

2017-02-01

The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear out the regularity of periodic responses. For this purpose, a surrogate data test is used in order to check the hypotheses for the presence of chaotic behavior. The analyses from the experimental results support the hypothesis from simulation that chaotic response is likely occur on the real system.

An introduction to chaotic and random time series analysis

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Highly dissipative Hénon map behavior in the four-level model of the CO 2 laser with modulated losses

NASA Astrophysics Data System (ADS)

Pando L., C. L.; Acosta, G. A. Luna; Meucci, R.; Ciofini, M.

1995-02-01

We show that the four-level model for the CO 2 laser with modulated losses behaves in a qualitatively similar way as the highly dissipative Hénon map. The ubiquity of elements of the universal sequence, their related symbolic dynamics, and the presence of reverse bifurcations of chaotic bands in the model are reminiscent of the logistic map which is the limit of the Hénon map when the Jacobian equals zero. The coexistence of attractors, its dynamics related to contraction of volumes in phase space and the associated return maps can be correlated with those of the highly dissipative Hénon map.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

A Spatiotemporal-Chaos-Based Cryptosystem Taking Advantage of Both Synchronous and Self-Synchronizing Schemes

NASA Astrophysics Data System (ADS)

Lü, Hua-Ping; Wang, Shi-Hong; Li, Xiao-Wen; Tang, Guo-Ning; Kuang, Jin-Yu; Ye, Wei-Ping; Hu, Gang

2004-06-01

Two-dimensional one-way coupled map lattices are used for cryptography where multiple space units produce chaotic outputs in parallel. One of the outputs plays the role of driving for synchronization of the decryption system while the others perform the function of information encoding. With this separation of functions the receiver can establish a self-checking and self-correction mechanism, and enjoys the advantages of both synchronous and self-synchronizing schemes. A comparison between the present system with the system of advanced encryption standard (AES) is presented in the aspect of channel noise influence. Numerical investigations show that our system is much stronger than AES against channel noise perturbations, and thus can be better used for secure communications with large channel noise.

Transient chaos in the Lorenz-type map with periodic forcing.

PubMed

Maslennikov, Oleg V; Nekorkin, Vladimir I; Kurths, Jürgen

2018-03-01

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.

On chaos synchronization and secure communication.

PubMed

Kinzel, W; Englert, A; Kanter, I

2010-01-28

Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems. This journal is © 2010 The Royal Society

Transient chaos in the Lorenz-type map with periodic forcing

NASA Astrophysics Data System (ADS)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.; Kurths, Jürgen

2018-03-01

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.

Chaotic reconfigurable ZCMT precoder for OFDM data encryption and PAPR reduction

NASA Astrophysics Data System (ADS)

Chen, Han; Yang, Xuelin; Hu, Weisheng

2017-12-01

A secure orthogonal frequency division multiplexing (OFDM) transmission scheme precoded by chaotic Zadoff-Chu matrix transform (ZCMT) is proposed and demonstrated. It is proved that the reconfigurable ZCMT matrices after row/column permutations can be applied as an alternative precoder for peak-to-average power ratio (PAPR) reduction. The permutations and the reconfigurable parameters in ZCMT matrix are generated by a hyper digital chaos, in which a huge key space of ∼ 10800 is created for physical-layer OFDM data encryption. An encrypted data transmission of 8.9 Gb/s optical OFDM signals is successfully demonstrated over 20 km standard single-mode fiber (SSMF) for 16-QAM. The BER performance of the encrypted signals is improved by ∼ 2 dB (BER@ 10-3), which is mainly attributed to the effective reduction of PAPR via chaotic ZCMT precoding. Moreover, the chaotic ZCMT precoding scheme requires no sideband information, thus the spectrum efficiency is enhanced during transmission.

A secure image encryption method based on dynamic harmony search (DHS) combined with chaotic map

NASA Astrophysics Data System (ADS)

Mirzaei Talarposhti, Khadijeh; Khaki Jamei, Mehrzad

2016-06-01

In recent years, there has been increasing interest in the security of digital images. This study focuses on the gray scale image encryption using dynamic harmony search (DHS). In this research, first, a chaotic map is used to create cipher images, and then the maximum entropy and minimum correlation coefficient is obtained by applying a harmony search algorithm on them. This process is divided into two steps. In the first step, the diffusion of a plain image using DHS to maximize the entropy as a fitness function will be performed. However, in the second step, a horizontal and vertical permutation will be applied on the best cipher image, which is obtained in the previous step. Additionally, DHS has been used to minimize the correlation coefficient as a fitness function in the second step. The simulation results have shown that by using the proposed method, the maximum entropy and the minimum correlation coefficient, which are approximately 7.9998 and 0.0001, respectively, have been obtained.

Recurrence-plot-based measures of complexity and their application to heart-rate-variability data.

PubMed

Marwan, Norbert; Wessel, Niels; Meyerfeldt, Udo; Schirdewan, Alexander; Kurths, Jürgen

2002-08-01

The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.

Regular and chaotic motions of the Chaplygin sleigh with periodically switched location of nonholonomic constraint

NASA Astrophysics Data System (ADS)

Kuznetsov, Sergey P.

2017-04-01

We consider motions of the Chaplygin sleigh on a plane supposing that the nonholonomic constraint is located periodically turn by turn at each of three legs supporting the sleigh. We assume that at switching on the constraint the respective element (“knife-edge”) is directed along the local velocity vector and becomes fixed relatively to the sleigh for a certain time interval till the next switch. Differential equations of the mathematical model are formulated and analytical derivation of a 2D map for the state transformation on the switching period is provided. The dynamics takes place with conservation of the mechanical energy. Numerical simulations show phenomena characteristic to nonholonomic systems with complex dynamics. In particular, on the energy surface attractors may occur responsible for regular sustained motions settling in domains of prevalent area compression by the map. In addition, chaotic and quasi-periodic regimes take place similar to those observed in conservative nonlinear dynamics.

Analysis of X-ray structures of matrix metalloproteinases via chaotic map clustering.

PubMed

Giangreco, Ilenia; Nicolotti, Orazio; Carotti, Angelo; De Carlo, Francesco; Gargano, Gianfranco; Bellotti, Roberto

2010-10-08

Matrix metalloproteinases (MMPs) are well-known biological targets implicated in tumour progression, homeostatic regulation, innate immunity, impaired delivery of pro-apoptotic ligands, and the release and cleavage of cell-surface receptors. With this in mind, the perception of the intimate relationships among diverse MMPs could be a solid basis for accelerated learning in designing new selective MMP inhibitors. In this regard, decrypting the latent molecular reasons in order to elucidate similarity among MMPs is a key challenge. We describe a pairwise variant of the non-parametric chaotic map clustering (CMC) algorithm and its application to 104 X-ray MMP structures. In this analysis electrostatic potentials are computed and used as input for the CMC algorithm. It was shown that differences between proteins reflect genuine variation of their electrostatic potentials. In addition, the analysis has been also extended to analyze the protein primary structures and the molecular shapes of the MMP co-crystallised ligands. The CMC algorithm was shown to be a valuable tool in knowledge acquisition and transfer from MMP structures. Based on the variation of electrostatic potentials, CMC was successful in analysing the MMP target family landscape and different subsites. The first investigation resulted in rational figure interpretation of both domain organization as well as of substrate specificity classifications. The second made it possible to distinguish the MMP classes, demonstrating the high specificity of the S1' pocket, to detect both the occurrence of punctual mutations of ionisable residues and different side-chain conformations that likely account for induced-fit phenomena. In addition, CMC demonstrated a potential comparable to the most popular UPGMA (Unweighted Pair Group Method with Arithmetic mean) method that, at present, represents a standard clustering bioinformatics approach. Interestingly, CMC and UPGMA resulted in closely comparable outcomes, but often CMC produced more informative and more easy interpretable dendrograms. Finally, CMC was successful for standard pairwise analysis (i.e., Smith-Waterman algorithm) of protein sequences and was used to convincingly explain the complementarity existing between the molecular shapes of the co-crystallised ligand molecules and the accessible MMP void volumes.

Chaotic and stable perturbed maps: 2-cycles and spatial models

NASA Astrophysics Data System (ADS)

Braverman, E.; Haroutunian, J.

2010-06-01

As the growth rate parameter increases in the Ricker, logistic and some other maps, the models exhibit an irreversible period doubling route to chaos. If a constant positive perturbation is introduced, then the Ricker model (but not the classical logistic map) experiences period doubling reversals; the break of chaos finally gives birth to a stable two-cycle. We outline the maps which demonstrate a similar behavior and also study relevant discrete spatial models where the value in each cell at the next step is defined only by the values at the cell and its nearest neighbors. The stable 2-cycle in a scalar map does not necessarily imply 2-cyclic-type behavior in each cell for the spatial generalization of the map.

Multi-Baker Map as a Model of Digital PD Control

NASA Astrophysics Data System (ADS)

Csernák, Gábor; Gyebrószki, Gergely; Stépán, Gábor

Digital stabilization of unstable equilibria of linear systems may lead to small amplitude stochastic-like oscillations. We show that these vibrations can be related to a deterministic chaotic dynamics induced by sampling and quantization. A detailed analytical proof of chaos is presented for the case of a PD controlled oscillator: it is shown that there exists a finite attracting domain in the phase-space, the largest Lyapunov exponent is positive and the existence of a Smale horseshoe is also pointed out. The corresponding two-dimensional micro-chaos map is a multi-baker map, i.e. it consists of a finite series of baker’s maps.

The dynamical structure of the MEO region: long-term stability, chaos, and transport

NASA Astrophysics Data System (ADS)

Daquin, Jérôme; Rosengren, Aaron J.; Alessi, Elisa Maria; Deleflie, Florent; Valsecchi, Giovanni B.; Rossi, Alessandro

2016-04-01

It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.

The Influence of Road Bumps Characteristics on the Chaotic Vibration of a Nonlinear Full-Vehicle Model with Driver

NASA Astrophysics Data System (ADS)

Fakhraei, J.; Khanlo, H. M.; Ghayour, M.; Faramarzi, Kh.

In this paper, the chaotic behavior of a ground vehicle system with driver subjected to road disturbances is studied and the relationship between the nonlinear vibration of the vehicle and ride comfort is evaluated. The vehicle system is modeled as fully nonlinear with seven degrees of freedom and an additional degree of freedom for driver (8-DOF). The excitation force is the road irregularities that are assumed as road speed control bumps. The sinusoidal, consecutive half-sine and dented-rectangular waveforms are considered to simulate the road speed control bumps. The nonlinearities of the system are due to the nonlinear springs and dampers that are used in the suspension system and tires. The governing differential equations are extracted under Newton-Euler laws and solved via numerical methods. The chaotic behaviors were studied in more detail with special techniques such as bifurcation diagrams, phase plane portrait, Poincaré map and Lyapunov exponents. The ride comfort was evaluated as the RMS value of the vertical displacement of the vehicle body and driver. Firstly, the effect of amplitude (height) and frequency (vehicle’s speed) of these speed control bumps on chaotic vibrations of vehicle are studied. The obtained results show that various forms of vibrations, such as periodic, subharmonic and chaotic vibrations, can be detected in the system behavior with the change of the height and frequency of speed control bumps and present different types of strange attractors in the vehicle with and without driver. Then, the influence of nonlinear vibration on ride comfort and the relationship between chaotic vibrations of the vehicle and driving comfort are investigated. The results of analyzing the RMS diagrams reveal that the chaotic behaviors can directly affect the driving comfort and lead to the driver’s comfort being reduced. The obtained results can be used in the design of vehicle and road bumps pavement.

A quasi-intermittency

NASA Astrophysics Data System (ADS)

He, Da-Ren; Wang, Xu-Ming; Wang, Ying-Mei; Wang, Wen-Xiu; Chen, He-Sheng

2002-03-01

A kind of discontinuous and noninvertible area-preserving maps can display behaviors as a dissipative one, so it may be addressed as a "quasi-dissipative system"^1. In a quasi-dissipative system the disappearance of some elliptic periodic orbits and the elliptic islands around them via a collision with the discontinuous border of the system function can be observed. A chaotic quasi-attractor dominates behavior of the system after the disappearance of the elliptic periodic orbit and a sequence of transition elliptic periodic orbits. When the chaotic quasi-attractor just appears, the chaotic time sequence shows a random intersperse between laminar and turbulence phases. All these are very similar to the properties of type V intermittency happened in a dissipative system. So, we may call the phenomenon as a "type V quasi-intermittency". However, there can be only some remnants of the last disappeared transition elliptic island instead of its "ghost", therefore type V quasi-intermittency does not obey the characteristic scaling laws of type V intermittency. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

Chaotic Image Encryption of Regions of Interest

NASA Astrophysics Data System (ADS)

Xiao, Di; Fu, Qingqing; Xiang, Tao; Zhang, Yushu

Since different regions of an image have different importance, therefore only the important information of the image regions, which the users are really interested in, needs to be encrypted and protected emphatically in some special multimedia applications. However, the regions of interest (ROI) are always some irregular parts, such as the face and the eyes. Assuming the bulk data in transmission without being damaged, we propose a chaotic image encryption algorithm for ROI. ROI with irregular shapes are chosen and detected arbitrarily. Then the chaos-based image encryption algorithm with scrambling, S-box and diffusion parts is used to encrypt the ROI. Further, the whole image is compressed with Huffman coding. At last, a message authentication code (MAC) of the compressed image is generated based on chaotic maps. The simulation results show that the encryption algorithm has a good security level and can resist various attacks. Moreover, the compression method improves the storage and transmission efficiency to some extent, and the MAC ensures the integrity of the transmission data.

Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication.

PubMed

Lakshmanan, Shanmugam; Prakash, Mani; Lim, Chee Peng; Rakkiyappan, Rajan; Balasubramaniam, Pagavathigounder; Nahavandi, Saeid

2018-01-01

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

Epileptic Seizure Prediction Using a New Similarity Index for Chaotic Signals

NASA Astrophysics Data System (ADS)

Niknazar, Hamid; Nasrabadi, Ali Motie

Epileptic seizures are generated by abnormal activity of neurons. The prediction of epileptic seizures is an important issue in the field of neurology, since it may improve the quality of life of patients suffering from drug resistant epilepsy. In this study a new similarity index based on symbolic dynamic techniques which can be used for extracting behavior of chaotic time series is presented. Using Freiburg EEG dataset, it is found that the method is able to detect the behavioral changes of the neural activity prior to epileptic seizures, so it can be used for prediction of epileptic seizure. A sensitivity of 63.75% with 0.33 false positive rate (FPR) in all 21 patients and sensitivity of 96.66% with 0.33 FPR in eight patients were achieved using the proposed method. Moreover, the method was evaluated by applying on Logistic and Tent map with different parameters to demonstrate its robustness and ability in determining similarity between two time series with the same chaotic characterization.

A multi-GHz chaotic optoelectronic oscillator based on laser terminal voltage

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, C. Y., E-mail: cychang@gatech.edu; UMI 2958 Georgia Tech-CNRS, Georgia Tech Lorraine, 2 Rue Marconi, F-57070 Metz; Choi, Daeyoung

2016-05-09

A multi-GHz chaotic optoelectronic oscillator based on an external cavity semiconductor laser (ECL) is demonstrated. Unlike the standard optoelectronic oscillators for microwave applications, we do not employ the dynamic light output incident on a photodiode to generate the microwave signal, but instead generate the microwave signal directly by measuring the terminal voltage V(t) of the laser diode of the ECL under constant-current operation, thus obviating the photodiode entirely.

Color image encryption based on gyrator transform and Arnold transform

NASA Astrophysics Data System (ADS)

Sui, Liansheng; Gao, Bo

2013-06-01

A color image encryption scheme using gyrator transform and Arnold transform is proposed, which has two security levels. In the first level, the color image is separated into three components: red, green and blue, which are normalized and scrambled using the Arnold transform. The green component is combined with the first random phase mask and transformed to an interim using the gyrator transform. The first random phase mask is generated with the sum of the blue component and a logistic map. Similarly, the red component is combined with the second random phase mask and transformed to three-channel-related data. The second random phase mask is generated with the sum of the phase of the interim and an asymmetrical tent map. In the second level, the three-channel-related data are scrambled again and combined with the third random phase mask generated with the sum of the previous chaotic maps, and then encrypted into a gray scale ciphertext. The encryption result has stationary white noise distribution and camouflage property to some extent. In the process of encryption and decryption, the rotation angle of gyrator transform, the iterative numbers of Arnold transform, the parameters of the chaotic map and generated accompanied phase function serve as encryption keys, and hence enhance the security of the system. Simulation results and security analysis are presented to confirm the security, validity and feasibility of the proposed scheme.

Anticontrol of chaos in continuous-time systems via time-delay feedback.

PubMed

Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

2000-12-01

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

An Intelligent Fingerprint-Biometric Image Scrambling Scheme

NASA Astrophysics Data System (ADS)

Khan, Muhammad Khurram; Zhang, Jiashu

To obstruct the attacks, and to hamper with the liveness and retransmission issues of biometrics images, we have researched on the challenge/response-based biometrics scrambled image transmission. We proposed an intelligent biometrics sensor, which has computational power to receive challenges from the authentication server and generate response against the challenge with the encrypted biometric image. We utilized the FRT for biometric image encryption and used its scaling factors and random phase mask as the additional secret keys. In addition, we chaotically generated the random phase masks by a chaotic map to further improve the encryption security. Experimental and simulation results have shown that the presented system is secure, robust, and deters the risks of attacks of biometrics image transmission.

Chaotic dynamics in premixed hydrogen/air channel flow combustion

NASA Astrophysics Data System (ADS)

Pizza, Gianmarco; Frouzakis, Christos E.; Mantzaras, John

2012-04-01

The complex oscillatory behaviour observed in fuel-lean premixed hydrogen/air atmospheric pressure flames in an open planar channel with prescribed wall temperature is investigated by means of direct numerical simulations, employing detailed chemistry descriptions and species transport, and nonlinear dynamics analysis. As the inflow velocity is varied, the sequence of transitions includes harmonic single frequency oscillations, intermittency, mixed mode oscillations, and finally a period-doubling cascade leading to chaotic dynamics. The observed modes are described and characterised by means of phase-space portraits and next amplitude maps. It is shown that the interplay of chemistry, transport, and wall-bounded developing flow leads to considerably richer dynamics compared to fuel-lean hydrogen/air continuously stirred tank reactor studies.

Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion

NASA Astrophysics Data System (ADS)

Annaby, M. H.; Rushdi, M. A.; Nehary, E. A.

2018-04-01

The recent tremendous proliferation of color imaging applications has been accompanied by growing research in data encryption to secure color images against adversary attacks. While recent color image encryption techniques perform reasonably well, they still exhibit vulnerabilities and deficiencies in terms of statistical security measures due to image data redundancy and inherent weaknesses. This paper proposes two encryption algorithms that largely treat these deficiencies and boost the security strength through novel integration of the random fractional Fourier transforms, phase retrieval algorithms, as well as chaotic scrambling and diffusion. We show through detailed experiments and statistical analysis that the proposed enhancements significantly improve security measures and immunity to attacks.

Chaotic behavior of a spin-glass model on a Cayley tree

NASA Astrophysics Data System (ADS)

da Costa, F. A.; de Araújo, J. M.; Salinas, S. R.

2015-06-01

We investigate the phase diagram of a spin-1 Ising spin-glass model on a Cayley tree. According to early work of Thompson and collaborators, this problem can be formulated in terms of a set of nonlinear discrete recursion relations along the branches of the tree. Physically relevant solutions correspond to the attractors of these mapping equations. In the limit of infinite coordination of the tree, and for some choices of the model parameters, we make contact with findings for the phase diagram of more recently investigated versions of the Blume-Emery-Griffiths spin-glass model. In addition to the anticipated phases, we numerically characterize the existence of modulated and chaotic structures.

Chaotic one-dimensional domains induced by periodic potentials in normal-dispersion fiber lasers

NASA Astrophysics Data System (ADS)

Urzagasti, Deterlino; Vargas, Bryan A.; Quispe-Flores, Luzmila A.

2017-10-01

We investigate numerically the effects of external time-periodic potentials on time-localized perturbations to the amplitude of electromagnetic waves propagating in normal-dispersion fiber lasers which are described by the complex Ginzburg-Landau equation. Two main effects were found: The formation of domains enclosed by two maxima of the external periodic field and the generation of a chaotic behavior of these domains in the region of relatively high amplitudes and low frequencies of the external fields. Maps and bifurcation diagrams of the largest Lyapunov exponent and moments, such as energy and momentum, are also provided for different values of the amplitude and frequency of such external potentials.

Control of complex dynamics and chaos in distributed parameter systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakravarti, S.; Marek, M.; Ray, W.H.

This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in themore » complex quasi-periodic or chaotic spatiotemporal patterns.« less

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

Information flow in layered networks of non-monotonic units

NASA Astrophysics Data System (ADS)

Schittler Neves, Fabio; Martim Schubert, Benno; Erichsen, Rubem, Jr.

2015-07-01

Layered neural networks are feedforward structures that yield robust parallel and distributed pattern recognition. Even though much attention has been paid to pattern retrieval properties in such systems, many aspects of their dynamics are not yet well characterized or understood. In this work we study, at different temperatures, the memory activity and information flows through layered networks in which the elements are the simplest binary odd non-monotonic function. Our results show that, considering a standard Hebbian learning approach, the network information content has its maximum always at the monotonic limit, even though the maximum memory capacity can be found at non-monotonic values for small enough temperatures. Furthermore, we show that such systems exhibit rich macroscopic dynamics, including not only fixed point solutions of its iterative map, but also cyclic and chaotic attractors that also carry information.

Recent Developments Related To An Optically Controlled Microwave Phased Array Antenna.

NASA Astrophysics Data System (ADS)

Kittel, A.; Peinke, J.; Klein, M.; Baier, G.; Parisi, J.; Rössler, O. E.

1990-12-01

A generic 3-dimensional diffeomorphic map, with constant Jacobian determinant, is proposed and looked at numerically. It contains a lower-dimensional basin boundary along which a chaotic motion takes place. This boundary is nowhere differentiable in one direction. Therefore, nowhere differentiable limit sets exist generically in nature.

Experiments with a Magnetically Controlled Pendulum

ERIC Educational Resources Information Center

Kraftmakher, Yaakov

2007-01-01

A magnetically controlled pendulum is used for observing free and forced oscillations, including nonlinear oscillations and chaotic motion. A data-acquisition system stores the data and displays time series of the oscillations and related phase plane plots, Poincare maps, Fourier spectra and histograms. The decay constant of the pendulum can be…

The Political Geography of Europe: 1900-2000 A.D.

ERIC Educational Resources Information Center

Blouet, Brian W.

1996-01-01

Traces the often chaotic restructuring of European national boundaries from before World War I to after the collapse of the Soviet Union. Offers a concise and interesting overview of the political, economic, and military events that shaped modern Europe. Includes seven detailed maps showing shifting boundaries and alliances. (MJP)

Maps on statistical manifolds exactly reduced from the Perron-Frobenius equations for solvable chaotic maps

NASA Astrophysics Data System (ADS)

Goto, Shin-itiro; Umeno, Ken

2018-03-01

Maps on a parameter space for expressing distribution functions are exactly derived from the Perron-Frobenius equations for a generalized Boole transform family. Here the generalized Boole transform family is a one-parameter family of maps, where it is defined on a subset of the real line and its probability distribution function is the Cauchy distribution with some parameters. With this reduction, some relations between the statistical picture and the orbital one are shown. From the viewpoint of information geometry, the parameter space can be identified with a statistical manifold, and then it is shown that the derived maps can be characterized. Also, with an induced symplectic structure from a statistical structure, symplectic and information geometric aspects of the derived maps are discussed.

New type of chimera and mutual synchronization of spatiotemporal structures in two coupled ensembles of nonlocally interacting chaotic maps

NASA Astrophysics Data System (ADS)

Bukh, Andrei; Rybalova, Elena; Semenova, Nadezhda; Strelkova, Galina; Anishchenko, Vadim

2017-11-01

We study numerically the dynamics of a network made of two coupled one-dimensional ensembles of discrete-time systems. The first ensemble is represented by a ring of nonlocally coupled Henon maps and the second one by a ring of nonlocally coupled Lozi maps. We find that the network of coupled ensembles can realize all the spatio-temporal structures which are observed both in the Henon map ensemble and in the Lozi map ensemble while uncoupled. Moreover, we reveal a new type of spatiotemporal structure, a solitary state chimera, in the considered network. We also establish and describe the effect of mutual synchronization of various complex spatiotemporal patterns in the system of two coupled ensembles of Henon and Lozi maps.

A Double Perturbation Method for Reducing Dynamical Degradation of the Digital Baker Map

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Lin, Jun; Miao, Suoxia; Liu, Bocheng

2017-06-01

The digital Baker map is widely used in different kinds of cryptosystems, especially for image encryption. However, any chaotic map which is realized on the finite precision device (e.g. computer) will suffer from dynamical degradation, which refers to short cycle lengths, low complexity and strong correlations. In this paper, a novel double perturbation method is proposed for reducing the dynamical degradation of the digital Baker map. Both state variables and system parameters are perturbed by the digital logistic map. Numerical experiments show that the perturbed Baker map can achieve good statistical and cryptographic properties. Furthermore, a new image encryption algorithm is provided as a simple application. With a rather simple algorithm, the encrypted image can achieve high security, which is competitive to the recently proposed image encryption algorithms.

A generalized geologic map of Mars.

NASA Technical Reports Server (NTRS)

Carr, M. H.; Masursky, H.; Saunders, R. S.

1973-01-01

A geologic map of Mars has been constructed largely on the basis of photographic evidence. Four classes of units are recognized: (1) primitive cratered terrain, (2) sparsely cratered volcanic eolian plains, (3) circular radially symmetric volcanic constructs such as shield volcanoes, domes, and craters, and (4) tectonic erosional units such as chaotic and channel deposits. Grabens are the main structural features; compressional and strike slip features are almost completely absent. Most grabens are part of a set radial to the main volcanic area, Tharsis.

A secure and efficient chaotic map-based authenticated key agreement scheme for telecare medicine information systems.

PubMed

Mishra, Dheerendra; Srinivas, Jangirala; Mukhopadhyay, Sourav

2014-10-01

Advancement in network technology provides new ways to utilize telecare medicine information systems (TMIS) for patient care. Although TMIS usually faces various attacks as the services are provided over the public network. Recently, Jiang et al. proposed a chaotic map-based remote user authentication scheme for TMIS. Their scheme has the merits of low cost and session key agreement using Chaos theory. It enhances the security of the system by resisting various attacks. In this paper, we analyze the security of Jiang et al.'s scheme and demonstrate that their scheme is vulnerable to denial of service attack. Moreover, we demonstrate flaws in password change phase of their scheme. Further, our aim is to propose a new chaos map-based anonymous user authentication scheme for TMIS to overcome the weaknesses of Jiang et al.'s scheme, while also retaining the original merits of their scheme. We also show that our scheme is secure against various known attacks including the attacks found in Jiang et al.'s scheme. The proposed scheme is comparable in terms of the communication and computational overheads with Jiang et al.'s scheme and other related existing schemes. Moreover, we demonstrate the validity of the proposed scheme through the BAN (Burrows, Abadi, and Needham) logic.

Chaos in the gauge/gravity correspondence

NASA Astrophysics Data System (ADS)

Pando Zayas, Leopoldo A.; Terrero-Escalante, César A.

2010-09-01

We study the motion of a string in the background of the Schwarzschild black hole in AdS 5 by applying the standard arsenal of dynamical systems. Our description of the phase space includes: the power spectrum, the largest Lyapunov exponent, Poincare sections and basins of attractions. We find convincing evidence that the motion is chaotic. We discuss the implications of some of the quantities associated with chaotic systems for aspects of the gauge/gravity correspondence. In particular, we suggest some potential relevance for the information loss paradox.

Public-key encryption with chaos.

PubMed

Kocarev, Ljupco; Sterjev, Marjan; Fekete, Attila; Vattay, Gabor

2004-12-01

We propose public-key encryption algorithms based on chaotic maps, which are generalization of well-known and commercially used algorithms: Rivest-Shamir-Adleman (RSA), ElGamal, and Rabin. For the case of generalized RSA algorithm we discuss in detail its software implementation and properties. We show that our algorithm is as secure as RSA algorithm.

Public-key encryption with chaos

NASA Astrophysics Data System (ADS)

Kocarev, Ljupco; Sterjev, Marjan; Fekete, Attila; Vattay, Gabor

2004-12-01

We propose public-key encryption algorithms based on chaotic maps, which are generalization of well-known and commercially used algorithms: Rivest-Shamir-Adleman (RSA), ElGamal, and Rabin. For the case of generalized RSA algorithm we discuss in detail its software implementation and properties. We show that our algorithm is as secure as RSA algorithm.

Logistic Map for Cancellable Biometrics

NASA Astrophysics Data System (ADS)

Supriya, V. G., Dr; Manjunatha, Ramachandra, Dr

2017-08-01

This paper presents design and implementation of secured biometric template protection system by transforming the biometric template using binary chaotic signals and 3 different key streams to obtain another form of template and demonstrating its efficiency by the results and investigating on its security through analysis including, key space analysis, information entropy and key sensitivity analysis.

Computation of entropy and Lyapunov exponent by a shift transform.

PubMed

Matsuoka, Chihiro; Hiraide, Koichi

2015-10-01

We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown that the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy.

Computation of entropy and Lyapunov exponent by a shift transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matsuoka, Chihiro, E-mail: matsuoka.chihiro.mm@ehime-u.ac.jp; Hiraide, Koichi

2015-10-15

We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown thatmore » the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy.« less

Tori and chaos in a simple C1-system

NASA Astrophysics Data System (ADS)

Roessler, O. E.; Kahiert, C.; Ughleke, B.

A piecewise-linear autonomous 3-variable ordinary differential equation is presented which permits analytical modeling of chaotic attractors. A once-differentiable system of equations is defined which consists of two linear half-systems which meet along a threshold plane. The trajectories described by each equation is thereby continuous along the divide, forming a one-parameter family of invariant tori. The addition of a damping term produces a system of equations for various chaotic attractors. Extension of the system by means of a 4-variable generalization yields hypertori and hyperchaos. It is noted that the hierarchy established is amenable to analysis by the use of Poincare half-maps. Applications of the systems of ordinary differential equations to modeling turbulent flows are discussed.

Verifier-based three-party authentication schemes using extended chaotic maps for data exchange in telecare medicine information systems.

PubMed

Lee, Tian-Fu

2014-12-01

Telecare medicine information systems provide a communicating platform for accessing remote medical resources through public networks, and help health care workers and medical personnel to rapidly making correct clinical decisions and treatments. An authentication scheme for data exchange in telecare medicine information systems enables legal users in hospitals and medical institutes to establish a secure channel and exchange electronic medical records or electronic health records securely and efficiently. This investigation develops an efficient and secure verified-based three-party authentication scheme by using extended chaotic maps for data exchange in telecare medicine information systems. The proposed scheme does not require server's public keys and avoids time-consuming modular exponential computations and scalar multiplications on elliptic curve used in previous related approaches. Additionally, the proposed scheme is proven secure in the random oracle model, and realizes the lower bounds of messages and rounds in communications. Compared to related verified-based approaches, the proposed scheme not only possesses higher security, but also has lower computational cost and fewer transmissions. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Security analysis of a chaotic map-based authentication scheme for telecare medicine information systems.

PubMed

Yau, Wei-Chuen; Phan, Raphael C-W

2013-12-01

Many authentication schemes have been proposed for telecare medicine information systems (TMIS) to ensure the privacy, integrity, and availability of patient records. These schemes are crucial for TMIS systems because otherwise patients' medical records become susceptible to tampering thus hampering diagnosis or private medical conditions of patients could be disclosed to parties who do not have a right to access such information. Very recently, Hao et al. proposed a chaotic map-based authentication scheme for telecare medicine information systems in a recent issue of Journal of Medical Systems. They claimed that the authentication scheme can withstand various attacks and it is secure to be used in TMIS. In this paper, we show that this authentication scheme is vulnerable to key-compromise impersonation attacks, off-line password guessing attacks upon compromising of a smart card, and parallel session attacks. We also exploit weaknesses in the password change phase of the scheme to mount a denial-of-service attack. Our results show that this scheme cannot be used to provide security in a telecare medicine information system.

Diffusion of chaotic field lines in tokamaks

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh

2006-10-01

An important instability for the destruction of magnetic surfaces in tokamaks due to island overlapping is the tearing modes. Magnetic fields perturbed by tearing modes are given by the sinusoidal form Br=-1rR∑m,nbm^n ( mθ-n ) . The sinusoidal nature of perturbation creates islands structure near resonant surfaces. In this work, we consider two modes, ( m1,n1 )and ( m2,n2 )that interact with each other, leading to two chains of islands, called primary islands. We use a previously derived Hamiltonian map, the ψ-θ map, with and without higher order control terms to study the diffusion of chaotic field lines. We will present and discuss the results of this work, and discuss its implications with regard to magnetic transport barriers for a fixed q-profile and increasing strength of magnetic perturbations. This work is done under the DOE grant number DE-FG02-01ER54624. 1.A. Punjabi et al, Phys. Rev. lett., 69, 3322 (1992). 2. H. Ali, A. Punjabi, and A. Boozer, Int. J. Comp. Num. Ana. Applications 6, 17 (2005).

Memcapacitor model and its application in chaotic oscillator with memristor.

PubMed

Wang, Guangyi; Zang, Shouchi; Wang, Xiaoyuan; Yuan, Fang; Iu, Herbert Ho-Ching

2017-01-01

Memristors and memcapacitors are two new nonlinear elements with memory. In this paper, we present a Hewlett-Packard memristor model and a charge-controlled memcapacitor model and design a new chaotic oscillator based on the two models for exploring the characteristics of memristors and memcapacitors in nonlinear circuits. Furthermore, many basic dynamical behaviors of the oscillator, including equilibrium sets, Lyapunov exponent spectrums, and bifurcations with various circuit parameters, are investigated theoretically and numerically. Our analysis results show that the proposed oscillator possesses complex dynamics such as an infinite number of equilibria, coexistence oscillation, and multi-stability. Finally, a discrete model of the chaotic oscillator is given and the main statistical properties of this oscillator are verified via Digital Signal Processing chip experiments and National Institute of Standards and Technology tests.

Transition from a conservative system to a quasi-dissipative one

NASA Astrophysics Data System (ADS)

Ding, Xiao-Ling; Lu, Yun-Qing; Jiang, Yu-Mei; Chen, He-Sheng; He, Da-Ren

2002-03-01

A quasi-dissipative system can display some dissipative properties and also some conservative properties. Such a system can be realized by a discontinuous and noninvertible two-dimensional area-preserving map. The first example is a model of an electronic relaxation oscillator with over-voltage protection^1. When the system gradually changes from the state without over-voltage protection to the state with protection, it displays a transition from a conservative system to a quasi-dissipative one. Firstly, with a chosen group of parameters, a stochastic web formed by the image set of the discontinuous borderline of the system function becomes chaotic supertransients. The chaotic motion in the web escapes to some elliptic islands. Then, as the over-voltage protection increases, the image set gradually loses the characteristics of a web. More and more it looks like a typical chaotic attractor in a dissipative system. Some other phenomena those happened only in dissipative systems, such as crisis and intermittency, can be also observed in this case. Such a transition can be found also in a kicked rotator. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

Breaking time reversal in a simple smooth chaotic system.

PubMed

Tomsovic, Steven; Ullmo, Denis; Nagano, Tatsuro

2003-06-01

Within random matrix theory, the statistics of the eigensolutions depend fundamentally on the presence (or absence) of time reversal symmetry. Accepting the Bohigas-Giannoni-Schmit conjecture, this statement extends to quantum systems with chaotic classical analogs. For practical reasons, much of the supporting numerical studies of symmetry breaking have been done with billiards or maps, and little with simple, smooth systems. There are two main difficulties in attempting to break time reversal invariance in a continuous time system with a smooth potential. The first is avoiding false time reversal breaking. The second is locating a parameter regime in which the symmetry breaking is strong enough to transform the fluctuation properties fully to the broken symmetry case, and yet remain weak enough so as not to regularize the dynamics sufficiently that the system is no longer chaotic. We give an example of a system of two coupled quartic oscillators whose energy level statistics closely match with those of the Gaussian unitary ensemble, and which possesses only a minor proportion of regular motion in its phase space.

Statistical and dynamical properties of a dissipative kicked rotator

NASA Astrophysics Data System (ADS)

Oliveira, Diego F. M.; Leonel, Edson D.

2014-11-01

Some dynamical and statistical properties for a conservative as well as the dissipative problem of relativistic particles in a waveguide are considered. For the first time, two different types of dissipation namely: (i) due to viscosity and; (ii) due to inelastic collision (upon the kick) are considered individually and acting together. For the first case, and contrary to what is expected for the original Zaslavsky’s relativistic model, we show there is a critical parameter where a transition from local to global chaos occurs. On the other hand, after considering the introduction of dissipation also on the kick, the structure of the phase space changes in the sense that chaotic and periodic attractors appear. We study also the chaotic sea by using scaling arguments and we proposed an analytical argument to reinforce the validity of the scaling exponents obtained numerically. In principle such an approach can be extended to any two-dimensional map. Finally, based on the Lyapunov exponent, we show that the parameter space exhibits infinite families of self-similar shrimp-shape structures, corresponding to periodic attractors, embedded in a large region corresponding to chaotic attractors.

Statistical independence of the initial conditions in chaotic mixing.

PubMed

García de la Cruz, J M; Vassilicos, J C; Rossi, L

2017-11-01

Experimental evidence of the scalar convergence towards a global strange eigenmode independent of the scalar initial condition in chaotic mixing is provided. This convergence, underpinning the independent nature of chaotic mixing in any passive scalar, is presented by scalar fields with different initial conditions casting statistically similar shapes when advected by periodic unsteady flows. As the scalar patterns converge towards a global strange eigenmode, the scalar filaments, locally aligned with the direction of maximum stretching, as described by the Lagrangian stretching theory, stack together in an inhomogeneous pattern at distances smaller than their asymptotic minimum widths. The scalar variance decay becomes then exponential and independent of the scalar diffusivity or initial condition. In this work, mixing is achieved by advecting the scalar using a set of laminar flows with unsteady periodic topology. These flows, that resemble the tendril-whorl map, are obtained by morphing the forcing geometry in an electromagnetic free surface 2D mixing experiment. This forcing generates a velocity field which periodically switches between two concentric hyperbolic and elliptic stagnation points. In agreement with previous literature, the velocity fields obtained produce a chaotic mixer with two regions: a central mixing and an external extensional area. These two regions are interconnected through two pairs of fluid conduits which transfer clean and dyed fluid from the extensional area towards the mixing region and a homogenized mixture from the mixing area towards the extensional region.

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos.

PubMed

Parthasarathy, S; Manikandakumar, K

2007-12-01

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.

On the Chaotic Vibrations of Electrostatically Actuated Arch Micro/Nano Resonators: A Parametric Study

NASA Astrophysics Data System (ADS)

Tajaddodianfar, Farid; Hairi Yazdi, Mohammad Reza; Pishkenari, Hossein Nejat

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler-Bernoulli beam theory, is used for the investigation in this paper. We numerically integrate the obtained equation to study the chaotic vibrations of the proposed system. Moreover, we investigate the effects of various parameters including the arch curvature, the actuation parameters and the quality factor of the resonator, which are effective in the formation of both static and dynamic behaviors of the system. Using appropriate numerical tools, including Poincaré maps, bifurcation diagrams, Fourier spectrum and Lyapunov exponents we scrutinize the effects of various parameters on the formation of chaotic regions in the parametric space of the resonator. Results of this work provide better insight into the problem of nonlinear dynamics of the investigated family of bistable micro/nano resonators, and facilitate the design of arch resonators for applications such as filters.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vaníček, Jiří; Heller, Eric J.

2003-11-01

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it also gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 1070 semiclassical contributions. Remarkably, it also explicitly contains the “building blocks” of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and show that within this approximation, the so-called “diagonal approximation” is automatic and does not require ensemble averaging.

Exact coherent structures and chaotic dynamics in a model of cardiac tissue

DOE Office of Scientific and Technical Information (OSTI.GOV)

Byrne, Greg; Marcotte, Christopher D.; Grigoriev, Roman O., E-mail: roman.grigoriev@physics.gatech.edu

Unstable nonchaotic solutions embedded in the chaotic attractor can provide significant new insight into chaotic dynamics of both low- and high-dimensional systems. In particular, in turbulent fluid flows, such unstable solutions are referred to as exact coherent structures (ECS) and play an important role in both initiating and sustaining turbulence. The nature of ECS and their role in organizing spatiotemporally chaotic dynamics, however, is reasonably well understood only for systems on relatively small spatial domains lacking continuous Euclidean symmetries. Construction of ECS on large domains and in the presence of continuous translational and/or rotational symmetries remains a challenge. This ismore » especially true for models of excitable media which display spiral turbulence and for which the standard approach to computing ECS completely breaks down. This paper uses the Karma model of cardiac tissue to illustrate a potential approach that could allow computing a new class of ECS on large domains of arbitrary shape by decomposing them into a patchwork of solutions on smaller domains, or tiles, which retain Euclidean symmetries locally.« less

Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures

NASA Astrophysics Data System (ADS)

Russell, Francis P.; Düben, Peter D.; Niu, Xinyu; Luk, Wayne; Palmer, T. N.

2017-12-01

Reconfigurable architectures are becoming mainstream: Amazon, Microsoft and IBM are supporting such architectures in their data centres. The computationally intensive nature of atmospheric modelling is an attractive target for hardware acceleration using reconfigurable computing. Performance of hardware designs can be improved through the use of reduced-precision arithmetic, but maintaining appropriate accuracy is essential. We explore reduced-precision optimisation for simulating chaotic systems, targeting atmospheric modelling, in which even minor changes in arithmetic behaviour will cause simulations to diverge quickly. The possibility of equally valid simulations having differing outcomes means that standard techniques for comparing numerical accuracy are inappropriate. We use the Hellinger distance to compare statistical behaviour between reduced-precision CPU implementations to guide reconfigurable designs of a chaotic system, then analyse accuracy, performance and power efficiency of the resulting implementations. Our results show that with only a limited loss in accuracy corresponding to less than 10% uncertainty in input parameters, the throughput and energy efficiency of a single-precision chaotic system implemented on a Xilinx Virtex-6 SX475T Field Programmable Gate Array (FPGA) can be more than doubled.

Regional variations in the stability and diffusion of water-ice in the Martian regolith

NASA Technical Reports Server (NTRS)

Mellon, Michael T.; Jakosky, Bruce M.

1992-01-01

Geologic evidence suggests subsurface water-ice has played an important role in the formation of Martian landforms. Forms of mass-wasting such as debris aprons and flow patterns on valley floors suggest creep deformation of ice-laden soil, while thermokarst and chaotic terrain suggest once extensive deposits of ground ice that were later removed. The global distribution of ice-related morphology was mapped. The mapping showed regional variation, in both latitude and longitude, in the distribution of debris aprons, concentric fill craters, and 'softened' crater profiles.

Numerical computation of orbits and rigorous verification of existence of snapback repellers.

PubMed

Peng, Chen-Chang

2007-03-01

In this paper we show how analysis from numerical computation of orbits can be applied to prove the existence of snapback repellers in discrete dynamical systems. That is, we present a computer-assisted method to prove the existence of a snapback repeller of a specific map. The existence of a snapback repeller of a dynamical system implies that it has chaotic behavior [F. R. Marotto, J. Math. Anal. Appl. 63, 199 (1978)]. The method is applied to the logistic map and the discrete predator-prey system.

Stochastic Ion Heating by the Lower-Hybrid Waves

NASA Technical Reports Server (NTRS)

Khazanov, G.; Tel'nikhin, A.; Krotov, A.

2011-01-01

The resonance lower-hybrid wave-ion interaction is described by a group (differentiable map) of transformations of phase space of the system. All solutions to the map belong to a strange attractor, and chaotic motion of the attractor manifests itself in a number of macroscopic effects, such as the energy spectrum and particle heating. The applicability of the model to the problem of ion heating by waves at the front of collisionless shock as well as ion acceleration by a spectrum of waves is discussed. Keywords: plasma; ion-cyclotron heating; shocks; beat-wave accelerator.

The onset of dynamical instability and chaos in navigation satellite orbits

NASA Astrophysics Data System (ADS)

Rosengren, Aaron Jay; Daquin, Jérôme; Alessi, Elisa Maria; Valsecchi, Giovanni B.; Rossi, Alessandro; Deleflie, Florent

2015-05-01

Orbital resonances are ubiquitous in the Solar System and are harbingers for the onset of dynamical instability and chaos. It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Here we will show that the same underlying physical mechanism, the overlapping of secular resonances, responsible for the eventual destabilization of Mercury and recently proposed to explain the orbital architecture of extrasolar planetary systems (Lithwick Y., Wu Y., 2014, PNAS; Batygin K., Morbidelli A., Holman M.J., 2015, ApJ) is at the heart of the orbital instabilities of seemingly more mundane celestial bodies---the Earth's navigation satellites. We will demonstrate that the occurrence and nature of the secular resonances driving these dynamics depend chiefly on one aspect of the Moon's perturbed motion, the regression of the line of nodes. This talk will present analytical models that accurately reflect the true nature of the resonant interactions, and will show how chaotic diffusion is mediated by the web-like structure of secular resonances. We will also present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. The obtained results have remarkable practical applications for space debris mitigation and for satellite technology, and are both of essential dynamical and theoretical importance, with broad implications for planetary science.

Network structure of multivariate time series.

PubMed

Lacasa, Lucas; Nicosia, Vincenzo; Latora, Vito

2015-10-21

Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multivariate time series, based on the mapping of a multidimensional time series into a multilayer network, which allows to extract information on a high dimensional dynamical system through the analysis of the structure of the associated multiplex network. The method is simple to implement, general, scalable, does not require ad hoc phase space partitioning, and is thus suitable for the analysis of large, heterogeneous and non-stationary time series. We show that simple structural descriptors of the associated multiplex networks allow to extract and quantify nontrivial properties of coupled chaotic maps, including the transition between different dynamical phases and the onset of various types of synchronization. As a concrete example we then study financial time series, showing that a multiplex network analysis can efficiently discriminate crises from periods of financial stability, where standard methods based on time-series symbolization often fail.

Classifying and quantifying basins of attraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sprott, J. C.; Xiong, Anda

2015-08-15

A scheme is proposed to classify the basins for attractors of dynamical systems in arbitrary dimensions. There are four basic classes depending on their size and extent, and each class can be further quantified to facilitate comparisons. The calculation uses a Monte Carlo method and is applied to numerous common dissipative chaotic maps and flows in various dimensions.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.

PubMed

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption

NASA Astrophysics Data System (ADS)

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 21345. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.

Nonlinear solar cycle forecasting: theory and perspectives

NASA Astrophysics Data System (ADS)

Baranovski, A. L.; Clette, F.; Nollau, V.

2008-02-01

In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters - the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

A new version of Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Felea, D.; Beşliu, C.; Jipa, Al.; Grossu, I. V.

2009-11-01

This work presents a new version of a software package for the study of chaotic flows, maps and fractals [1]. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well-known examples are implemented, with the capability of the users inserting their own ODE or iterative equations. New version program summaryProgram title: Chaos v2.0 Catalogue identifier: AEAP_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1275 No. of bytes in distributed program, including test data, etc.: 7135 Distribution format: tar.gz Programming language: Scilab 5.1.1. Scilab 5.1.1 should be installed before running the program. Information about the installation can be found at http://wiki.scilab.org/howto/install/windows. Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 150 Megabytes Classification: 6.2 Catalogue identifier of previous version: AEAP_v1_0 Journal reference of previous version: Comput. Phys. Comm. 178 (2008) 788 Does the new version supersede the previous version?: Yes Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations for the study of chaotic flows. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincare sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Numerical solving of iterative equations for the study of maps and fractals. Reasons for new version: The program has been updated to use the new version 5.1.1 of Scilab with new graphical capabilities [2]. Moreover, new use cases have been added which make the handling of the program easier and more efficient. Summary of revisions: A new use case concerning coupled predator-prey models has been added [3]. Three new use cases concerning fractals (Sierpinsky gasket, Barnsley's Fern and Tree) have been added [3]. The graphical user interface (GUI) of the program has been reconstructed to include the new use cases. The program has been updated to use Scilab 5.1.1 with the new graphical capabilities. Additional comments: The program package contains 12 subprograms. interface.sce - the graphical user interface (GUI) that permits the choice of a routine as follows 1.sci - Lorenz dynamical system 2.sci - Chua dynamical system 3.sci - Rosler dynamical system 4.sci - Henon map 5.sci - Lyapunov exponents for Lorenz dynamical system 6.sci - Lyapunov exponent for the logistic map 7.sci - Shannon entropy for the logistic map 8.sci - Coupled predator-prey model 1f.sci - Sierpinsky gasket 2f.sci - Barnsley's Fern 3f.sci - Barnsley's Tree Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE, Lyapunov exponents calculation and fractals. References: C.C. Bordeianu, C. Besliu, Al. Jipa, D. Felea, I. V. Grossu, Comput. Phys. Comm. 178 (2008) 788. S. Campbell, J.P. Chancelier, R. Nikoukhah, Modeling and Simulation in Scilab/Scicos, Springer, 2006. R.H. Landau, M.J. Paez, C.C. Bordeianu, A Survey of Computational Physics, Introductory Computational Science, Princeton University Press, 2008.

The structure of mode-locking regions of piecewise-linear continuous maps: II. Skew sawtooth maps

NASA Astrophysics Data System (ADS)

Simpson, D. J. W.

2018-05-01

In two-parameter bifurcation diagrams of piecewise-linear continuous maps on , mode-locking regions typically have points of zero width known as shrinking points. Near any shrinking point, but outside the associated mode-locking region, a significant proportion of parameter space can be usefully partitioned into a two-dimensional array of annular sectors. The purpose of this paper is to show that in these sectors the dynamics is well-approximated by a three-parameter family of skew sawtooth circle maps, where the relationship between the skew sawtooth maps and the N-dimensional map is fixed within each sector. The skew sawtooth maps are continuous, degree-one, and piecewise-linear, with two different slopes. They approximate the stable dynamics of the N-dimensional map with an error that goes to zero with the distance from the shrinking point. The results explain the complicated radial pattern of periodic, quasi-periodic, and chaotic dynamics that occurs near shrinking points.

Chaotic dynamics of flexible Euler-Bernoulli beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl; Krysko, A. V., E-mail: anton.krysko@gmail.com; Kutepov, I. E., E-mail: iekutepov@gmail.com

2013-12-15

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions ismore » carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.« less

Ordering process in the diffusively coupled logistic lattice

NASA Astrophysics Data System (ADS)

Conrado, Claudine V.; Bohr, Tomas

1991-08-01

We study the ordering process in a lattice of diffusively coupled logistic maps for increasing lattice size. Within a window of parameters, the system goes into a weakly chaotic state with long range "antiferromagnetic" order. This happens for arbitrary lattice size L and the ordering time behaves as t ~ L2 as we would expect from a picture of diffusing defects.

A new security solution to JPEG using hyper-chaotic system and modified zigzag scan coding

NASA Astrophysics Data System (ADS)

Ji, Xiao-yong; Bai, Sen; Guo, Yu; Guo, Hui

2015-05-01

Though JPEG is an excellent compression standard of images, it does not provide any security performance. Thus, a security solution to JPEG was proposed in Zhang et al. (2014). But there are some flaws in Zhang's scheme and in this paper we propose a new scheme based on discrete hyper-chaotic system and modified zigzag scan coding. By shuffling the identifiers of zigzag scan encoded sequence with hyper-chaotic sequence and accurately encrypting the certain coefficients which have little relationship with the correlation of the plain image in zigzag scan encoded domain, we achieve high compression performance and robust security simultaneously. Meanwhile we present and analyze the flaws in Zhang's scheme through theoretical analysis and experimental verification, and give the comparisons between our scheme and Zhang's. Simulation results verify that our method has better performance in security and efficiency.

Modified Levenberg-Marquardt Method for RÖSSLER Chaotic System Fuzzy Modeling Training

NASA Astrophysics Data System (ADS)

Wang, Yu-Hui; Wu, Qing-Xian; Jiang, Chang-Sheng; Xue, Ya-Li; Fang, Wei

Generally, fuzzy approximation models require some human knowledge and experience. Operator's experience is involved in the mathematics of fuzzy theory as a collection of heuristic rules. The main goal of this paper is to present a new method for identifying unknown nonlinear dynamics such as Rössler system without any human knowledge. Instead of heuristic rules, the presented method uses the input-output data pairs to identify the Rössler chaotic system. The training algorithm is a modified Levenberg-Marquardt (L-M) method, which can adjust the parameters of each linear polynomial and fuzzy membership functions on line, and do not rely on experts' experience excessively. Finally, it is applied to training Rössler chaotic system fuzzy identification. Comparing this method with the standard L-M method, the convergence speed is accelerated. The simulation results demonstrate the effectiveness of the proposed method.

Testing the FLI in the region of the Pallas asteroid family

NASA Astrophysics Data System (ADS)

Todorović, N.; Novaković, B.

2015-08-01

Computation of the fast Lyapunov indicator (FLI) is one of the most efficient numerical ways to characterize dynamical nature of motion and to detect phase-space structures in a large variety of dynamical models. Despite its effectiveness, FLI was mainly used for symplectic maps or simple Hamiltonians, but it has never been used to study dynamics of asteroids to a greater extent. This research shows that FLI could also be successfully applied to real (Solar system) dynamics. For this purpose, we focus on the main belt region where the Pallas asteroid family is located. By using the full Solar system model, different sets of initial conditions and different integration times, we managed not only to visualize a large multiplet of resonances located in the region, but also their structures, chaotic boundaries, stability islands therein and the positions of their mutual interaction. In the end, we have identified some of the most dominant resonances present in the region and established a link between these resonances and chaotic areas visible in our maps. We have illustrated that FLI once again has shown its efficiency to detect dynamical structures in the main belt, e.g. in the Pallas asteroid family, with a surprisingly good clarity.

Chaotic Image Encryption Algorithm Based on Bit Permutation and Dynamic DNA Encoding.

PubMed

Zhang, Xuncai; Han, Feng; Niu, Ying

2017-01-01

With the help of the fact that chaos is sensitive to initial conditions and pseudorandomness, combined with the spatial configurations in the DNA molecule's inherent and unique information processing ability, a novel image encryption algorithm based on bit permutation and dynamic DNA encoding is proposed here. The algorithm first uses Keccak to calculate the hash value for a given DNA sequence as the initial value of a chaotic map; second, it uses a chaotic sequence to scramble the image pixel locations, and the butterfly network is used to implement the bit permutation. Then, the image is coded into a DNA matrix dynamic, and an algebraic operation is performed with the DNA sequence to realize the substitution of the pixels, which further improves the security of the encryption. Finally, the confusion and diffusion properties of the algorithm are further enhanced by the operation of the DNA sequence and the ciphertext feedback. The results of the experiment and security analysis show that the algorithm not only has a large key space and strong sensitivity to the key but can also effectively resist attack operations such as statistical analysis and exhaustive analysis.

Chaotic Image Encryption Algorithm Based on Bit Permutation and Dynamic DNA Encoding

PubMed Central

2017-01-01

With the help of the fact that chaos is sensitive to initial conditions and pseudorandomness, combined with the spatial configurations in the DNA molecule's inherent and unique information processing ability, a novel image encryption algorithm based on bit permutation and dynamic DNA encoding is proposed here. The algorithm first uses Keccak to calculate the hash value for a given DNA sequence as the initial value of a chaotic map; second, it uses a chaotic sequence to scramble the image pixel locations, and the butterfly network is used to implement the bit permutation. Then, the image is coded into a DNA matrix dynamic, and an algebraic operation is performed with the DNA sequence to realize the substitution of the pixels, which further improves the security of the encryption. Finally, the confusion and diffusion properties of the algorithm are further enhanced by the operation of the DNA sequence and the ciphertext feedback. The results of the experiment and security analysis show that the algorithm not only has a large key space and strong sensitivity to the key but can also effectively resist attack operations such as statistical analysis and exhaustive analysis. PMID:28912802

Consistency properties of chaotic systems driven by time-delayed feedback

NASA Astrophysics Data System (ADS)

Jüngling, T.; Soriano, M. C.; Oliver, N.; Porte, X.; Fischer, I.

2018-04-01

Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the delay-driven laser and confirms the general theoretical results.

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ravishankar, A.S. Ghosal, A.

1999-01-01

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper, the authors analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. The authors first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zeromore » or positive, then the robot equations cannot exhibit chaos. The authors show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, they analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator, respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, the authors resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and the authors show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.« less

Onset of chaos in a single-phase power electronic inverter.

PubMed

Avrutin, Viktor; Mosekilde, Erik; Zhusubaliyev, Zhanybai T; Gardini, Laura

2015-04-01

Supported by experiments on a power electronic DC/AC converter, this paper considers an unusual transition from the domain of stable periodic dynamics (corresponding to the desired mode of operation) to chaotic dynamics. The behavior of the converter is studied by means of a 1D stroboscopic map derived from a non-autonomous ordinary differential equation with discontinuous right-hand side. By construction, this stroboscopic map has a high number of border points. It is shown that the onset of chaos occurs stepwise, via irregular cascades of different border collisions, some of which lead to bifurcations while others do not.

A Novel Bit-level Image Encryption Method Based on Chaotic Map and Dynamic Grouping

NASA Astrophysics Data System (ADS)

Zhang, Guo-Ji; Shen, Yan

2012-10-01

In this paper, a novel bit-level image encryption method based on dynamic grouping is proposed. In the proposed method, the plain-image is divided into several groups randomly, then permutation-diffusion process on bit level is carried out. The keystream generated by logistic map is related to the plain-image, which confuses the relationship between the plain-image and the cipher-image. The computer simulation results of statistical analysis, information entropy analysis and sensitivity analysis show that the proposed encryption method is secure and reliable enough to be used for communication application.

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Li-Yan; He, Yi; Liu, Jia

2017-11-01

We investigate a new spatiotemporal dynamics with fractional order differential logistic map and spatial nonlinear coupling. The spatial nonlinear coupling features such as the higher percentage of lattices in chaotic behaviors for most of parameters and none periodic windows in bifurcation diagrams are held, which are more suitable for encryptions than the former adjacent coupled map lattices. Besides, the proposed model has new features such as the wider parameter range and wider range of state amplitude for ergodicity, which contributes a wider range of key space when applied in encryptions. The simulations and theoretical analyses are developed in this paper.

Encryption key distribution via chaos synchronization

NASA Astrophysics Data System (ADS)

Keuninckx, Lars; Soriano, Miguel C.; Fischer, Ingo; Mirasso, Claudio R.; Nguimdo, Romain M.; van der Sande, Guy

2017-02-01

We present a novel encryption scheme, wherein an encryption key is generated by two distant complex nonlinear units, forced into synchronization by a chaotic driver. The concept is sufficiently generic to be implemented on either photonic, optoelectronic or electronic platforms. The method for generating the key bitstream from the chaotic signals is reconfigurable. Although derived from a deterministic process, the obtained bit series fulfill the randomness conditions as defined by the National Institute of Standards test suite. We demonstrate the feasibility of our concept on an electronic delay oscillator circuit and test the robustness against attacks using a state-of-the-art system identification method.

Chaotic hybrid inflation with a gauged B -L

NASA Astrophysics Data System (ADS)

Carpenter, Linda M.; Raby, Stuart

2014-11-01

In this paper we present a novel formulation of chaotic hybrid inflation in supergravity. The model includes a waterfall field which spontaneously breaks a gauged U1 (B- L) at a GUT scale. This allows for the possibility of future model building which includes the standard formulation of baryogenesis via leptogenesis with the waterfall field decaying into right-handed neutrinos. We have not considered the following issues in this short paper, i.e. supersymmetry breaking, dark matter or the gravitino or moduli problems. Our focus is on showing the compatibility of the present model with Planck, WMAP and Bicep2 data.

Photonic generation of polarization-resolved wideband chaos with time-delay concealment in three-cascaded vertical-cavity surface-emitting lasers.

PubMed

Liu, Huijie; Li, Nianqiang; Zhao, Qingchun

2015-05-10

Optical chaos generated by chaotic lasers has been widely used in several important applications, such as chaos-based communications and high-speed random-number generators. However, these applications are susceptible to degradation by the presence of time-delay (TD) signature identified from the chaotic output. Here we propose to achieve the concealment of TD signature, along with the enhancement of chaos bandwidth, in three-cascaded vertical-cavity surface-emitting lasers (VCSELs). The cascaded system is composed of an external-cavity master VCSEL, a solitary intermediate VCSEL, and a solitary slave VCSEL. Through mapping the evolutions of TD signature and chaos bandwidth in the parameter space of the injection strength and frequency detuning, photonic generation of polarization-resolved wideband chaos with TD concealment is numerically demonstrated for wide regions of the injection parameters.

Universality and chaoticity in ultracold K+KRb chemical reactions

DOE PAGES

Croft, J. F. E.; Makrides, C.; Li, M.; ...

2017-07-19

A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K 2Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysismore » of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.« less

Trace identities and their semiclassical implications

NASA Astrophysics Data System (ADS)

Smilansky, Uzy

2000-03-01

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically integrable maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions. The same technique is not applicable for chaotic maps, and the compatibility of the semiclassical theory in this case remains unsettled. However, the trace identities are applied to maps which appear naturally in the theory of quantum graphs, revealing some features of the periodic orbit theory for these paradigms of quantum chaos.

Visibility graphs and symbolic dynamics

NASA Astrophysics Data System (ADS)

Lacasa, Lucas; Just, Wolfram

2018-07-01

Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology nontrivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility graphs generated by the one-parameter logistic map, for a range of values of the parameter for which the map shows chaotic behaviour. Numerically, we observe that in the chaotic region the block entropies of these sequences systematically converge to the Lyapunov exponent of the time series. Hence, Pesin's identity suggests that these block entropies are converging to the Kolmogorov-Sinai entropy of the physical measure, which ultimately suggests that the algorithm is implicitly and adaptively constructing phase space partitions which might have the generating property. To give analytical insight, we explore the relation k(x) , x ∈ [ 0 , 1 ] that, for a given datum with value x, assigns in graph space a node with degree k. In the case of the out-degree sequence, such relation is indeed a piece-wise constant function. By making use of explicit methods and tools from symbolic dynamics we are able to analytically show that the algorithm indeed performs an effective partition of the phase space and that such partition is naturally expressed as a countable union of subintervals, where the endpoints of each subinterval are related to the fixed point structure of the iterates of the map and the subinterval enumeration is associated with particular ordering structures that we called motifs.

New Secure E-mail System Based on Bio-Chaos Key Generation and Modified AES Algorithm

NASA Astrophysics Data System (ADS)

Hoomod, Haider K.; Radi, A. M.

2018-05-01

The E-mail messages exchanged between sender’s Mailbox and recipient’s Mailbox over the open systems and insecure Networks. These messages may be vulnerable to eavesdropping and itself poses a real threat to the privacy and data integrity from unauthorized persons. The E-mail Security includes the following properties (Confidentiality, Authentication, Message integrity). We need a safe encryption algorithm to encrypt Email messages such as the algorithm Advanced Encryption Standard (AES) or Data Encryption Standard DES, as well as biometric recognition and chaotic system. The proposed E-mail system security uses modified AES algorithm and uses secret key-bio-chaos that consist of biometric (Fingerprint) and chaotic system (Lu and Lorenz). This modification makes the proposed system more sensitive and random. The execution time for both encryption and decryption of the proposed system is much less from original AES, in addition to being compatible with all Mail Servers.

Chaotic operation and chaos control of travelling wave ultrasonic motor.

PubMed

Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

2013-08-01

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

Chaos and crises in a model for cooperative hunting: a symbolic dynamics approach.

PubMed

Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2009-12-01

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K,C(0)) and (K,sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K(c) decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Hybrid information privacy system: integration of chaotic neural network and RSA coding

NASA Astrophysics Data System (ADS)

Hsu, Ming-Kai; Willey, Jeff; Lee, Ting N.; Szu, Harold H.

2005-03-01

Electronic mails are adopted worldwide; most are easily hacked by hackers. In this paper, we purposed a free, fast and convenient hybrid privacy system to protect email communication. The privacy system is implemented by combining private security RSA algorithm with specific chaos neural network encryption process. The receiver can decrypt received email as long as it can reproduce the specified chaos neural network series, so called spatial-temporal keys. The chaotic typing and initial seed value of chaos neural network series, encrypted by the RSA algorithm, can reproduce spatial-temporal keys. The encrypted chaotic typing and initial seed value are hidden in watermark mixed nonlinearly with message media, wrapped with convolution error correction codes for wireless 3rd generation cellular phones. The message media can be an arbitrary image. The pattern noise has to be considered during transmission and it could affect/change the spatial-temporal keys. Since any change/modification on chaotic typing or initial seed value of chaos neural network series is not acceptable, the RSA codec system must be robust and fault-tolerant via wireless channel. The robust and fault-tolerant properties of chaos neural networks (CNN) were proved by a field theory of Associative Memory by Szu in 1997. The 1-D chaos generating nodes from the logistic map having arbitrarily negative slope a = p/q generating the N-shaped sigmoid was given first by Szu in 1992. In this paper, we simulated the robust and fault-tolerance properties of CNN under additive noise and pattern noise. We also implement a private version of RSA coding and chaos encryption process on messages.

Ergodic theory and experimental visualization of chaos in 3D flows

NASA Astrophysics Data System (ADS)

Sotiropoulos, Fotis; Mezic, Igor

2000-11-01

In his motivation for the ergodic hypothesis Gibbs invoked an analogy with fluid mixing: “…Yet no fact is more familiar to us than that stirring tends to bring a liquid to a state of uniform mixture, or uniform densities of its components…”. Although proof of the ergodic hypothesis is possible only for the simplest of systems using methods from ergodic theory, the use of the hypothesis has led to many accurate predictions in statistical mechanics. The problem of fluid mixing, however, turned out to be considerably more complicated than Gibbs envisioned. Chaotic advection can indeed lead to efficient mixing even in non-turbulent flows, but many non-mixed islands are known to persist within well-mixed regions. In numerical studies, Poincaré maps can be used to reveal the structure of such islands but their visualization in the laboratory requires laborious experimental procedures and is possible only for certain types of flows. Here we propose the first non-intrusive, simple to implement, and generally applicable technique for constructing experimental Poincaré maps and apply it to a steady, 3D, vortex breakdown bubble. We employ standard laser-induced fluorescence (LIF) and construct Poincaré maps by time averaging a sufficiently long sequence of instantaneous LIF images. We also show that ergodic theory methods provide a rigorous theoretical justification for this approach whose main objective is to reveal the non-ergodic regions of the flow.

Encryption key distribution via chaos synchronization

PubMed Central

Keuninckx, Lars; Soriano, Miguel C.; Fischer, Ingo; Mirasso, Claudio R.; Nguimdo, Romain M.; Van der Sande, Guy

2017-01-01

We present a novel encryption scheme, wherein an encryption key is generated by two distant complex nonlinear units, forced into synchronization by a chaotic driver. The concept is sufficiently generic to be implemented on either photonic, optoelectronic or electronic platforms. The method for generating the key bitstream from the chaotic signals is reconfigurable. Although derived from a deterministic process, the obtained bit series fulfill the randomness conditions as defined by the National Institute of Standards test suite. We demonstrate the feasibility of our concept on an electronic delay oscillator circuit and test the robustness against attacks using a state-of-the-art system identification method. PMID:28233876

A Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

On the design of henon and logistic map-based random number generator

NASA Astrophysics Data System (ADS)

Magfirawaty; Suryadi, M. T.; Ramli, Kalamullah

2017-10-01

The key sequence is one of the main elements in the cryptosystem. True Random Number Generators (TRNG) method is one of the approaches to generating the key sequence. The randomness source of the TRNG divided into three main groups, i.e. electrical noise based, jitter based and chaos based. The chaos based utilizes a non-linear dynamic system (continuous time or discrete time) as an entropy source. In this study, a new design of TRNG based on discrete time chaotic system is proposed, which is then simulated in LabVIEW. The principle of the design consists of combining 2D and 1D chaotic systems. A mathematical model is implemented for numerical simulations. We used comparator process as a harvester method to obtain the series of random bits. Without any post processing, the proposed design generated random bit sequence with high entropy value and passed all NIST 800.22 statistical tests.

Polarization-resolved time-delay signatures of chaos induced by FBG-feedback in VCSEL.

PubMed

Zhong, Zhu-Qiang; Li, Song-Sui; Chan, Sze-Chun; Xia, Guang-Qiong; Wu, Zheng-Mao

2015-06-15

Polarization-resolved chaotic emission intensities from a vertical-cavity surface-emitting laser (VCSEL) subject to feedback from a fiber Bragg grating (FBG) are numerically investigated. Time-delay (TD) signatures of the feedback are examined through various means including self-correlations of intensity time-series of individual polarizations, cross-correlation of intensities time-series between both polarizations, and permutation entropies calculated for the individual polarizations. The results show that the TD signatures can be clearly suppressed by selecting suitable operation parameters such as the feedback strength, FBG bandwidth, and Bragg frequency. Also, in the operational parameter space, numerical maps of TD signatures and effective bandwidths are obtained, which show regions of chaotic signals with both wide bandwidths and weak TD signatures. Finally, by comparing with a VCSEL subject to feedback from a mirror, the VCSEL subject to feedback from the FBG generally shows better concealment of the TD signatures with similar, or even wider, bandwidths.

Complex dynamics of a delayed discrete neural network of two nonidentical neurons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Yuanlong; Huang, Tingwen; Huang, Yu, E-mail: stshyu@mail.sysu.edu.cn

2014-03-15

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zoumore » [J. Nonlinear Sci. 15, 291–303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415–432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869–1878 (2013)]. We also give some numeric simulations to verify our theoretical results.« less

Complex dynamics of a delayed discrete neural network of two nonidentical neurons.

PubMed

Chen, Yuanlong; Huang, Tingwen; Huang, Yu

2014-03-01

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291-303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415-432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869-1878 (2013)]. We also give some numeric simulations to verify our theoretical results.

Global dynamics and diffusion in triaxial galactic models

NASA Astrophysics Data System (ADS)

Papaphilippou, Y.

We apply the Frequency Map Analysis method to the 3--dimensional logarithmic galactic potential in order to clarify the dynamical behaviour of triaxial power--law galactic models. All the fine dynamical details are displayed in the complete frequency map, a direct representation of the system's Arnol'd web. The influence of resonant lines and the extent of the chaotic zones are directly associated with the physical space of the system. Some new results related with the diffusion of galactic orbits are also discussed. This approach reveals many unknown dynamical features of triaxial galactic potentials and provides strong indications that chaos should be an innate characteristic of triaxial configurations.

Power law asymptotics in the creation of strange attractors in the quasi-periodically forced quadratic family

NASA Astrophysics Data System (ADS)

Ohlson Timoudas, Thomas

2017-12-01

Let Φ be a quasi-periodically forced quadratic map, where the rotation constant ω is a Diophantine irrational. A strange non-chaotic attractor (SNA) is an invariant (under Φ) attracting graph of a nowhere continuous measurable function ψ from the circle {T} to [0, 1] . This paper investigates how a smooth attractor degenerates into a strange one, as a parameter \

Design of fuzzy cognitive maps using neural networks for predicting chaotic time series.

PubMed

Song, H J; Miao, C Y; Shen, Z Q; Roel, W; Maja, D H; Francky, C

2010-12-01

As a powerful paradigm for knowledge representation and a simulation mechanism applicable to numerous research and application fields, Fuzzy Cognitive Maps (FCMs) have attracted a great deal of attention from various research communities. However, the traditional FCMs do not provide efficient methods to determine the states of the investigated system and to quantify causalities which are the very foundation of the FCM theory. Therefore in many cases, constructing FCMs for complex causal systems greatly depends on expert knowledge. The manually developed models have a substantial shortcoming due to model subjectivity and difficulties with accessing its reliability. In this paper, we propose a fuzzy neural network to enhance the learning ability of FCMs so that the automatic determination of membership functions and quantification of causalities can be incorporated with the inference mechanism of conventional FCMs. In this manner, FCM models of the investigated systems can be automatically constructed from data, and therefore are independent of the experts. Furthermore, we employ mutual subsethood to define and describe the causalities in FCMs. It provides more explicit interpretation for causalities in FCMs and makes the inference process easier to understand. To validate the performance, the proposed approach is tested in predicting chaotic time series. The simulation studies show the effectiveness of the proposed approach. Copyright © 2010 Elsevier Ltd. All rights reserved.

Chaotic dynamics and diffusion in a piecewise linear equation

NASA Astrophysics Data System (ADS)

Shahrear, Pabel; Glass, Leon; Edwards, Rod

2015-03-01

Genetic interactions are often modeled by logical networks in which time is discrete and all gene activity states update simultaneously. However, there is no synchronizing clock in organisms. An alternative model assumes that the logical network is preserved and plays a key role in driving the dynamics in piecewise nonlinear differential equations. We examine dynamics in a particular 4-dimensional equation of this class. In the equation, two of the variables form a negative feedback loop that drives a second negative feedback loop. By modifying the original equations by eliminating exponential decay, we generate a modified system that is amenable to detailed analysis. In the modified system, we can determine in detail the Poincaré (return) map on a cross section to the flow. By analyzing the eigenvalues of the map for the different trajectories, we are able to show that except for a set of measure 0, the flow must necessarily have an eigenvalue greater than 1 and hence there is sensitive dependence on initial conditions. Further, there is an irregular oscillation whose amplitude is described by a diffusive process that is well-modeled by the Irwin-Hall distribution. There is a large class of other piecewise-linear networks that might be analyzed using similar methods. The analysis gives insight into possible origins of chaotic dynamics in periodically forced dynamical systems.

Analysis of chaotic saddles in a nonlinear vibro-impact system

NASA Astrophysics Data System (ADS)

Feng, Jinqian

2017-07-01

In this paper, a computational investigation of chaotic saddles in a nonlinear vibro-impact system is presented. For a classical Duffing vibro-impact oscillator, we employ the bisection procedure and an improved stagger-and-step method to present evidence of visual chaotic saddles on the fractal basin boundary and in the internal basin, respectively. The results show that the period saddles play an important role in the evolution of chaotic saddle. The dynamics mechanics of three types of bifurcation such as saddle-node bifurcation, chaotic saddle crisis bifurcation and interior chaotic crisis bifurcation are discussed. The results reveal that the period saddle created at saddle-node bifurcation is responsible for the switch of the internal chaotic saddle to the boundary chaotic saddle. At chaotic saddle crisis bifurcation, a large chaotic saddle can divide into two different chaotic saddle connected by a period saddle. The intersection points between stable and unstable manifolds of this period saddle supply access for chaotic orbits from one chaotic saddle to another and eventually induce the coupling of these two chaotic saddle. Interior chaotic crisis bifurcation is associated with the intersection of stable and unstable manifolds of the period saddle connecting two chaotic invariant sets. In addition, the gaps in chaotic saddle is responsible for the fractal structure.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity

NASA Astrophysics Data System (ADS)

Minati, Ludovico; Frasca, Mattia; OświÈ©cimka, Paweł; Faes, Luca; DroŻdŻ, Stanisław

2017-07-01

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

Atypical transistor-based chaotic oscillators: Design, realization, and diversity.

PubMed

Minati, Ludovico; Frasca, Mattia; Oświȩcimka, Paweł; Faes, Luca; Drożdż, Stanisław

2017-07-01

In this paper, we show that novel autonomous chaotic oscillators based on one or two bipolar junction transistors and a limited number of passive components can be obtained via random search with suitable heuristics. Chaos is a pervasive occurrence in these circuits, particularly after manual adjustment of a variable resistor placed in series with the supply voltage source. Following this approach, 49 unique circuits generating chaotic signals when physically realized were designed, representing the largest collection of circuits of this kind to date. These circuits are atypical as they do not trivially map onto known topologies or variations thereof. They feature diverse spectra and predominantly anti-persistent monofractal dynamics. Notably, we recurrently found a circuit comprising one resistor, one transistor, two inductors, and one capacitor, which generates a range of attractors depending on the parameter values. We also found a circuit yielding an irregular quantized spike-train resembling some aspects of neural discharge and another one generating a double-scroll attractor, which represent the smallest known transistor-based embodiments of these behaviors. Through three representative examples, we additionally show that diffusive coupling of heterogeneous oscillators of this kind may give rise to complex entrainment, such as lag synchronization with directed information transfer and generalized synchronization. The replicability and reproducibility of the experimental findings are good.

Dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization

NASA Astrophysics Data System (ADS)

Li, Li

2018-03-01

In order to extract target from complex background more quickly and accurately, and to further improve the detection effect of defects, a method of dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization was proposed. Firstly, the method of single-threshold selection based on Arimoto entropy was extended to dual-threshold selection in order to separate the target from the background more accurately. Then intermediate variables in formulae of Arimoto entropy dual-threshold selection was calculated by recursion to eliminate redundant computation effectively and to reduce the amount of calculation. Finally, the local search phase of artificial bee colony algorithm was improved by chaotic sequence based on tent mapping. The fast search for two optimal thresholds was achieved using the improved bee colony optimization algorithm, thus the search could be accelerated obviously. A large number of experimental results show that, compared with the existing segmentation methods such as multi-threshold segmentation method using maximum Shannon entropy, two-dimensional Shannon entropy segmentation method, two-dimensional Tsallis gray entropy segmentation method and multi-threshold segmentation method using reciprocal gray entropy, the proposed method can segment target more quickly and accurately with superior segmentation effect. It proves to be an instant and effective method for image segmentation.

Quantifying chaos for ecological stoichiometry.

PubMed

Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2010-09-01

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

Universality and chaotic dynamics in reactive scattering of ultracold KRb molecules with K atoms

NASA Astrophysics Data System (ADS)

Li, Ming; Makrides, Constantinos; Petrov, Alexander; Kotochigova, Svetlana; Croft, James F. E.; Balakrishnan, Naduvalath; Kendrick, Brian K.

2017-04-01

We study the benchmark reaction between the most-celebrated ultracold polar molecule, KRb, with an ultracold K atom. For the first time we map out an accurate ab initio ground potential energy surface of the K2Rb complex in full dimensionality and performed a numerically exact quantum-mechanical calculation of reaction dynamics based on coupled-channels approach in hyperspherical coordinates. An analysis of the adiabatic hyperspherical potentials reveals a chaotic distribution for the short-range complex that plays a key role in governing the reaction outcome. The equivalent distribution for a lighter collisional system with a smaller density of states (here the Li2Yb trimer) only shows random behavior. We find an extreme sensitivity of our chaotic system to a small perturbation associated with the weak non-additive three-body potential contribution that does not affect the total reaction rate coefficient but leads to a significant change in the rotational distribution in the product molecule. In both cases the distribution of these rates is random or Poissonian. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and PHY-1619788 (S.K.), ARO MURI Grant No. W911NF-12-1-0476 (N.B. & S.K.), and DOE LDRD Grant No. 20170221ER (B.K.).

A novel high-resolution chaotic lidar with optical injection to chaotic laser diode

NASA Astrophysics Data System (ADS)

Wang, Yun-cai; Wang, An-bang

2008-03-01

A novel chaotic lidar with high resolution is proposed and studied theoretically. In chaotic lidar system, the chaotic laser emitted from chaotic laser diode is split into two beams: the probe and the reference light. The ranging is achieved by correlating the reference waveform with the delayed probe waveform backscattered from the target. In chaotic lidar systems presented previously, the chaotic signal source is laser diode with optical feedback or with optical injection by another one. The ranging resolution is limited by the bandwidth of chaotic laser which determined by the configuration of chaotic signal source. We proposed a novel chaotic lidar which ranging resolution is enhanced significantly by external optical injected chaotic laser diode. With the bandwidth-enhanced chaotic laser, the range resolution of the chaotic lidar system with optical injection is roughly two times compared with that of without optical injection. The resolution increases with injection strength increasing in a certain frequency detuning range.

New type of chaos synchronization in discrete-time systems: the F-M synchronization

NASA Astrophysics Data System (ADS)

Ouannas, Adel; Grassi, Giuseppe; Karouma, Abdulrahman; Ziar, Toufik; Wang, Xiong; Pham, Viet-Thanh

2018-04-01

In this paper, a new type of synchronization for chaotic (hyperchaotic) maps with different dimensions is proposed. The novel scheme is called F - M synchronization, since it combines the inverse generalized synchronization (based on a functional relationship F) with the matrix projective synchronization (based on a matrix M). In particular, the proposed approach enables F - M synchronization with index d to be achieved between n-dimensional drive system map and m-dimensional response system map, where the synchronization index d corresponds to the dimension of the synchronization error. The technique, which exploits nonlinear controllers and Lyapunov stability theory, proves to be effective in achieving the F - M synchronization not only when the synchronization index d equals n or m, but even if the synchronization index d is larger than the map dimensions n and m. Finally, simulation results are reported, with the aim to illustrate the capabilities of the novel scheme proposed herein.

Simulations of submonolayer Xe on Pt(111): The case for a chaotic low temperature phase

NASA Astrophysics Data System (ADS)

Novaco, Anthony D.; Bavaresco, Jessica

2018-04-01

Molecular dynamics simulations are reported for the structural and thermodynamic properties of submonolayer xenon adsorbed on the (111) surface of platinum for temperatures up to the (apparently incipient) triple point and beyond. While the motion of the atoms in the surface plane is treated with a standard two-dimensional molecular dynamics simulation, the model takes into consideration the thermal excitation of quantum states associated with surface-normal dynamics in an attempt to describe the apparent smoothing of the corrugation with increasing temperature. We examine the importance of this thermal smoothing to the relative stability of several observed and proposed low-temperature structures. Structure factor calculations are compared to experimental results in an attempt to determine the low temperature structure of this system. These calculations provide strong evidence that, at very low temperatures, the domain wall structure of a xenon monolayer adsorbed on a Pt(111) substrate possesses a chaotic-like nature, exhibiting long-lived meta-stable states with pinned domain walls, these walls having narrow widths and irregular shapes. This result is contrary to the standard wisdom regarding this system, namely, that the very low temperature phase of this system is a striped incommensurate phase. We present the case for further experimental investigation of this and similar systems as possible examples of chaotic low temperature phases in two dimensions.

Periodic p-adic Gibbs Measures of q-State Potts Model on Cayley Trees I: The Chaos Implies the Vastness of the Set of p-Adic Gibbs Measures

NASA Astrophysics Data System (ADS)

Ahmad, Mohd Ali Khameini; Liao, Lingmin; Saburov, Mansoor

2018-06-01

We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts-Bethe mapping over Q_p for the prime numbers p≡1 (mod 3). In fact, for 0< |θ -1|_p< |q|_p^2 < 1 where θ =\\exp _p(J) and J is a coupling constant, there exists a subsystem that is isometrically conjugate to the full shift on three symbols. Meanwhile, for 0< |q|_p^2 ≤ |θ -1|_p< |q|_p < 1, there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r ≥ 4. However, these subshifts on r symbols are all topologically conjugate to the full shift on three symbols. The p-adic Gibbs measures of the same model for the prime numbers p=2,3 and the corresponding Potts-Bethe mapping are also discussed. On the other hand, for 0< |θ -1|_p< |q|_p < 1, we remark that the Potts-Bethe mapping is not chaotic when p=3 and p≡ 2 (mod 3) and we could not conclude the vastness of the set of the periodic p-adic Gibbs measures. In a forthcoming paper with the same title, we will treat the case 0< |q|_p ≤ |θ -1|_p < 1 for all prime numbers p.

Mechanisms of chaos in billiards: dispersing, defocusing and nothing else

NASA Astrophysics Data System (ADS)

Bunimovich, Leonid A.

2018-02-01

We explain and justify that the only mechanisms of chaotic dynamics for billiards are dispersing and defocusing. We also introduce boomerang billiards which dynamics demonstrate that two rather broadly accepted views about some features of nonlinear dynamics are actually wrong. Namely correlations in billiards having focusing components of the boundary can decay exponentially, and continuous time correlations for a billiard flow may decay faster than discrete time correlations for a billiard map.

Virtual Libraries: Interactive Support Software and an Application in Chaotic Models.

ERIC Educational Resources Information Center

Katsirikou, Anthi; Skiadas, Christos; Apostolou, Apostolos; Rompogiannakis, Giannis

This paper begins with a discussion of the characteristics and the singularity of chaotic systems, including dynamic systems theory, chaotic orbit, fractals, chaotic attractors, and characteristics of chaotic systems. The second section addresses the digital libraries (DL) concept and the appropriateness of chaotic models, including definition and…

Urey Prize Lecture - Chaotic dynamics in the solar system

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

Case study: Mapping tsunami hazards associated with debris flow into a reservoir

USGS Publications Warehouse

Walder, J.S.; Watts, P.; Waythomas, C.F.

2006-01-01

Debris-flow generated impulse waves (tsunamis) pose hazards in lakes, especially those used for hydropower or recreation. We describe a method for assessing tsunami-related hazards for the case in which inundation by coherent water waves, rather than chaotic splashing, is of primary concern. The method involves an experimentally based initial condition (tsunami source) and a Boussinesq model for tsunami propagation and inundation. Model results are used to create hazard maps that offer guidance for emergency planners and responders. An example application explores tsunami hazards associated with potential debris flows entering Baker Lake, a reservoir on the flanks of the Mount Baker volcano in the northwestern United States. ?? 2006 ASCE.

Estimation of chaotic coupled map lattices using symbolic vector dynamics

NASA Astrophysics Data System (ADS)

Wang, Kai; Pei, Wenjiang; Cheung, Yiu-ming; Shen, Yi; He, Zhenya

2010-01-01

In [K. Wang, W.J. Pei, Z.Y. He, Y.M. Cheung, Phys. Lett. A 367 (2007) 316], an original symbolic vector dynamics based method has been proposed for initial condition estimation in additive white Gaussian noisy environment. The estimation precision of this estimation method is determined by symbolic errors of the symbolic vector sequence gotten by symbolizing the received signal. This Letter further develops the symbolic vector dynamical estimation method. We correct symbolic errors with backward vector and the estimated values by using different symbols, and thus the estimation precision can be improved. Both theoretical and experimental results show that this algorithm enables us to recover initial condition of coupled map lattice exactly in both noisy and noise free cases. Therefore, we provide novel analytical techniques for understanding turbulences in coupled map lattice.

On the chaotic diffusion in multidimensional Hamiltonian systems

NASA Astrophysics Data System (ADS)

Cincotta, P. M.; Giordano, C. M.; Martí, J. G.; Beaugé, C.

2018-01-01

We present numerical evidence that diffusion in the herein studied multidimensional near-integrable Hamiltonian systems departs from a normal process, at least for realistic timescales. Therefore, the derivation of a diffusion coefficient from a linear fit on the variance evolution of the unperturbed integrals fails. We review some topics on diffusion in the Arnold Hamiltonian and yield numerical and theoretical arguments to show that in the examples we considered, a standard coefficient would not provide a good estimation of the speed of diffusion. However, numerical experiments concerning diffusion would provide reliable information about the stability of the motion within chaotic regions of the phase space. In this direction, we present an extension of previous results concerning the dynamical structure of the Laplace resonance in Gliese-876 planetary system considering variations of the orbital parameters accordingly to the error introduced by the radial velocity determination. We found that a slight variation of the eccentricity of planet c would destabilize the inner region of the resonance that, though chaotic, shows stable when adopting the best fit values for the parameters.

Brain-Inspired Photonic Signal Processor for Generating Periodic Patterns and Emulating Chaotic Systems

NASA Astrophysics Data System (ADS)

Antonik, Piotr; Haelterman, Marc; Massar, Serge

2017-05-01

Reservoir computing is a bioinspired computing paradigm for processing time-dependent signals. Its hardware implementations have received much attention because of their simplicity and remarkable performance on a series of benchmark tasks. In previous experiments, the output was uncoupled from the system and, in most cases, simply computed off-line on a postprocessing computer. However, numerical investigations have shown that feeding the output back into the reservoir opens the possibility of long-horizon time-series forecasting. Here, we present a photonic reservoir computer with output feedback, and we demonstrate its capacity to generate periodic time series and to emulate chaotic systems. We study in detail the effect of experimental noise on system performance. In the case of chaotic systems, we introduce several metrics, based on standard signal-processing techniques, to evaluate the quality of the emulation. Our work significantly enlarges the range of tasks that can be solved by hardware reservoir computers and, therefore, the range of applications they could potentially tackle. It also raises interesting questions in nonlinear dynamics and chaos theory.

Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes

NASA Astrophysics Data System (ADS)

Zhang, W.; Liu, T.; Xi, A.; Wang, Y. N.

2018-06-01

This paper is focused on the resonant responses and chaotic dynamics of a composite laminated circular cylindrical shell with radially pre-stretched membranes at both ends and clamped along a generatrix. Based on the two-degree-of-freedom non-autonomous nonlinear equations of this system, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equation. The resonant case considered here is the primary parametric resonance-1/2 subharmonic resonance and 1:1 internal resonance. Corresponding to several selected parameters, the frequency-response curves are obtained. From the numerical results, we find that the hardening-spring-type behaviors and jump phenomena are exhibited. The jump phenomena also occur in the amplitude curves of the temperature parameter excitation. Moreover, it is found that the temperature parameter excitation, the coupling degree of two order modes and the detuning parameters can effect the nonlinear oscillations of this system. The periodic and chaotic motions of the composite laminated circular cylindrical shell clamped along a generatrix are demonstrated by the bifurcation diagrams, the maximum Lyapunov exponents, the phase portraits, the waveforms, the power spectrums and the Poincaré map. The temperature parameter excitation shows that the Pomeau-Manneville type intermittent chaos occur under the certain initial conditions. It is also found that there exist the twin phenomena between the Pomeau-Manneville type intermittent chaos and the period-doubling bifurcation.

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms.

PubMed

Asgharnia, Amirhossein; Shahnazi, Reza; Jamali, Ali

2018-05-11

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Stability analysis of an implicitly defined labor market model

NASA Astrophysics Data System (ADS)

Mendes, Diana A.; Mendes, Vivaldo M.

2008-06-01

Until very recently, the pervasive existence of models exhibiting well-defined backward dynamics but ill-defined forward dynamics in economics and finance has apparently posed no serious obstacles to the analysis of their dynamics and stability, despite the problems that may arise from possible erroneous conclusions regarding theoretical considerations and policy prescriptions from such models. A large number of papers have dealt with this problem in the past by assuming the existence of symmetry between forward and backward dynamics, even in the case when the map cannot be invertible either forward or backwards. However, this procedure has been seriously questioned over the last few years in a series of papers dealing with implicit difference equations and inverse limit spaces. This paper explores the search and matching labor market model developed by Bhattacharya and Bunzel [J. Bhattacharya, H. Bunzel, Chaotic Planning Solution in the Textbook Model of Equilibrium Labor Market Search and Matching, Mimeo, Iowa State University, 2002; J. Bhattacharya, H. Bunzel, Economics Bulletin 5 (19) (2003) 1-10], with the following objectives in mind: (i) to show that chaotic dynamics may still be present in the model for acceptable parameter values, (ii) to clarify some open questions related with the admissible dynamics in the forward looking setting, by providing a rigorous proof of the existence of cyclic and chaotic dynamics through the application of tools from symbolic dynamics and inverse limit theory.

A New Color Image Encryption Scheme Using CML and a Fractional-Order Chaotic System

PubMed Central

Wu, Xiangjun; Li, Yang; Kurths, Jürgen

2015-01-01

The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML) and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks. PMID:25826602

Privacy Protection for Telecare Medicine Information Systems Using a Chaotic Map-Based Three-Factor Authenticated Key Agreement Scheme.

PubMed

Zhang, Liping; Zhu, Shaohui; Tang, Shanyu

2017-03-01

Telecare medicine information systems (TMIS) provide flexible and convenient e-health care. However, the medical records transmitted in TMIS are exposed to unsecured public networks, so TMIS are more vulnerable to various types of security threats and attacks. To provide privacy protection for TMIS, a secure and efficient authenticated key agreement scheme is urgently needed to protect the sensitive medical data. Recently, Mishra et al. proposed a biometrics-based authenticated key agreement scheme for TMIS by using hash function and nonce, they claimed that their scheme could eliminate the security weaknesses of Yan et al.'s scheme and provide dynamic identity protection and user anonymity. In this paper, however, we demonstrate that Mishra et al.'s scheme suffers from replay attacks, man-in-the-middle attacks and fails to provide perfect forward secrecy. To overcome the weaknesses of Mishra et al.'s scheme, we then propose a three-factor authenticated key agreement scheme to enable the patient to enjoy the remote healthcare services via TMIS with privacy protection. The chaotic map-based cryptography is employed in the proposed scheme to achieve a delicate balance of security and performance. Security analysis demonstrates that the proposed scheme resists various attacks and provides several attractive security properties. Performance evaluation shows that the proposed scheme increases efficiency in comparison with other related schemes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiuping, E-mail: yangxiuping-1990@163.com; Min, Lequan, E-mail: minlequan@sina.com; Wang, Xue, E-mail: wangxue-20130818@163.com

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% keymore » streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2{sup 1345}. As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.« less

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Breaking chaotic secure communication using a spectrogram

NASA Astrophysics Data System (ADS)

Yang, Tao; Yang, Lin-Bao; Yang, Chun-Mei

1998-10-01

We present the results of breaking a kind of chaotic secure communication system called chaotic switching scheme, also known as chaotic shift keying, in which a binary message signal is scrambled by two chaotic attractors. The spectrogram which can reveal the energy evolving process in the spectral-temporal space is used to distinguish the two different chaotic attractors, which are qualitatively and statistically similar in phase space. Then mathematical morphological filters are used to decode the binary message signal without the knowledge of the binary message signal and the transmitter. The computer experimental results are provided to show how our method works when both the chaotic and hyper-chaotic transmitter are used.

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

PubMed Central

Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

2017-01-01

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

A novel chaotic image encryption scheme using DNA sequence operations

NASA Astrophysics Data System (ADS)

Wang, Xing-Yuan; Zhang, Ying-Qian; Bao, Xue-Mei

2015-10-01

In this paper, we propose a novel image encryption scheme based on DNA (Deoxyribonucleic acid) sequence operations and chaotic system. Firstly, we perform bitwise exclusive OR operation on the pixels of the plain image using the pseudorandom sequences produced by the spatiotemporal chaos system, i.e., CML (coupled map lattice). Secondly, a DNA matrix is obtained by encoding the confused image using a kind of DNA encoding rule. Then we generate the new initial conditions of the CML according to this DNA matrix and the previous initial conditions, which can make the encryption result closely depend on every pixel of the plain image. Thirdly, the rows and columns of the DNA matrix are permuted. Then, the permuted DNA matrix is confused once again. At last, after decoding the confused DNA matrix using a kind of DNA decoding rule, we obtain the ciphered image. Experimental results and theoretical analysis show that the scheme is able to resist various attacks, so it has extraordinarily high security.

Quantum signature of chaos and thermalization in the kicked Dicke model

NASA Astrophysics Data System (ADS)

Ray, S.; Ghosh, A.; Sinha, S.

2016-09-01

We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.

Stickiness in Hamiltonian systems: From sharply divided to hierarchical phase space

NASA Astrophysics Data System (ADS)

Altmann, Eduardo G.; Motter, Adilson E.; Kantz, Holger

2006-02-01

We investigate the dynamics of chaotic trajectories in simple yet physically important Hamiltonian systems with nonhierarchical borders between regular and chaotic regions with positive measures. We show that the stickiness to the border of the regular regions in systems with such a sharply divided phase space occurs through one-parameter families of marginally unstable periodic orbits and is characterized by an exponent γ=2 for the asymptotic power-law decay of the distribution of recurrence times. Generic perturbations lead to systems with hierarchical phase space, where the stickiness is apparently enhanced due to the presence of infinitely many regular islands and Cantori. In this case, we show that the distribution of recurrence times can be composed of a sum of exponentials or a sum of power laws, depending on the relative contribution of the primary and secondary structures of the hierarchy. Numerical verification of our main results are provided for area-preserving maps, mushroom billiards, and the newly defined magnetic mushroom billiards.

Quantum signature of chaos and thermalization in the kicked Dicke model.

PubMed

Ray, S; Ghosh, A; Sinha, S

2016-09-01

We study the quantum dynamics of the kicked Dicke model (KDM) in terms of the Floquet operator, and we analyze the connection between chaos and thermalization in this context. The Hamiltonian map is constructed by suitably taking the classical limit of the Heisenberg equation of motion to study the corresponding phase-space dynamics, which shows a crossover from regular to chaotic motion by tuning the kicking strength. The fixed-point analysis and calculation of the Lyapunov exponent (LE) provide us with a complete picture of the onset of chaos in phase-space dynamics. We carry out a spectral analysis of the Floquet operator, which includes a calculation of the quasienergy spacing distribution and structural entropy to show the correspondence to the random matrix theory in the chaotic regime. Finally, we analyze the thermodynamics and statistical properties of the bosonic sector as well as the spin sector, and we discuss how such a periodically kicked system relaxes to a thermalized state in accordance with the laws of statistical mechanics.

Dynamics of Two Point Vortices in an External Compressible Shear Flow

NASA Astrophysics Data System (ADS)

Vetchanin, Evgeny V.; Mamaev, Ivan S.

2017-12-01

This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincaré map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the "reversible pitch-fork" bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration.

Chryse Basin channels: low-gradients and ponded flows.

USGS Publications Warehouse

Lucchitta, B.K.; Ferguson, H.M.

1983-01-01

Gradients on the floors of the Martian outflow channels that are derived from radar-elevation profiles across Lunae Planum and Chryse Basin have much lower values than those obtained from the U.S. Geological Survey's topographic map. Whereas the gradients of Maja and Ares Valles are similar to those of the catastrophic flood channels in the Scablands of Washington State, the gradients of Simud and Tiu Valles are essentially level, and the movement of fluids to the N poses problems. It is proposed that ponding may have formed lakes in depressions associated with the Valles Marineris grabens, ancient craters in the chaotic terrain area, and possibly even the regional low where most chaotic terrains occur. It is envisaged that lakes eventually overflowed, forming the present channels. When dams broke, floods were released catastrophically, with a final gigantic flood from the Valles Marineris system of troughs, which would have had sufficient head to move fluids across nearly level gradients through the Simud and Tiu channels. -P.Br.

Parameter space of experimental chaotic circuits with high-precision control parameters.

PubMed

de Sousa, Francisco F G; Rubinger, Rero M; Sartorelli, José C; Albuquerque, Holokx A; Baptista, Murilo S

2016-08-01

We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chua's circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (∼21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family.

Chaos-assisted tunneling in the presence of Anderson localization.

PubMed

Doggen, Elmer V H; Georgeot, Bertrand; Lemarié, Gabriel

2017-10-01

Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate. Here we study chaos-assisted tunneling in the presence of Anderson localization effects in the chaotic sea. Our results show that the standard tunneling rate distribution is strongly modified by localization, going from the Cauchy distribution in the ergodic regime to a log-normal distribution in the strongly localized case, for both a deterministic and a disordered model. We develop a single-parameter scaling description which accurately describes the numerical data. Several possible experimental implementations using cold atoms, photonic lattices, or microwave billiards are discussed.

Hybrid electronic/optical synchronized chaos communication system.

PubMed

Toomey, J P; Kane, D M; Davidović, A; Huntington, E H

2009-04-27

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents.

PubMed

Hua, Zhongyun; Yi, Shuang; Zhou, Yicong; Li, Chengqing; Wu, Yue

2018-02-01

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.

BOOK REVIEW:

NASA Astrophysics Data System (ADS)

Berkolaiko, G.

2003-12-01

The book represents the collected lectures given at the Summer School on Mathematical Aspects of Quantum Maps held at Bologna University in September 2001. Quantum maps gained their prominence as a testing ground for mathematical understanding of various concepts in quantum chaos, such as the spectral statistics, quantum ergodicity, scarring of the eigenfunctions and the connection to algebraic number theory. The book is nicely structured. It begins by reviewing the relevant concepts and results from dynamical systems (a contribution by A Knauf) and number theory (by Z Rudnick). A contribution by the editors, M Degli Esposti and S Graffi, explains the quantization procedure for the quantum maps and proceeds to discuss some properties of the quantized maps, such as ergodicity and scarring, and the number theoretical techniques involved in proving these properties. The contribution by A Bäacker discusses the numerical methods used to study quantum chaotic systems. It contains both the mathematical background and a detailed explanation of the numerical techniques, possible pitfalls at the implementation stage and how to avoid them. It even contains a computer program in Python used by the author to compute the eigenvalues of a perturbed cat map. The last contribution, by R Artuso, while very interesting in itself, feels somewhat disconnected from the rest of the book. It deals with deterministic transport in hyperbolic and weakly chaotic systems, where one can observe normal and anomalous diffusion respectively. Although being a collection of contributions from various authors, the book feels very much like a well-coordinated team effort, with frequent cross-contributional references underlying the connections between different facets of the discussed subjects. I consider it an invaluable reference for researchers in the field of quantum chaos and would recommend it as a first read for people just entering the field. It contains both the necessary background information and tasters of the main results and concepts of quantum chaos. The only slight drawback of the book is the misprints in some of the contributions, which can make an understanding more difficult than it should be.

Chaos in Magnetic Flux Ropes

NASA Astrophysics Data System (ADS)

Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.

2013-12-01

Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time which reflects the change and possibly type of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2) O. Russo et al., Phys. Rev. Lett., 99, 154102 (2007), J. Maggs, G.Morales, 55, 085015 (2013)

Earthquake hazard assessment in the Zagros Orogenic Belt of Iran using a fuzzy rule-based model

NASA Astrophysics Data System (ADS)

Farahi Ghasre Aboonasr, Sedigheh; Zamani, Ahmad; Razavipour, Fatemeh; Boostani, Reza

2017-08-01

Producing accurate seismic hazard map and predicting hazardous areas is necessary for risk mitigation strategies. In this paper, a fuzzy logic inference system is utilized to estimate the earthquake potential and seismic zoning of Zagros Orogenic Belt. In addition to the interpretability, fuzzy predictors can capture both nonlinearity and chaotic behavior of data, where the number of data is limited. In this paper, earthquake pattern in the Zagros has been assessed for the intervals of 10 and 50 years using fuzzy rule-based model. The Molchan statistical procedure has been used to show that our forecasting model is reliable. The earthquake hazard maps for this area reveal some remarkable features that cannot be observed on the conventional maps. Regarding our achievements, some areas in the southern (Bandar Abbas), southwestern (Bandar Kangan) and western (Kermanshah) parts of Iran display high earthquake severity even though they are geographically far apart.

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp; Yamada, Michio; Chian, Abraham C.-L.

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originatemore » from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.« less

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation.

PubMed

Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C-L; Miranda, Rodrigo A; Rempel, Erico L

2015-10-01

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

Conduction at the onset of chaos

NASA Astrophysics Data System (ADS)

Baldovin, Fulvio

2017-02-01

After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge.

Secure coherent optical multi-carrier system with four-dimensional modulation space and Stokes vector scrambling.

PubMed

Zhang, Lijia; Liu, Bo; Xin, Xiangjun

2015-06-15

A secure enhanced coherent optical multi-carrier system based on Stokes vector scrambling is proposed and experimentally demonstrated. The optical signal with four-dimensional (4D) modulation space has been scrambled intra- and inter-subcarriers, where a multi-layer logistic map is adopted as the chaotic model. An experiment with 61.71-Gb/s encrypted multi-carrier signal is successfully demonstrated with the proposed method. The results indicate a promising solution for the physical secure optical communication.

Public channel cryptography: chaos synchronization and Hilbert's tenth problem.

PubMed

Kanter, Ido; Kopelowitz, Evi; Kinzel, Wolfgang

2008-08-22

The synchronization process of two mutually delayed coupled deterministic chaotic maps is demonstrated both analytically and numerically. The synchronization is preserved when the mutually transmitted signals are concealed by two commutative private filters, a convolution of the truncated time-delayed output signals or some powers of the delayed output signals. The task of a passive attacker is mapped onto Hilbert's tenth problem, solving a set of nonlinear Diophantine equations, which was proven to be in the class of NP-complete problems [problems that are both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP problem can be translated into this problem)]. This bridge between nonlinear dynamics and NP-complete problems opens a horizon for new types of secure public-channel protocols.

Stick-slip chaos in a mechanical oscillator with dry friction

NASA Astrophysics Data System (ADS)

Kousaka, Takuji; Asahara, Hiroyuki; Inaba, Naohiko

2018-03-01

This study analyzes a forced mechanical dynamical system with dry friction that can generate chaotic stick-slip vibrations. We find that the dynamics proposed by Yoshitake et al. [Trans. Jpn. Soc. Mech. Eng. C 61, 768 (1995)] can be expressed as a nonautonomous constraint differential equation owing to the static friction force. The object is constrained to the surface of a moving belt by a static friction force from when it sticks to the surface until the force on the object exceeds the maximal static friction force. We derive a 1D Poincaré return map from the constrained mechanical system, and prove numerically that this 1D map has an absolutely continuous invariant measure and a positive Lyapunov exponent, providing strong evidence for chaos.

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Santana, W. M.; Rempel, E. L.; Borotto, F. A.; Hada, T.; Kamide, Y.

2007-01-01

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

Bifurcation and Fractal of the Coupled Logistic Map

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Luo, Chao

The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.

Multiple attractors and boundary crises in a tri-trophic food chain.

PubMed

Boer, M P; Kooi, B W; Kooijman, S A

2001-02-01

The asymptotic behaviour of a model of a tri-trophic food chain in the chemostat is analysed in detail. The Monod growth model is used for all trophic levels, yielding a non-linear dynamical system of four ordinary differential equations. Mass conservation makes it possible to reduce the dimension by 1 for the study of the asymptotic dynamic behaviour. The intersections of the orbits with a Poincaré plane, after the transient has died out, yield a two-dimensional Poincaré next-return map. When chaotic behaviour occurs, all image points of this next-return map appear to lie close to a single curve in the intersection plane. This motivated the study of a one-dimensional bi-modal, non-invertible map of which the graph resembles this curve. We will show that the bifurcation structure of the food chain model can be understood in terms of the local and global bifurcations of this one-dimensional map. Homoclinic and heteroclinic connecting orbits and their global bifurcations are discussed also by relating them to their counterparts for a two-dimensional map which is invertible like the next-return map. In the global bifurcations two homoclinic or two heteroclinic orbits collide and disappear. In the food chain model two attractors coexist; a stable limit cycle where the top-predator is absent and an interior attractor. In addition there is a saddle cycle. The stable manifold of this limit cycle forms the basin boundary of the interior attractor. We will show that this boundary has a complicated structure when there are heteroclinic orbits from a saddle equilibrium to this saddle limit cycle. A homoclinic bifurcation to a saddle limit cycle will be associated with a boundary crisis where the chaotic attractor disappears suddenly when a bifurcation parameter is varied. Thus, similar to a tangent local bifurcation for equilibria or limit cycles, this homoclinic global bifurcation marks a region in the parameter space where the top-predator goes extinct. The 'Paradox of Enrichment' says that increasing the concentration of nutrient input can cause destabilization of the otherwise stable interior equilibrium of a bi-trophic food chain. For a tri-trophic food chain enrichment of the environment can even lead to extinction of the highest trophic level.

Network-induced chaos in integrate-and-fire neuronal ensembles.

PubMed

Zhou, Douglas; Rangan, Aaditya V; Sun, Yi; Cai, David

2009-09-01

It has been shown that a single standard linear integrate-and-fire (IF) neuron under a general time-dependent stimulus cannot possess chaotic dynamics despite the firing-reset discontinuity. Here we address the issue of whether conductance-based, pulsed-coupled network interactions can induce chaos in an IF neuronal ensemble. Using numerical methods, we demonstrate that all-to-all, homogeneously pulse-coupled IF neuronal networks can indeed give rise to chaotic dynamics under an external periodic current drive. We also provide a precise characterization of the largest Lyapunov exponent for these high dimensional nonsmooth dynamical systems. In addition, we present a stable and accurate numerical algorithm for evaluating the largest Lyapunov exponent, which can overcome difficulties encountered by traditional methods for these nonsmooth dynamical systems with degeneracy induced by, e.g., refractoriness of neurons.

Optimizing homogenization by chaotic unmixing?

NASA Astrophysics Data System (ADS)

Weijs, Joost; Bartolo, Denis

2016-11-01

A number of industrial processes rely on the homogeneous dispersion of non-brownian particles in a viscous fluid. An ideal mixing would yield a so-called hyperuniform particle distribution. Such configurations are characterized by density fluctuations that grow slower than the standard √{ N}-fluctuations. Even though such distributions have been found in several natural structures, e.g. retina receptors in birds, they have remained out of experimental reach until very recently. Over the last 5 years independent experiments and numerical simulations have shown that periodically driven suspensions can self-assemble hyperuniformally. Simple as the recipe may be, it has one important disadvantage. The emergence of hyperuniform states co-occurs with a critical phase transition from reversible to non reversible particle dynamics. As a consequence the homogenization dynamics occurs over a time that diverges with the system size (critical slowing down). Here, we discuss how this process can be sped up by exploiting the stirring properties of chaotic advection. Among the questions that we answer are: What are the physical mechanisms in a chaotic flow that are relevant for hyperuniformity? How can we tune the flow parameters such to obtain optimal hyperuniformity in the fastest way? JW acknowledges funding by NWO (Netherlands Organisation for Scientific Research) through a Rubicon Grant.

A novel procedure for the identification of chaos in complex biological systems

NASA Astrophysics Data System (ADS)

Bazeia, D.; Pereira, M. B. P. N.; Brito, A. V.; Oliveira, B. F. De; Ramos, J. G. G. S.

2017-03-01

We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior. The finding opens up a quantitative approach that relates the correlation length to the average density of maxima of a typical species, and an ensemble of stochastic simulations is implemented to support the procedure. The main result of the work shows how a single and simple experimental realization that counts the density of maxima associated with the chaotic evolution of the species serves to infer its correlation length. We use the result to investigate others distinct complex systems, one dealing with a set of differential equations that can be used to model a diversity of natural and artificial chaotic systems, and another one, focusing on the ocean water level.

The big contradiction between the perturbation theory and the chaotic state. A detailed mathematical analysis indicates when the plasma is stable or unstable

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xaplanteris, C. L., E-mail: cxaplanteris@yahoo.com; Xaplanteris, S. C.

2016-05-15

In the present manuscript enough observations and interpretations of three issues of Plasma Physics are presented. The first issue is linked to the common experimental confirmation of plasma waves which appear to be repeated in a standard way while there are also cases where plasma waves change to an unstable state or even to chaotic state. The second issue is associated with a mathematical analysis of the movement of a charged particle using the perturbation theory; which could be used as a guide for new researchers on similar issues. Finally, the suitability and applicability of the perturbation theory or themore » chaotic theory is presented. Although this study could be conducted on many plasma phenomena (e.g. plasma diffusion) or plasma quantities (e.g. plasma conductivity), here it was decided this study to be conducted on plasma waves and particularly on drift waves. This was because of the significance of waves on the plasmatic state and especially their negative impact on the thermonuclear fusion, but also due to the long-time experience of the plasma laboratory of Demokritos on drift waves.« less

Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jung, Jinwoo; Lee, Jewon; Song, Hanjung

2011-03-15

This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performedmore » simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-{mu}m single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with {+-}2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.« less

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

PubMed

Duarte, Jorge; Rodrigues, Carla; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2015-12-01

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

An enhanced mobile-healthcare emergency system based on extended chaotic maps.

PubMed

Lee, Cheng-Chi; Hsu, Che-Wei; Lai, Yan-Ming; Vasilakos, Athanasios

2013-10-01

Mobile Healthcare (m-Healthcare) systems, namely smartphone applications of pervasive computing that utilize wireless body sensor networks (BSNs), have recently been proposed to provide smartphone users with health monitoring services and received great attentions. An m-Healthcare system with flaws, however, may leak out the smartphone user's personal information and cause security, privacy preservation, or user anonymity problems. In 2012, Lu et al. proposed a secure and privacy-preserving opportunistic computing (SPOC) framework for mobile-Healthcare emergency. The brilliant SPOC framework can opportunistically gather resources on the smartphone such as computing power and energy to process the computing-intensive personal health information (PHI) in case of an m-Healthcare emergency with minimal privacy disclosure. To balance between the hazard of PHI privacy disclosure and the necessity of PHI processing and transmission in m-Healthcare emergency, in their SPOC framework, Lu et al. introduced an efficient user-centric privacy access control system which they built on the basis of an attribute-based access control mechanism and a new privacy-preserving scalar product computation (PPSPC) technique. However, we found out that Lu et al.'s protocol still has some secure flaws such as user anonymity and mutual authentication. To fix those problems and further enhance the computation efficiency of Lu et al.'s protocol, in this article, the authors will present an improved mobile-Healthcare emergency system based on extended chaotic maps. The new system is capable of not only providing flawless user anonymity and mutual authentication but also reducing the computation cost.

A Secure Dynamic Identity and Chaotic Maps Based User Authentication and Key Agreement Scheme for e-Healthcare Systems.

PubMed

Li, Chun-Ta; Lee, Cheng-Chi; Weng, Chi-Yao; Chen, Song-Jhih

2016-11-01

Secure user authentication schemes in many e-Healthcare applications try to prevent unauthorized users from intruding the e-Healthcare systems and a remote user and a medical server can establish session keys for securing the subsequent communications. However, many schemes does not mask the users' identity information while constructing a login session between two or more parties, even though personal privacy of users is a significant topic for e-Healthcare systems. In order to preserve personal privacy of users, dynamic identity based authentication schemes are hiding user's real identity during the process of network communications and only the medical server knows login user's identity. In addition, most of the existing dynamic identity based authentication schemes ignore the inputs verification during login condition and this flaw may subject to inefficiency in the case of incorrect inputs in the login phase. Regarding the use of secure authentication mechanisms for e-Healthcare systems, this paper presents a new dynamic identity and chaotic maps based authentication scheme and a secure data protection approach is employed in every session to prevent illegal intrusions. The proposed scheme can not only quickly detect incorrect inputs during the phases of login and password change but also can invalidate the future use of a lost/stolen smart card. Compared the functionality and efficiency with other authentication schemes recently, the proposed scheme satisfies desirable security attributes and maintains acceptable efficiency in terms of the computational overheads for e-Healthcare systems.

Theoretical and numerical studies of chaotic mixing

NASA Astrophysics Data System (ADS)

Kim, Ho Jun

Theoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral element algorithm for solution of the incompressible Navier-Stokes and species transport equations is developed. Using Taylor series expansions in time marching, the new algorithm employs an algebraic factorization scheme on multi-dimensional staggered spectral element grids, and extends classical conforming Galerkin formulations to nonconforming spectral elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the mixing device using spectral element and fourth order Runge-Kutta discretizations in space and time, respectively. Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in microfluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. These are the stirring index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the probability density function of the stretching field, and mixing index inverse, based on the standard deviation of scalar species distribution. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ∝ ln(Pe) scaling is demonstrated for fully chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified in a zeta potential patterned straight micro channel, where a continuous flow is generated by superposition of a steady pressure driven flow and time periodic electroosmotic flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in two-dimensional cavity.

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

NASA Astrophysics Data System (ADS)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Distinguishability notion based on Wootters statistical distance: Application to discrete maps

NASA Astrophysics Data System (ADS)

Gomez, Ignacio S.; Portesi, M.; Lamberti, P. W.

2017-08-01

We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d ¯ for an arbitrary discrete map. Moreover, from d ¯ , we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d ¯ , which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d ¯ and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.

A study in three-dimensional chaotic dynamics: Granular flow and transport in a bi-axial spherical tumbler

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christov, Ivan C.; Lueptow, Richard M.; Ottino, Julio M.

We study three-dimensional (3D) chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial “blinking” tumbler). The flow is essentially quasi-two-dimensional in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (inmore » the absence of stochasticity) particle trajectories are restricted to two-dimensional (2D) surfaces consisting of a portion of a hemispherical shell closed by a “cap''; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of the granular material, and their dependence on the protocol parameters (rates and durations of rotations). Exploiting the restriction of trajectories to 2D surfaces in the case of equal rotation rates about the axes, a method is proposed for identifying and constructing 3D Kolmogorov--Arnold--Moser (KAM) tubes around the normally elliptic period-one curves. The invariant manifold structure arising from the normally hyperbolic period-one curves is also examined. When the motion is restricted to 2D surfaces, the structure of manifolds of the hyperbolic points in the bulk differs from that corresponding to hyperbolic points in the flowing layer. Each is reminiscent of a template provided by a non-integrable perturbation to a Hamiltonian system, though the governing LTM is not. This highlights the novel 3D chaotic behaviors observed in this model dynamical system.« less

A study in three-dimensional chaotic dynamics: Granular flow and transport in a bi-axial spherical tumbler

DOE PAGES

Christov, Ivan C.; Lueptow, Richard M.; Ottino, Julio M.; ...

2014-05-22

We study three-dimensional (3D) chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial “blinking” tumbler). The flow is essentially quasi-two-dimensional in any vertical slice of the sphere during rotation about a single axis, and we provide an explicit exact solution to the model in this case. Hence, the cross-sectional flow can be represented by a twist map, allowing us to express the 3D flow as a linked twist map (LTM). We prove that if the rates of rotation about each axis are equal, then (inmore » the absence of stochasticity) particle trajectories are restricted to two-dimensional (2D) surfaces consisting of a portion of a hemispherical shell closed by a “cap''; if the rotation rates are unequal, then particles can leave the surface they start on and traverse a volume of the tumbler. The period-one structures of the governing LTM are examined in detail: analytical expressions are provided for the location of period-one curves, their extent into the bulk of the granular material, and their dependence on the protocol parameters (rates and durations of rotations). Exploiting the restriction of trajectories to 2D surfaces in the case of equal rotation rates about the axes, a method is proposed for identifying and constructing 3D Kolmogorov--Arnold--Moser (KAM) tubes around the normally elliptic period-one curves. The invariant manifold structure arising from the normally hyperbolic period-one curves is also examined. When the motion is restricted to 2D surfaces, the structure of manifolds of the hyperbolic points in the bulk differs from that corresponding to hyperbolic points in the flowing layer. Each is reminiscent of a template provided by a non-integrable perturbation to a Hamiltonian system, though the governing LTM is not. This highlights the novel 3D chaotic behaviors observed in this model dynamical system.« less

A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.

PubMed

Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki

2005-01-01

We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.

Maxwell Demon Dynamics: Deterministic Chaos, the Szilard Map, and the Intelligence of Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Boyd, Alexander B.; Crutchfield, James P.

2016-05-01

We introduce a deterministic chaotic system—the Szilard map—that encapsulates the measurement, control, and erasure protocol by which Maxwellian demons extract work from a heat reservoir. Implementing the demon's control function in a dynamical embodiment, our construction symmetrizes the demon and the thermodynamic system, allowing one to explore their functionality and recover the fundamental trade-off between the thermodynamic costs of dissipation due to measurement and those due to erasure. The map's degree of chaos—captured by the Kolmogorov-Sinai entropy—is the rate of energy extraction from the heat bath. Moreover, an engine's statistical complexity quantifies the minimum necessary system memory for it to function. In this way, dynamical instability in the control protocol plays an essential and constructive role in intelligent thermodynamic systems.

Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO.

PubMed

Pan, Indranil; Das, Saptarshi

2016-05-01

This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Amplitude-Phase Modulation, Topological Horseshoe and Scaling Attractor of a Dynamical System

NASA Astrophysics Data System (ADS)

Li, Chun-Lai; Li, Wen; Zhang, Jing; Xie, Yuan-Xi; Zhao, Yi-Bo

2016-09-01

A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincaré map, power spectrum, Kaplan-Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key. Supported by Hunan Provincial Natural Science Foundation of China under Grant No. 2016JJ4036, University Natural Science Foundation of Jiangsu Province under Grant No. 14KJB120007 and the National Natural Science Foundation of China under Grant Nos. 11504176 and 11602084

Detection of chaotic determinism in time series from randomly forced maps

NASA Technical Reports Server (NTRS)

Chon, K. H.; Kanters, J. K.; Cohen, R. J.; Holstein-Rathlou, N. H.

1997-01-01

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists

NASA Technical Reports Server (NTRS)

Ross, Shane D.; Grover, Piyush

2007-01-01

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps.

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

NASA Astrophysics Data System (ADS)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Associative memory model with spontaneous neural activity

NASA Astrophysics Data System (ADS)

Kurikawa, Tomoki; Kaneko, Kunihiko

2012-05-01

We propose a novel associative memory model wherein the neural activity without an input (i.e., spontaneous activity) is modified by an input to generate a target response that is memorized for recall upon the same input. Suitable design of synaptic connections enables the model to memorize input/output (I/O) mappings equaling 70% of the total number of neurons, where the evoked activity distinguishes a target pattern from others. Spontaneous neural activity without an input shows chaotic dynamics but keeps some similarity with evoked activities, as reported in recent experimental studies.

A Bayesian nonparametric approach to dynamical noise reduction

NASA Astrophysics Data System (ADS)

Kaloudis, Konstantinos; Hatjispyros, Spyridon J.

2018-06-01

We propose a Bayesian nonparametric approach for the noise reduction of a given chaotic time series contaminated by dynamical noise, based on Markov Chain Monte Carlo methods. The underlying unknown noise process (possibly) exhibits heavy tailed behavior. We introduce the Dynamic Noise Reduction Replicator model with which we reconstruct the unknown dynamic equations and in parallel we replicate the dynamics under reduced noise level dynamical perturbations. The dynamic noise reduction procedure is demonstrated specifically in the case of polynomial maps. Simulations based on synthetic time series are presented.

Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979

NASA Technical Reports Server (NTRS)

Helleman, R. H. G.

1980-01-01

Papers were presented on turbulence, ergodic and integrable behavior, chaotic maps and flows, chemical and fully developed turbulence, and strange attractors. Specific attention was given to measures describing a turbulent flow, stochastization and collapse of vortex systems, a subharmonic route to turbulent convection, and weakly nonlinear turbulence in a rotating convection layer. The Korteweg-de Vries and Hill equations, plasma transport in three dimensions, a horseshoe in the dynamics of a forced beam, and the explosion of strange attractors exhibited by Duffing's equation were also considered.

Hyperbolic chaos in the klystron-type microwave vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Emel'yanov, V. V.; Kuznetsov, S. P.; Ryskin, N. M.

2010-12-01

The ring-loop oscillator consisting of two coupled klystrons which is capable of generating hyperbolic chaotic signal in the microwave band is considered. The system of delayed-differential equations describing the dynamics of the oscillator is derived. This system is further reduced to the two-dimensional return map under the assumption of the instantaneous build-up of oscillations in the cavities. The results of detailed numerical simulation for both models are presented showing that there exists large enough range of control parameters where the sustained regime corresponds to the structurally stable hyperbolic chaos.

Regional business cycle synchronization through expectations

NASA Astrophysics Data System (ADS)

Onozaki, Tamotsu; Yanagita, Tatsuo; Kaizoji, Taisei; Toyabe, Kazutaka

2007-09-01

This paper provides an example in which regional business cycles may synchronize via producers’ expectations, even though there is no interregional trade, by means of a system of globally coupled, noninvertible maps. We concentrate on the dependence of the dynamics on a parameter η which denotes the inverse of price elasticity of demand. Simulation results show that several phases (the short transient, the complete asynchronous, the long transient and the intermediate transient) appear one after another as η increases. In the long transient phase, the intermittent clustering process with a long chaotic transient appears repeatedly.

Autonomous choices among deterministic evolution-laws as source of uncertainty

NASA Astrophysics Data System (ADS)

Trujillo, Leonardo; Meyroneinc, Arnaud; Campos, Kilver; Rendón, Otto; Sigalotti, Leonardo Di G.

2018-03-01

We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these pseudo-random dynamical systems. Each chaotic system in this family exhibits a sensitivity to initial conditions that encompasses the sequence of choices of the evolution rule in some collection of maps. This opens a possibility to extend current theories of complex behaviors on the basis of intrinsic uncertainty in deterministic chaos.

Characterizing chaotic melodies in automatic music composition

NASA Astrophysics Data System (ADS)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

Stages of chaotic synchronization.

PubMed

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

Pseudochaos and anomalous transport: A study on saw-tooth map

NASA Astrophysics Data System (ADS)

Fan, Rong

The observation of chaotic dynamics in digital filter in late 1980s propelled the interest in piecewise linear map beyond the border of theoretical electrical engineering. Also, during last two decades, various physical models and phenomena, such as stochastic web and sticky orbits, not only broadened our knowledge of chaos but also urged us to further our understanding of meaning of chaos and randomness. In this dissertation, a piecewise linear kicked oscillator model: saw-tooth map, is studied as an example of pseudochaos. Physically, kicked oscillator model describes one-dimensional harmonic oscillator effected by delta-like kicks from external force source at certain fixed frequency. Starting from a special case of global periodicity, numerical investigations were carefully carried out in two cases that deviate from global periodicity. We observe the appearance of stochastic web structure and accompanying erratic dynamical behavior in the system that can't be fully explained by the classical Kolmogorov-Arnold-Moser theorem. Also anomalous transport occurs in both cases. We perform accurate analysis of Poincare recurrences and reconstruct the probability density function of Poincare recurrence times, which suggests a relation between the transport and the Poincare recurrence exponents. Saw-tooth map has non-uniform phase space, in which domains of regular dynamics and domains of chaotic dynamics are intertwined. The large-scale dynamics of the system is hugely impacted by the heterogeneity of the phase space, especially by the existence of hierarchy of periodic islands. We carefully study the characteristics of phase space and numerically compute fractal dimensions of the so-called exceptional set Delta in both cases. Our results suggest that the fractal dimension is strictly less than 2 and that the fractal structures are unifractal rather than multifractal. We present a phenomenological theoretical framework of Fractional Kinetic Equation (FKE) and Renormalization Group of Kinetics (RGK). FKE, which is fractional generalization of the Fokker-Planck-Kolmogorov equation, adopts the fractality of time and space and serves probabilistic description of chaos in Hamiltonian systems. RGK bridges the self-similar structure in phase space and large-scale behavior of the dynamics, and establishes relationships among fractality, transport and Poincare recurrences.

Chaotic Stochasticity: A Ubiquitous Source of Unpredictability in Epidemics

NASA Astrophysics Data System (ADS)

Rand, D. A.; Wilson, H. B.

1991-11-01

We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.

A real time QRS detection using delay-coordinate mapping for the microcontroller implementation.

PubMed

Lee, Jeong-Whan; Kim, Kyeong-Seop; Lee, Bongsoo; Lee, Byungchae; Lee, Myoung-Ho

2002-01-01

In this article, we propose a new algorithm using the characteristics of reconstructed phase portraits by delay-coordinate mapping utilizing lag rotundity for a real-time detection of QRS complexes in ECG signals. In reconstructing phase portrait the mapping parameters, time delay, and mapping dimension play important roles in shaping of portraits drawn in a new dimensional space. Experimentally, the optimal mapping time delay for detection of QRS complexes turned out to be 20 ms. To explore the meaning of this time delay and the proper mapping dimension, we applied a fill factor, mutual information, and autocorrelation function algorithm that were generally used to analyze the chaotic characteristics of sampled signals. From these results, we could find the fact that the performance of our proposed algorithms relied mainly on the geometrical property such as an area of the reconstructed phase portrait. For the real application, we applied our algorithm for designing a small cardiac event recorder. This system was to record patients' ECG and R-R intervals for 1 h to investigate HRV characteristics of the patients who had vasovagal syncope symptom and for the evaluation, we implemented our algorithm in C language and applied to MIT/BIH arrhythmia database of 48 subjects. Our proposed algorithm achieved a 99.58% detection rate of QRS complexes.

Bifurcation behaviors of synchronized regions in logistic map networks with coupling delay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tang, Longkun, E-mail: tomlk@hqu.edu.cn, E-mail: xqwu@whu.edu.cn; Wu, Xiaoqun, E-mail: tomlk@hqu.edu.cn, E-mail: xqwu@whu.edu.cn; Lu, Jun-an, E-mail: jalu@whu.edu.cn

2015-03-15

Network synchronized regions play an extremely important role in network synchronization according to the master stability function framework. This paper focuses on network synchronous state stability via studying the effects of nodal dynamics, coupling delay, and coupling way on synchronized regions in Logistic map networks. Theoretical and numerical investigations show that (1) network synchronization is closely associated with its nodal dynamics. Particularly, the synchronized region bifurcation points through which the synchronized region switches from one type to another are in good agreement with those of the uncoupled node system, and chaotic nodal dynamics can greatly impede network synchronization. (2) Themore » coupling delay generally impairs the synchronizability of Logistic map networks, which is also dominated by the parity of delay for some nodal parameters. (3) A simple nonlinear coupling facilitates network synchronization more than the linear one does. The results found in this paper will help to intensify our understanding for the synchronous state stability in discrete-time networks with coupling delay.« less

Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

NASA Astrophysics Data System (ADS)

Sun, Changchun; Chen, Zhongtang; Xu, Qicheng

2017-12-01

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Akgul, A.; Kaçar, S.; Çavuşoğlu, U.

2018-02-01

Hyperjerk systems have received significant interest in the literature because of their simple structure and complex dynamical properties. This work presents a new chaotic hyperjerk system having two exponential nonlinearities. Dynamical properties of the chaotic hyperjerk system are discovered through equilibrium point analysis, bifurcation diagram, dissipativity and Lyapunov exponents. Moreover, an adaptive backstepping controller is designed for the synchronization of the chaotic hyperjerk system. Also, a real circuit of the chaotic hyperjerk system has been carried out to show the feasibility of the theoretical hyperjerk model. The chaotic hyperjerk system can also be useful in scientific fields such as Random Number Generators (RNGs), data security, data hiding, etc. In this work, three implementations of the chaotic hyperjerk system, viz. RNG, image encryption and sound steganography have been performed by using complex dynamics characteristics of the system.

Chaotic Signal Denoising Based on Hierarchical Threshold Synchrosqueezed Wavelet Transform

NASA Astrophysics Data System (ADS)

Wang, Wen-Bo; Jing, Yun-yu; Zhao, Yan-chao; Zhang, Lian-Hua; Wang, Xiang-Li

2017-12-01

In order to overcoming the shortcoming of single threshold synchrosqueezed wavelet transform(SWT) denoising method, an adaptive hierarchical threshold SWT chaotic signal denoising method is proposed. Firstly, a new SWT threshold function is constructed based on Stein unbiased risk estimation, which is two order continuous derivable. Then, by using of the new threshold function, a threshold process based on the minimum mean square error was implemented, and the optimal estimation value of each layer threshold in SWT chaotic denoising is obtained. The experimental results of the simulating chaotic signal and measured sunspot signals show that, the proposed method can filter the noise of chaotic signal well, and the intrinsic chaotic characteristic of the original signal can be recovered very well. Compared with the EEMD denoising method and the single threshold SWT denoising method, the proposed method can obtain better denoising result for the chaotic signal.

Dynamics, Analysis and Implementation of a Multiscroll Memristor-Based Chaotic Circuit

NASA Astrophysics Data System (ADS)

Alombah, N. Henry; Fotsin, Hilaire; Ngouonkadi, E. B. Megam; Nguazon, Tekou

This article introduces a novel four-dimensional autonomous multiscroll chaotic circuit which is derived from the actual simplest memristor-based chaotic circuit. A fourth circuit element — another inductor — is introduced to generate the complex behavior observed. A systematic study of the chaotic behavior is performed with the help of some nonlinear tools such as Lyapunov exponents, phase portraits, and bifurcation diagrams. Multiple scroll attractors are observed in Matlab, Pspice environments and also experimentally. We also observe the phenomenon of antimonotonicity, periodic and chaotic bubbles, multiple periodic-doubling bifurcations, Hopf bifurcations, crises and the phenomenon of intermittency. The chaotic dynamics of this circuit is realized by laboratory experiments, Pspice simulations, numerical and analytical investigations. It is observed that the results from the three environments agree to a great extent. This topology is likely convenient to be used to intentionally generate chaos in memristor-based chaotic circuit applications, given the fact that multiscroll chaotic systems have found important applications as broadband signal generators, pseudorandom number generators for communication engineering and also in biometric authentication.

Period doubling cascades of prey-predator model with nonlinear harvesting and control of over exploitation through taxation

NASA Astrophysics Data System (ADS)

Gupta, R. P.; Banerjee, Malay; Chandra, Peeyush

2014-07-01

The present study investigates a prey predator type model for conservation of ecological resources through taxation with nonlinear harvesting. The model uses the harvesting function as proposed by Agnew (1979) [1] which accounts for the handling time of the catch and also the competition between standard vessels being utilized for harvesting of resources. In this paper we consider a three dimensional dynamic effort prey-predator model with Holling type-II functional response. The conditions for uniform persistence of the model have been derived. The existence and stability of bifurcating periodic solution through Hopf bifurcation have been examined for a particular set of parameter value. Using numerical examples it is shown that the system admits periodic, quasi-periodic and chaotic solutions. It is observed that the system exhibits periodic doubling route to chaos with respect to tax. Many forms of complexities such as chaotic bands (including periodic windows, period-doubling bifurcations, period-halving bifurcations and attractor crisis) and chaotic attractors have been observed. Sensitivity analysis is carried out and it is observed that the solutions are highly dependent to the initial conditions. Pontryagin's Maximum Principle has been used to obtain optimal tax policy to maximize the monetary social benefit as well as conservation of the ecosystem.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, Samuel Lee; Miller, William Michael; McWhorter, Paul Jackson

1997-01-01

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, S.L.; Miller, W.M.; McWhorter, P.J.

1997-10-21

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals. 32 figs.

Design and Hardware Implementation of a New Chaotic Secure Communication Technique

PubMed Central

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness. PMID:27548385

Design and Hardware Implementation of a New Chaotic Secure Communication Technique.

PubMed

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2004-03-01

We present a numerically feasible semiclassical method to evaluate quantum fidelity (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform semiclassical expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows a Monte-Carlo evaluation, this uniform expression is accurate at times where there are 10^70 semiclassical contributions. Remarkably, the method also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and thus provide a ``defense" of the linear response theory from the famous Van Kampen objection. We point out the potential use of our uniform expression in other areas because it gives a most direct link between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. Finally, we test the applicability of our method in integrable and mixed systems.

The development of GPU-based parallel PRNG for Monte Carlo applications in CUDA Fortran

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kargaran, Hamed, E-mail: h-kargaran@sbu.ac.ir; Minuchehr, Abdolhamid; Zolfaghari, Ahmad

The implementation of Monte Carlo simulation on the CUDA Fortran requires a fast random number generation with good statistical properties on GPU. In this study, a GPU-based parallel pseudo random number generator (GPPRNG) have been proposed to use in high performance computing systems. According to the type of GPU memory usage, GPU scheme is divided into two work modes including GLOBAL-MODE and SHARED-MODE. To generate parallel random numbers based on the independent sequence method, the combination of middle-square method and chaotic map along with the Xorshift PRNG have been employed. Implementation of our developed PPRNG on a single GPU showedmore » a speedup of 150x and 470x (with respect to the speed of PRNG on a single CPU core) for GLOBAL-MODE and SHARED-MODE, respectively. To evaluate the accuracy of our developed GPPRNG, its performance was compared to that of some other commercially available PPRNGs such as MATLAB, FORTRAN and Miller-Park algorithm through employing the specific standard tests. The results of this comparison showed that the developed GPPRNG in this study can be used as a fast and accurate tool for computational science applications.« less

Comparison of six methods for the detection of causality in a bivariate time series

NASA Astrophysics Data System (ADS)

Krakovská, Anna; Jakubík, Jozef; Chvosteková, Martina; Coufal, David; Jajcay, Nikola; Paluš, Milan

2018-04-01

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20 000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

Skeletal growth phases of the cold-water coral Lophelia pertusa shown by scanning electron microscope and electron backscatter diffraction

NASA Astrophysics Data System (ADS)

Mouchi, Vincent; Vonlanthen, Pierre; Verrecchia, Eric P.; Crowley, Quentin G.

2016-04-01

Lophelia pertusa is a cold-water coral, which may form reefs by the association of multiple coralites within which a polyp lives. Each individual polyp builds an aragonite skeleton by an initial phase of early mineralization (traditionally referred to as centres of calcification) from which aragonite fibres grow in thickening deposits. The skeleton wall features successive optically opaque and translucent bands previously attributed to different regimes of growth as either uniform in crystal orientation (translucent bands) or with a chaotic organization (opaque bands). The processes involved in any organizational changes are still unknown. Microlayers in the coral wall, which represent separate periods of skeletal growth, have been recently identified and described. These growth patterns are readily visible under scanning electron microscope (SEM) after etching in dilute formic acid, but they do not necessarily form continuously visible structures. Here we present high quality SEM images and electron backscatter diffraction (EBSD) maps to study aragonite fibre orientation across the wall of L. pertusa. Both microlayers and opaque and translucent bands are compared to the crystallographic orientation of the aragonite fibres. EBSD maps and SEM images indicate that aragonite fibres do not exhibit a chaotic orientation, even in opaque bands. The absence of continuity of microlayers is partially explained by an association of multiple crystallographic preferred orientations of aragonite fibres. In the case of L. pertusa, careful textural characterisation is necessary prior to elemental or isotope analysis in order to select a skeletal transect representing a linear and continuous time period.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

PubMed

Cotter, C J; Gottwald, G A; Holm, D D

2017-09-01

In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Novel permutation measures for image encryption algorithms

NASA Astrophysics Data System (ADS)

Abd-El-Hafiz, Salwa K.; AbdElHaleem, Sherif H.; Radwan, Ahmed G.

2016-10-01

This paper proposes two measures for the evaluation of permutation techniques used in image encryption. First, a general mathematical framework for describing the permutation phase used in image encryption is presented. Using this framework, six different permutation techniques, based on chaotic and non-chaotic generators, are described. The two new measures are, then, introduced to evaluate the effectiveness of permutation techniques. These measures are (1) Percentage of Adjacent Pixels Count (PAPC) and (2) Distance Between Adjacent Pixels (DBAP). The proposed measures are used to evaluate and compare the six permutation techniques in different scenarios. The permutation techniques are applied on several standard images and the resulting scrambled images are analyzed. Moreover, the new measures are used to compare the permutation algorithms on different matrix sizes irrespective of the actual parameters used in each algorithm. The analysis results show that the proposed measures are good indicators of the effectiveness of the permutation technique.

Cross over of recurrence networks to random graphs and random geometric graphs

NASA Astrophysics Data System (ADS)

Jacob, Rinku; Harikrishnan, K. P.; Misra, R.; Ambika, G.

2017-02-01

Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability density variations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measures and show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise to the time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.

Quantum-chaotic cryptography

NASA Astrophysics Data System (ADS)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators.

PubMed

Xu, Kesheng; Maidana, Jean Paul; Castro, Samy; Orio, Patricio

2018-05-30

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that - when isolated - can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Chimera states in coupled Kuramoto oscillators with inertia.

PubMed

Olmi, Simona

2015-12-01

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.

A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator

NASA Astrophysics Data System (ADS)

Tong, Xiaojun; Cui, Minggen; Wang, Zhu

2009-07-01

The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney's definition proof of chaos. The properties of compound chaotic functions are also proved rigorously. In order to improve the robustness against difference cryptanalysis and produce avalanche effect, a new feedback image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and a new image pixels method of permutation and substitution is designed in detail by array row and column random controlling based on the compound chaos. The results from entropy analysis, difference analysis, statistical analysis, sequence randomness analysis, cipher sensitivity analysis depending on key and plaintext have proven that the compound chaotic sequence cipher can resist cryptanalytic, statistical and brute-force attacks, and especially it accelerates encryption speed, and achieves higher level of security. By the dynamical compound chaos and perturbation technology, the paper solves the problem of computer low precision of one-dimensional chaotic function.

A New Method for Suppressing Periodic Narrowband Interference Based on the Chaotic van der Pol Oscillator

NASA Astrophysics Data System (ADS)

Lu, Jia; Zhang, Xiaoxing; Xiong, Hao

The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

NASA Astrophysics Data System (ADS)

Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

2018-02-01

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

Dynamics and circuit of a chaotic system with a curve of equilibrium points

NASA Astrophysics Data System (ADS)

Pham, Viet-Thanh; Volos, Christos; Kapitaniak, Tomasz; Jafari, Sajad; Wang, Xiong

2018-03-01

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.

Computations of Chaotic Flows in Micromixers

DTIC Science & Technology

2006-04-07

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6410--06-8948 Computations of Chaotic Flows in Micromixers April 7, 2006 Approved for...PAGES 17. LIMITATION OF ABSTRACT Computations of Chaotic Flows in Micromixers Carolyn R. Kaplan, Junhui Liu, David R. Mott, and Elaine S. Oran NRL/MR...striations form in time 1 _______________ Manuscript approved December 8, 2005. COMPUTATIONS OF CHAOTIC FLOWS IN MICROMIXERS or distance. Sometimes it is

Performance of Multi-chaotic PSO on a shifted benchmark functions set

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan

2015-03-10

In this paper the performance of Multi-chaotic PSO algorithm is investigated using two shifted benchmark functions. The purpose of shifted benchmark functions is to simulate the time-variant real-world problems. The results of chaotic PSO are compared with canonical version of the algorithm. It is concluded that using the multi-chaotic approach can lead to better results in optimization of shifted functions.

A perturbation method to the tent map based on Lyapunov exponent and its application

NASA Astrophysics Data System (ADS)

Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu

2015-10-01

Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).

Trojan resonant dynamics, stability, and chaotic diffusion, for parameters relevant to exoplanetary systems

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Efthymiopoulos, Christos

2015-02-01

The possibility that giant extrasolar planets could have small Trojan co-orbital companions has been examined in the literature from both viewpoints of the origin and dynamical stability of such a configuration. Here we aim to investigate the dynamics of hypothetical small Trojan exoplanets in domains of secondary resonances embedded within the tadpole domain of motion. To this end, we consider the limit of a massless Trojan companion of a giant planet. Without other planets, this is a case of the elliptic restricted three body problem (ERTBP). The presence of additional planets (hereafter referred to as the restricted multi-planet problem, RMPP) induces new direct and indirect secular effects on the dynamics of the Trojan body. The paper contains a theoretical and a numerical part. In the theoretical part, we develop a Hamiltonian formalism in action-angle variables, which allows us to treat in a unified way resonant dynamics and secular effects on the Trojan body in both the ERTBP or the RMPP. In both cases, our formalism leads to a decomposition of the Hamiltonian in two parts, . , called the basic model, describes resonant dynamics in the short-period (epicyclic) and synodic (libration) degrees of freedom, while contains only terms depending trigonometrically on slow (secular) angles. is formally identical in the ERTBP and the RMPP, apart from a re-definition of some angular variables. An important physical consequence of this analysis is that the slow chaotic diffusion along resonances proceeds in both the ERTBP and the RMPP by a qualitatively similar dynamical mechanism. We found that this is best approximated by the paradigm of `modulational diffusion'. In the paper's numerical part, we then focus on the ERTBP in order to make a detailed numerical demonstration of the chaotic diffusion process along resonances. Using color stability maps, we first provide a survey of the resonant web for characteristic mass parameter values of the primary, in which the secondary resonances from 1:5 to 1:12 (ratio of the short over the synodic period), as well as their transverse resonant multiplets, appear. We give numerical examples of diffusion of weakly chaotic orbits in the resonant web. We finally make a statistics of the escaping times in the resonant domain, and find power-law tails of the distribution of the escaping times for the slowly diffusing chaotic orbits. Implications of resonant dynamics in the search for Trojan exoplanets are discussed.

SIAM conference on applications of dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-01-01

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

SIAM conference on applications of dynamical systems. Abstracts and author index

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-12-31

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

Monte Carlo sampling in diffusive dynamical systems

NASA Astrophysics Data System (ADS)

Tapias, Diego; Sanders, David P.; Altmann, Eduardo G.

2018-05-01

We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements, where deviations from a diffusive process are most prominent. We search for initial conditions using a proposal that correlates states in the Markov chain constructed via a Metropolis-Hastings algorithm. We show that our method outperforms the direct sampling method and also Metropolis-Hastings methods with alternative proposals. We test our general method through numerical simulations in 1D (box-map) and 2D (Lorentz gas) systems.

A universal approach to the study of nonlinear systems

NASA Astrophysics Data System (ADS)

Hwa, Rudolph C.

2004-07-01

A large variety of nonlinear systems have been treated by a common approach that emphasizes the fluctuation of spatial patterns. By using the same method of analysis it is possible to discuss the chaotic behaviors of quark jets and logistic map in the same language. Critical behaviors of quark-hadron phase transition in heavy-ion collisions and of photon production at the threshold of lasing can also be described by a common scaling behavior. The universal approach also makes possible an insight into the recently discovered phenomenon of wind reversal in cryogenic turbulence as a manifestation of self-organized criticality.

Endogenous population growth may imply chaos.

PubMed

Prskawetz, A; Feichtinger, G

1995-01-01

The authors consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, they obtain numerical results on the qualitative behavior of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies--assumed to be characterized by low and high savings rate respectively--are characterized by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.

More memory under evolutionary learning may lead to chaos

NASA Astrophysics Data System (ADS)

Diks, Cees; Hommes, Cars; Zeppini, Paolo

2013-02-01

We show that an increase of memory of past strategy performance in a simple agent-based innovation model, with agents switching between costly innovation and cheap imitation, can be quantitatively stabilising while at the same time qualitatively destabilising. As memory in the fitness measure increases, the amplitude of price fluctuations decreases, but at the same time a bifurcation route to chaos may arise. The core mechanism leading to the chaotic behaviour in this model with strategy switching is that the map obtained for the system with memory is a convex combination of an increasing linear function and a decreasing non-linear function.

The Pasinetti-Solow Growth Model with Optimal Saving Behaviour: A Local Bifurcation Analysis

NASA Astrophysics Data System (ADS)

Commendatore, P.; Palmisani, C.

We present a discrete time version of the Pasinetti-Solow economic growth model. Workers and capitalists are assumed to save on the basis of rational choices. Workers face a finite time horizon and base their consumption choices on a life-cycle motive, whereas capitalists behave like an infinitely-lived dynasty. The accumulation of both capitalists' and workers' wealth through time is reduced to a two-dimensional map whose local asymptotic stability properties are studied. Various types of bifurcation emerge (flip, Neimark-Sacker, saddle-node and transcritical): a precondition for chaotic dynamics.

Nonlinear optimal control for the synchronization of chaotic and hyperchaotic finance systems

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Loia, V.; Ademi, S.; Ghosh, T.

2017-11-01

It is possible to make specific finance systems get synchronized to other finance systems exhibiting chaotic and hyperchaotic dynamics, by applying nonlinear optimal (H-infinity) control. This signifies that chaotic behavior can be generated in finance systems by exerting a suitable control input. Actually, a lead financial system is considered which exhibits inherently chaotic dynamics. Moreover, a follower finance system is introduced having parameters in its model that inherently prohibit the appearance of chaotic dynamics. Through the application of a suitable nonlinear optimal (H-infinity) control input it is proven that the follower finance system can replicate the chaotic dynamics of the lead finance system. By applying Lyapunov analysis it is proven that asymptotically the follower finance system gets synchronized with the lead system and that the tracking error between the state variables of the two systems vanishes.

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

NASA Technical Reports Server (NTRS)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2016-01-01

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter

NASA Astrophysics Data System (ADS)

Kiani-B, Arman; Fallahi, Kia; Pariz, Naser; Leung, Henry

2009-03-01

In recent years chaotic secure communication and chaos synchronization have received ever increasing attention. In this paper, for the first time, a fractional chaotic communication method using an extended fractional Kalman filter is presented. The chaotic synchronization is implemented by the EFKF design in the presence of channel additive noise and processing noise. Encoding chaotic communication achieves a satisfactory, typical secure communication scheme. In the proposed system, security is enhanced based on spreading the signal in frequency and encrypting it in time domain. In this paper, the main advantages of using fractional order systems, increasing nonlinearity and spreading the power spectrum are highlighted. To illustrate the effectiveness of the proposed scheme, a numerical example based on the fractional Lorenz dynamical system is presented and the results are compared to the integer Lorenz system.

Design and simulation of the micromixer with chaotic advection in twisted microchannels.

PubMed

Jen, Chun-Ping; Wu, Chung-Yi; Lin, Yu-Cheng; Wu, Ching-Yi

2003-05-01

Chaotic mixers with twisted microchannels were designed and simulated numerically in the present study. The phenomenon whereby a simple Eulerian velocity field may generate a chaotic response in the distribution of a Lagrangian marker is termed chaotic advection. Dynamic system theory indicates that chaotic particle motion can occur when a velocity field is either two-dimensional and time-dependent, or three-dimensional. In the present study, micromixers with three-dimensional structures of the twisted microchannel were designed in order to induce chaotic mixing. In addition to the basic T-mixer, three types of micromixers with inclined, oblique and wavelike microchannels were investigated. In the design of each twisted microchannel, the angle of the channels' bottoms alternates in each subsection. When the fluids enter the twisted microchannels, the flow sways around the varying structures within the microchannels. The designs of the twisted microchannels provide a third degree of freedom to the flow field in the microchannel. Therefore, chaotic regimes that lead to chaotic mixing may arise. The numerical results indicate that mixing occurs in the main channel and progressively larger mixing lengths are required as the Peclet number increased. The swaying of the flow in the twisted microchannel causes chaotic advection. Among the four micromixer designs, the micromixer with the inclined channel most improved mixing. Furthermore, using the inclined mixer with six subsections yielded optimum performance, decreasing the mixing length by up to 31% from that of the basic T-mixer.

Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating

NASA Astrophysics Data System (ADS)

Wen-Bo, Wang; Xiao-Dong, Zhang; Yuchan, Chang; Xiang-Li, Wang; Zhao, Wang; Xi, Chen; Lei, Zheng

2016-01-01

In this paper, a new method to reduce noises within chaotic signals based on ICA (independent component analysis) and EMD (empirical mode decomposition) is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the independent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions (IMFs) of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals. Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor. Project supported by the National Science and Technology, China (Grant No. 2012BAJ15B04), the National Natural Science Foundation of China (Grant Nos. 41071270 and 61473213), the Natural Science Foundation of Hubei Province, China (Grant No. 2015CFB424), the State Key Laboratory Foundation of Satellite Ocean Environment Dynamics, China (Grant No. SOED1405), the Hubei Provincial Key Laboratory Foundation of Metallurgical Industry Process System Science, China (Grant No. Z201303), and the Hubei Key Laboratory Foundation of Transportation Internet of Things, Wuhan University of Technology, China (Grant No.2015III015-B02).

The equal combination synchronization of a class of chaotic systems with discontinuous output

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luo, Runzi; Zeng, Yanhui

This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

Modelling of long-wave chaotic radar system for anti-stealth applications

NASA Astrophysics Data System (ADS)

Al-Suhail, Ghaida A.; Tahir, Fadhil Rahma; Abd, Mariam Hussien; Pham, Viet-Thanh; Fortuna, Luigi

2018-04-01

Although the Very Low-Frequency (VLF) waveforms have limited practical applications in acoustics (sonar) and secure military communications with radars and submarines; to this end; this paper presents a new and simple analytical model of VLF monostatic direct chaotic radar system. The model hypothetically depends on the two identical coupled time-delayed feedback chaotic systems which can generate and recover a long-wave chaotic signal. To resist the influence of positive Lyapunov exponents of the time-delay chaotic systems, the complete replacement of Pecaro and Carroll (PC) synchronization is employed. It can faithfully recover the chaotic signal from the back-scattered (echo) signal from the target over a noisy channel. The system performance is characterized in terms of the time series of synchronization in addition to the peak of the cross-correlation. Simulation results are conducted for substantial sensitivities of the chaotic signal to the system parameters and initial conditions. As a result, it is found that an effective and robust chaotic radar (CRADAR) model can be obtained when the signal-to-noise ratio (SNR) highly degrades to 0 dB, but with clear peak in correlation performance for detecting the target. Then, the model can be considered as a state of the art towards counter stealth technology and might be developed for other acoustic secure applications.

A new chaotic oscillator with free control

NASA Astrophysics Data System (ADS)

Li, Chunbiao; Sprott, Julien Clinton; Akgul, Akif; Iu, Herbert H. C.; Zhao, Yibo

2017-08-01

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.

Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barrio, Roberto, E-mail: rbarrio@unizar.es; Serrano, Sergio; Angeles Martínez, M.

2014-06-01

We study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification, and evaluation of Lyapunov exponents in bi-parameter diagrams. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines—exact bifurcation curves. We demonstrate how the organizing centers—points corresponding to codimension-two homoclinic bifurcations—along with fold and period-doubling bifurcation curves structure the biparametric plane, thus forming macro-chaotic regions of onion bulb shapes and revealing spike-adding cascades that generate micro-chaotic structures due to the hysteresis.

Periodic orbit spectrum in terms of Ruelle-Pollicott resonances

NASA Astrophysics Data System (ADS)

Leboeuf, P.

2004-02-01

Fully chaotic Hamiltonian systems possess an infinite number of classical solutions which are periodic, e.g., a trajectory “p” returns to its initial conditions after some fixed time τp. Our aim is to investigate the spectrum {τ1,τ2,…} of periods of the periodic orbits. An explicit formula for the density ρ(τ)=∑pδ(τ-τp) is derived in terms of the eigenvalues of the classical evolution operator. The density is naturally decomposed into a smooth part plus an interferent sum over oscillatory terms. The frequencies of the oscillatory terms are given by the imaginary part of the complex eigenvalues (Ruelle-Pollicott resonances). For large periods, corrections to the well-known exponential growth of the smooth part of the density are obtained. An alternative formula for ρ(τ) in terms of the zeros and poles of the Ruelle ζ function is also discussed. The results are illustrated with the geodesic motion in billiards of constant negative curvature. Connections with the statistical properties of the corresponding quantum eigenvalues, random-matrix theory, and discrete maps are also considered. In particular, a random-matrix conjecture is proposed for the eigenvalues of the classical evolution operator of chaotic billiards.

Dynamic bifurcation and strange nonchaos in a two-frequency parametrically driven nonlinear oscillator

NASA Astrophysics Data System (ADS)

Premraj, D.; Suresh, K.; Palanivel, J.; Thamilmaran, K.

2017-09-01

A periodically forced series LCR circuit with Chua's diode as a nonlinear element exhibits slow passage through Hopf bifurcation. This slow passage leads to a delay in the Hopf bifurcation. The delay in this bifurcation is a unique quantity and it can be predicted using various numerical analysis. We find that when an additional periodic force is added to the system, the delay in bifurcation becomes chaotic which leads to an unpredictability in bifurcation delay. Further, we study the bifurcation of the periodic delay to chaotic delay in the slow passage effect through strange nonchaotic delay. We also report the occurrence of strange nonchaotic dynamics while varying the parameter of the additional force included in the system. We observe that the system exhibits a hitherto unknown dynamical transition to a strange nonchaotic attractor. With the help of Lyapunov exponent, we explain the new transition to strange nonchaotic attractor and its mechanism is studied by making use of rational approximation theory. The birth of SNA has also been confirmed numerically, using Poincaré maps, phase sensitivity exponent, the distribution of finite-time Lyapunov exponents and singular continuous spectrum analysis.

Noise, chaos, and (ɛ, τ)-entropy per unit time

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

The degree of dynamical randomness of different time processes is characterized in terms of the (ε, τ)-entropy per unit time. The (ε, τ)-entropy is the amount of information generated per unit time, at different scales τ of time and ε of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (ε, τ)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice gas automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (ε, τ)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.

Color image encryption by using Yang-Gu mixture amplitude-phase retrieval algorithm in gyrator transform domain and two-dimensional Sine logistic modulation map

NASA Astrophysics Data System (ADS)

Sui, Liansheng; Liu, Benqing; Wang, Qiang; Li, Ye; Liang, Junli

2015-12-01

A color image encryption scheme is proposed based on Yang-Gu mixture amplitude-phase retrieval algorithm and two-coupled logistic map in gyrator transform domain. First, the color plaintext image is decomposed into red, green and blue components, which are scrambled individually by three random sequences generated by using the two-dimensional Sine logistic modulation map. Second, each scrambled component is encrypted into a real-valued function with stationary white noise distribution in the iterative amplitude-phase retrieval process in the gyrator transform domain, and then three obtained functions are considered as red, green and blue channels to form the color ciphertext image. Obviously, the ciphertext image is real-valued function and more convenient for storing and transmitting. In the encryption and decryption processes, the chaotic random phase mask generated based on logistic map is employed as the phase key, which means that only the initial values are used as private key and the cryptosystem has high convenience on key management. Meanwhile, the security of the cryptosystem is enhanced greatly because of high sensitivity of the private keys. Simulation results are presented to prove the security and robustness of the proposed scheme.

Chaotic behaviour of Zeeman machines at introductory course of mechanics

NASA Astrophysics Data System (ADS)

Nagy, Péter; Tasnádi, Péter

2016-05-01

Investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics into the basic course of mechanics taught to engineering students. In the present paper it will be demonstrated that Zeeman Machine can be a versatile and motivating tool for students to get introductory knowledge about chaotic motion via interactive simulations. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple the experimental investigation and the theoretical description can be connected intuitively. Although Zeeman Machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman Machine a wide range of chaotic properties of the simple systems can be demonstrated such as bifurcation diagrams, chaotic attractors, transient chaos and so on. The main goal of this paper is the presentation of an interactive learning material for teaching the basic features of the chaotic systems through the investigation of the Zeeman Machine.

A combination chaotic system and application in color image encryption

NASA Astrophysics Data System (ADS)

Parvaz, R.; Zarebnia, M.

2018-05-01

In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

PubMed

Wang, Lipo; Li, Sa; Tian, Fuyu; Fu, Xiuju

2004-10-01

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Synchronisation and Circuit Realisation of Chaotic Hartley System

NASA Astrophysics Data System (ADS)

Varan, Metin; Akgül, Akif; Güleryüz, Emre; Serbest, Kasım

2018-06-01

Hartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

Generating random numbers by means of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-07-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the angular displacements of chaotic motion, random binary numerical arrays can be generated. To check the randomness of generated numerical arrays, the NIST Special Publication 800-20 method was adopted. As a result, it was found that all the random arrays which were generated by the chaotic motion could pass the validity criteria and some of them were even better than the quality of pseudo-random numbers generated by a computer. Through the experiments, it is demonstrated that chaotic pendulum can be used as an efficient mechanical facility in generating random numbers, and can be applied in teaching random motion to the students.

Bouncing droplets on a billiard table.

PubMed

Shirokoff, David

2013-03-01

In a set of experiments, Couder et al. demonstrate that an oscillating fluid bed may propagate a bouncing droplet through the guidance of the surface waves. I present a dynamical systems model, in the form of an iterative map, for a droplet on an oscillating bath. I examine the droplet bifurcation from bouncing to walking, and prescribe general requirements for the surface wave to support stable walking states. I show that in addition to walking, there is a region of large forcing that may support the chaotic motion of the droplet. Using the map, I then investigate the droplet trajectories in a square (billiard ball) domain. I show that in large domains, the long time trajectories are either non-periodic dense curves or approach a quasiperiodic orbit. In contrast, in small domains, at low forcing, trajectories tend to approach an array of circular attracting sets. As the forcing increases, the attracting sets break down and the droplet travels throughout space.

Bifurcations of a periodically forced microbial continuous culture model with restrained growth rate

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yuan, Qigang

2017-08-01

A three dimensional microbial continuous culture model with a restrained microbial growth rate is studied in this paper. Two types of dilution rates are considered to investigate the dynamic behaviors of the model. For the unforced system, fold bifurcation and Hopf bifurcation are detected, and numerical simulations reveal that the system undergoes degenerate Hopf bifurcation. When the system is periodically forced, bifurcation diagrams for periodic solutions of period-one and period-two are given by researching the Poincaré map, corresponding to different bifurcation cases in the unforced system. Stable and unstable quasiperiodic solutions are obtained by Neimark-Sacker bifurcation with different parameter values. Periodic solutions of various periods can occur or disappear and even change their stability, when the Poincaré map of the forced system undergoes Neimark-Sacker bifurcation, flip bifurcation, and fold bifurcation. Chaotic attractors generated by a cascade of period doublings and some phase portraits are given at last.

Research on Image Encryption Based on DNA Sequence and Chaos Theory

NASA Astrophysics Data System (ADS)

Tian Zhang, Tian; Yan, Shan Jun; Gu, Cheng Yan; Ren, Ran; Liao, Kai Xin

2018-04-01

Nowadays encryption is a common technique to protect image data from unauthorized access. In recent years, many scientists have proposed various encryption algorithms based on DNA sequence to provide a new idea for the design of image encryption algorithm. Therefore, a new method of image encryption based on DNA computing technology is proposed in this paper, whose original image is encrypted by DNA coding and 1-D logistic chaotic mapping. First, the algorithm uses two modules as the encryption key. The first module uses the real DNA sequence, and the second module is made by one-dimensional logistic chaos mapping. Secondly, the algorithm uses DNA complementary rules to encode original image, and uses the key and DNA computing technology to compute each pixel value of the original image, so as to realize the encryption of the whole image. Simulation results show that the algorithm has good encryption effect and security.

Correlation dimension and phase space contraction via extreme value theory

NASA Astrophysics Data System (ADS)

Faranda, Davide; Vaienti, Sandro

2018-04-01

We show how to obtain theoretical and numerical estimates of correlation dimension and phase space contraction by using the extreme value theory. The maxima of suitable observables sampled along the trajectory of a chaotic dynamical system converge asymptotically to classical extreme value laws where: (i) the inverse of the scale parameter gives the correlation dimension and (ii) the extremal index is associated with the rate of phase space contraction for backward iteration, which in dimension 1 and 2, is closely related to the positive Lyapunov exponent and in higher dimensions is related to the metric entropy. We call it the Dynamical Extremal Index. Numerical estimates are straightforward to obtain as they imply just a simple fit to a univariate distribution. Numerical tests range from low dimensional maps, to generalized Henon maps and climate data. The estimates of the indicators are particularly robust even with relatively short time series.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Using the small alignment index chaos indicator to characterize the vibrational dynamics of a molecular system: LiNC-LiCN.

PubMed

Benitez, P; Losada, J C; Benito, R M; Borondo, F

2015-10-01

A study of the dynamical characteristics of the phase space corresponding to the vibrations of the LiNC-LiCN molecule using an analysis based on the small alignment index (SALI) is presented. SALI is a good indicator of chaos that can easily determine whether a given trajectory is regular or chaotic regardless of the dimensionality of the system, and can also provide a wealth of dynamical information when conveniently implemented. In two-dimensional (2D) systems SALI maps are computed as 2D phase space representations, where the SALI asymptotic values are represented in color scale. We show here how these maps provide full information on the dynamical phase space structure of the LiNC-LiCN system, even quantifying numerically the volume of the different zones of chaos and regularity as a function of the molecule excitation energy.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics

PubMed Central

Cotter, C. J.

2017-01-01

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316

Chaos based video encryption using maps and Ikeda time delay system

NASA Astrophysics Data System (ADS)

Valli, D.; Ganesan, K.

2017-12-01

Chaos based cryptosystems are an efficient method to deal with improved speed and highly secured multimedia encryption because of its elegant features, such as randomness, mixing, ergodicity, sensitivity to initial conditions and control parameters. In this paper, two chaos based cryptosystems are proposed: one is the higher-dimensional 12D chaotic map and the other is based on the Ikeda delay differential equation (DDE) suitable for designing a real-time secure symmetric video encryption scheme. These encryption schemes employ a substitution box (S-box) to diffuse the relationship between pixels of plain video and cipher video along with the diffusion of current input pixel with the previous cipher pixel, called cipher block chaining (CBC). The proposed method enhances the robustness against statistical, differential and chosen/known plain text attacks. Detailed analysis is carried out in this paper to demonstrate the security and uniqueness of the proposed scheme.

Statistical properties of bidimensional patterns generated from delayed and extended maps

NASA Astrophysics Data System (ADS)

Giacomelli, Giovanni; Lepri, Stefano; Politi, Antonio

1995-05-01

The space-time chaotic patterns associated with a class of dynamical systems ranging from delayed to extended maps are investigated. All the systems are constructed in such a way that the corresponding two-dimensional (2D) representation is characterized by the same updating rule in the bulk. The main difference among them is the direction of the ``time'' axis in the plane. Despite the different causality relations among the various models, the resulting patterns are shown to be statistically equivalent. In particular, the Kolmogorov-Sinai entropy density assumes always the same value. Therefore, it can be considered as an absolute indicator, measuring the amount of disorder of a 2D pattern. The Kaplan-Yorke dimension density is instead rule dependent: this indicator alone cannot be used to quantify the degrees of freedom of a given pattern; one must further specify the direction of propagation in the plane.

Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

2018-05-01

We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

Synchronization and an application of a novel fractional order King Cobra chaotic system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com; Ratnavelu, K., E-mail: kuru052001@gmail.com

2014-09-01

In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness ofmore » the proposed theoretical results.« less

Analytically solvable chaotic oscillator based on a first-order filter.

PubMed

Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N

2016-02-01

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

Analytically solvable chaotic oscillator based on a first-order filter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N.

2016-02-15

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform formore » any stable infinite-impulse response filter is chaotic.« less

A new 4D chaotic system with hidden attractor and its engineering applications: Analog circuit design and field programmable gate array implementation

NASA Astrophysics Data System (ADS)

Abdolmohammadi, Hamid Reza; Khalaf, Abdul Jalil M.; Panahi, Shirin; Rajagopal, Karthikeyan; Pham, Viet-Thanh; Jafari, Sajad

2018-06-01

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper, a new 4D chaotic system is proposed. This new chaotic system has no equilibria, and so it belongs to the category of systems with hidden attractors. Dynamical features of this system are investigated with the help of its state-space portraits, bifurcation diagram, Lyapunov exponents diagram, and basin of attraction. Also a hardware realisation of this system is proposed by using field programmable gate arrays (FPGA). In addition, an electronic circuit design for the chaotic system is introduced.

Chaotic ultra-wideband radio generator based on an optoelectronic oscillator with a built-in microwave photonic filter.

PubMed

Wang, Li Xian; Zhu, Ning Hua; Zheng, Jian Yu; Liu, Jian Guo; Li, Wei

2012-05-20

We induce a microwave photonic bandpass filter into an optoelectronic oscillator to generate a chaotic ultra-wideband signal in both the optical and electrical domain. The theoretical analysis and numerical simulation indicate that this system is capable of generating band-limited high-dimensional chaos. Experimental results coincide well with the theoretical prediction and show that the power spectrum of the generated chaotic signal basically meets the Federal Communications Commission indoor mask. The generated chaotic carrier is further intensity modulated by a 10 MHz square wave, and the waveform of the output ultra-wideband signal is measured for demonstrating the chaotic on-off keying modulation.

The chaotic saddle of a three degrees of freedom scattering system reconstructed from cross-section data

NASA Astrophysics Data System (ADS)

Drótos, G.; Jung, C.

2016-06-01

The topic of this paper is hyperbolic chaotic scattering in a three degrees of freedom system. We generalize how shadows in the domain of the doubly differential cross-section are found: they are traced out by the appropriately filtered unstable manifolds of the periodic trajectories in the chaotic saddle. These shadows are related to the rainbow singularities in the doubly differential cross-section. As a result of this relation, we discover a method of how to recognize in the cross section a smoothly deformed image of the chaotic saddle, allowing the reconstruction of the symbolic dynamics of the chaotic saddle, its topology and its scaling factors.

A new transiently chaotic flow with ellipsoid equilibria

NASA Astrophysics Data System (ADS)

Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

2018-03-01

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

NASA Astrophysics Data System (ADS)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

Correlation Plenoptic Imaging.

PubMed

D'Angelo, Milena; Pepe, Francesco V; Garuccio, Augusto; Scarcelli, Giuliano

2016-06-03

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable three-dimensional imaging in a single shot. However, in standard plenoptic imaging systems, the maximum spatial and angular resolutions are fundamentally linked; thereby, the maximum achievable depth of field is inversely proportional to the spatial resolution. We propose to take advantage of the second-order correlation properties of light to overcome this fundamental limitation. In this Letter, we demonstrate that the correlation in both momentum and position of chaotic light leads to the enhanced refocusing power of correlation plenoptic imaging with respect to standard plenoptic imaging.

Correlation Plenoptic Imaging

NASA Astrophysics Data System (ADS)

D'Angelo, Milena; Pepe, Francesco V.; Garuccio, Augusto; Scarcelli, Giuliano

2016-06-01

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable three-dimensional imaging in a single shot. However, in standard plenoptic imaging systems, the maximum spatial and angular resolutions are fundamentally linked; thereby, the maximum achievable depth of field is inversely proportional to the spatial resolution. We propose to take advantage of the second-order correlation properties of light to overcome this fundamental limitation. In this Letter, we demonstrate that the correlation in both momentum and position of chaotic light leads to the enhanced refocusing power of correlation plenoptic imaging with respect to standard plenoptic imaging.

Using periodic orbits to compute chaotic transport rates between resonance zones.

PubMed

Sattari, Sulimon; Mitchell, Kevin A

2017-11-01

Transport properties of chaotic systems are computable from data extracted from periodic orbits. Given a sufficient number of periodic orbits, the escape rate can be computed using the spectral determinant, a function that incorporates the eigenvalues and periods of periodic orbits. The escape rate computed from periodic orbits converges to the true value as more and more periodic orbits are included. Escape from a given region of phase space can be computed by considering only periodic orbits that lie within the region. An accurate symbolic dynamics along with a corresponding partitioning of phase space is useful for systematically obtaining all periodic orbits up to a given period, to ensure that no important periodic orbits are missing in the computation. Homotopic lobe dynamics (HLD) is an automated technique for computing accurate partitions and symbolic dynamics for maps using the topological forcing of intersections of stable and unstable manifolds of a few periodic anchor orbits. In this study, we apply the HLD technique to compute symbolic dynamics and periodic orbits, which are then used to find escape rates from different regions of phase space for the Hénon map. We focus on computing escape rates in parameter ranges spanning hyperbolic plateaus, which are parameter intervals where the dynamics is hyperbolic and the symbolic dynamics does not change. After the periodic orbits are computed for a single parameter value within a hyperbolic plateau, periodic orbit continuation is used to compute periodic orbits over an interval that spans the hyperbolic plateau. The escape rates computed from a few thousand periodic orbits agree with escape rates computed from Monte Carlo simulations requiring hundreds of billions of orbits.

A Locally Optimal Algorithm for Estimating a Generating Partition from an Observed Time Series and Its Application to Anomaly Detection.

PubMed

Ghalyan, Najah F; Miller, David J; Ray, Asok

2018-06-12

Estimation of a generating partition is critical for symbolization of measurements from discrete-time dynamical systems, where a sequence of symbols from a (finite-cardinality) alphabet may uniquely specify the underlying time series. Such symbolization is useful for computing measures (e.g., Kolmogorov-Sinai entropy) to identify or characterize the (possibly unknown) dynamical system. It is also useful for time series classification and anomaly detection. The seminal work of Hirata, Judd, and Kilminster (2004) derives a novel objective function, akin to a clustering objective, that measures the discrepancy between a set of reconstruction values and the points from the time series. They cast estimation of a generating partition via the minimization of their objective function. Unfortunately, their proposed algorithm is nonconvergent, with no guarantee of finding even locally optimal solutions with respect to their objective. The difficulty is a heuristic-nearest neighbor symbol assignment step. Alternatively, we develop a novel, locally optimal algorithm for their objective. We apply iterative nearest-neighbor symbol assignments with guaranteed discrepancy descent, by which joint, locally optimal symbolization of the entire time series is achieved. While most previous approaches frame generating partition estimation as a state-space partitioning problem, we recognize that minimizing the Hirata et al. (2004) objective function does not induce an explicit partitioning of the state space, but rather the space consisting of the entire time series (effectively, clustering in a (countably) infinite-dimensional space). Our approach also amounts to a novel type of sliding block lossy source coding. Improvement, with respect to several measures, is demonstrated over popular methods for symbolizing chaotic maps. We also apply our approach to time-series anomaly detection, considering both chaotic maps and failure application in a polycrystalline alloy material.

Institution Morphisms

NASA Technical Reports Server (NTRS)

Goguen, Joseph; Rosu, Grigore; Norvig, Peter (Technical Monitor)

2001-01-01

Institutions formalize the intuitive notion of logical system, including both syntax and semantics. A surprising number of different notions of morphisim have been suggested for forming categories with institutions as objects, and a surprising variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is both uniform and informative to replace the current rather chaotic nomenclature. Another goal is to investigate the properties and interrelations of these notions. Following brief expositions of indexed categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the 'plain maps' of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories; because of this duality, we prefer the name 'comorphism' over 'plain map.' We next consider 'theoroidal' morphisms and comorphisims, which generalize signatures to theories, finding that the 'maps' of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We then introduce 'forward' and 'semi-natural' morphisms, and appendices discuss institutions for hidden algebra, universal algebra, partial equational logic, and a variant of order sorted algebra supporting partiality.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olmi, Simona, E-mail: simona.olmi@fi.isc.cnr.it; INFN Sez. Firenze, via Sansone, 1 - I-50019 Sesto Fiorentino

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaoticmore » but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.« less

Synchronization of Chaotic Systems without Direct Connections Using Reinforcement Learning

NASA Astrophysics Data System (ADS)

Sato, Norihisa; Adachi, Masaharu

In this paper, we propose a control method for the synchronization of chaotic systems that does not require the systems to be connected, unlike existing methods such as that proposed by Pecora and Carroll in 1990. The method is based on the reinforcement learning algorithm. We apply our method to two discrete-time chaotic systems with mismatched parameters and achieve M step delay synchronization. Moreover, we extend the proposed method to the synchronization of continuous-time chaotic systems.

Multiswitching combination synchronisation of non-identical fractional-order chaotic systems

NASA Astrophysics Data System (ADS)

Bhat, Muzaffar Ahmad; Khan, Ayub

2018-06-01

In this paper, multiswitching combination synchronisation (MSCS) scheme has been investigated in a class of three non-identical fractional-order chaotic systems. The fractional-order Lorenz and Chen systems are taken as the drive systems. The combination of multidrive systems is then synchronised with the fractional-order Lü chaotic system. In MSCS, the state variables of the two drive systems synchronise with different state variables of the response system, simultaneously. Based on the stability of fractional-order chaotic systems, the MSCS of three fractional-order non-identical systems has been investigated. For the synchronisation of three non-identical fractional-order chaotic systems, suitable controllers have been designed. Theoretical analysis and numerical results are presented to demonstrate the validity and feasibility of the applied method.

Stability of uncertain impulsive complex-variable chaotic systems with time-varying delays.

PubMed

Zheng, Song

2015-09-01

In this paper, the robust exponential stabilization of uncertain impulsive complex-variable chaotic delayed systems is considered with parameters perturbation and delayed impulses. It is assumed that the considered complex-variable chaotic systems have bounded parametric uncertainties together with the state variables on the impulses related to the time-varying delays. Based on the theories of adaptive control and impulsive control, some less conservative and easily verified stability criteria are established for a class of complex-variable chaotic delayed systems with delayed impulses. Some numerical simulations are given to validate the effectiveness of the proposed criteria of impulsive stabilization for uncertain complex-variable chaotic delayed systems. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

The chaotic set and the cross section for chaotic scattering in three degrees of freedom

NASA Astrophysics Data System (ADS)

Jung, C.; Merlo, O.; Seligman, T. H.; Zapfe, W. P. K.

2010-10-01

This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.

Synchronization of chaotic systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pecora, Louis M.; Carroll, Thomas L.

2015-09-15

We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years tomore » a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.« less

Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework.

PubMed

Kwok, T; Smith, K A

2000-09-01

The aim of this paper is to study both the theoretical and experimental properties of chaotic neural network (CNN) models for solving combinatorial optimization problems. Previously we have proposed a unifying framework which encompasses the three main model types, namely, Chen and Aihara's chaotic simulated annealing (CSA) with decaying self-coupling, Wang and Smith's CSA with decaying timestep, and the Hopfield network with chaotic noise. Each of these models can be represented as a special case under the framework for certain conditions. This paper combines the framework with experimental results to provide new insights into the effect of the chaotic neurodynamics of each model. By solving the N-queen problem of various sizes with computer simulations, the CNN models are compared in different parameter spaces, with optimization performance measured in terms of feasibility, efficiency, robustness and scalability. Furthermore, characteristic chaotic neurodynamics crucial to effective optimization are identified, together with a guide to choosing the corresponding model parameters.

A new chaotic communication scheme based on adaptive synchronization.

PubMed

Xiang-Jun, Wu

2006-12-01

A new chaotic communication scheme using adaptive synchronization technique of two unified chaotic systems is proposed. Different from the existing secure communication methods, the transmitted signal is modulated into the parameter of chaotic systems. The adaptive synchronization technique is used to synchronize two identical chaotic systems embedded in the transmitter and the receiver. It is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical unified chaotic systems with unknown system parameters asymptotically synchronized; thus the parameter of the receiver system is identified. Then the recovery of the original information signal in the receiver is successfully achieved on the basis of the estimated parameter. It is noticed that the time required for recovering the information signal and the accuracy of the recovered signal very sensitively depends on the frequency of the information signal. Numerical results have verified the effectiveness of the proposed scheme.

Chaotic carrier pulse position modulation communication system and method

DOEpatents

Abarbanel, Henry D. I.; Larson, Lawrence E.; Rulkov, Nikolai F.; Sushchik, Mikhail M.; Tsimring, Lev S.; Volkovskii, Alexander R.

2001-01-01

A chaotic carrier pulse position modulation communication system and method is disclosed. The system includes a transmitter and receiver having matched chaotic pulse regenerators. The chaotic pulse regenerator in the receiver produces a synchronized replica of a chaotic pulse train generated by the regenerator in the transmitter. The pulse train from the transmitter can therefore act as a carrier signal. Data is encoded by the transmitter through selectively altering the interpulse timing between pulses in the chaotic pulse train. The altered pulse train is transmitted as a pulse signal. The receiver can detect whether a particular interpulse interval in the pulse signal has been altered by reference to the synchronized replica it generates, and can therefore detect the data transmitted by the receiver. Preferably, the receiver predicts the earliest moment in time it can expect a next pulse after observation of at least two consecutive pulses. It then decodes the pulse signal beginning at a short time before expected arrival of a pulse.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2018-03-01

Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Authenticity and privacy of a team of mini-UAVs by means of nonlinear recursive shuffling

NASA Astrophysics Data System (ADS)

Szu, Harold; Hsu, Ming-Kai; Baier, Patrick; Lee, Ting N.; Buss, James R.; Madan, Rabinder N.

2006-04-01

We have developed a real-time EOIR video counter-jittering sub-pixel image correction algorithm for a single mini- Unmanned Air Vehicle (m-UAV) for surveillance and communication (Szu et al. SPIE Proc. V 5439 5439, pp.183-197, April 12, 2004). In this paper, we wish to plan and execute the next challenge---- a team of m-UAVs. The minimum unit for a robust chain saw communication must have the connectivity of five second-nearest-neighbor members with a sliding, arbitrary center. The team members require an authenticity check (AC) among a unit of five, in order to carry out a jittering mosaic image processing (JMIP) on-board for every m-UAV without gimbals. The JMIP does not use any NSA security protocol ("cardinal rule: no-man, no-NSA codec"). Besides team flight dynamics (Szu et al "Nanotech applied to aerospace and aeronautics: swarming,' AIAA 2005-6933 Sept 26-29 2005), several new modules: AOA, AAM, DSK, AC, FPGA are designed, and the JMIP must develop their own control, command and communication system, safeguarded by the authenticity and privacy checks presented in this paper. We propose a Nonlinear Invertible (deck of card) Shuffler (NIS) algorithm, which has a Feistel structure similar to the Data Encryption Standard (DES) developed by Feistel et. al. at IBM in the 1970's; but DES is modified here by a set of chaotic dynamical shuffler Key (DSK), as re-computable lookup tables generated by every on-board Chaotic Neural Network (CNN). The initializations of CNN are periodically provided by the private version of RSA from the ground control to team members to avoid any inadvertent failure of broken chain among m-UAVs. Efficient utilization of communication bandwidth is necessary for a constantly moving and jittering m-UAV platform, e.g. the wireless LAN protocol wastes the bandwidth due to a constant need of hand-shaking procedures (as demonstrated by NRL; though sensible for PCs and 3 rd gen. mobile phones). Thus, the chaotic DSK must be embedded in a fault-tolerant Neural Network Associative Memory for the error-resilientconcealment mosaic image chip re-sent. However, the RSA public and private keys, chaos typing and initial value are given on set or sent to each m-UAV so that each platform knows only its private key. AC among 5 team members are possible using a reverse RSA protocol. A hashed image chip is coded by the sender's private key and nobody else knows in order to send to it to neighbors and the receiver can check the content by using the senders public key and compared the decrypted result with on-board image chips. We discover a fundamental problem of digital chaos approach in a finite state machine, of which a fallacy test of a discrete version is needed for a finite number of bits, as James Yorke advocated early. Thus, our proposed chaotic NIS for bits stream protection becomes desirable to further mixing the digital CNN outputs. The fault tolerance and the parallelism of Artificial Neural Network Associative Memory are necessary attributes for the neighborhood smoothness image restoration. The associated computational cost of O(N2) deems to be worthy, because the Chaotic version CNN of N-D can further provide the privacy only for the lost image chip (N=8x8) re-sent requested by its neighbors and the result is better performed than a simple 1-D logistic map. We gave a preliminary design of low end of FPGA firmware that to compute all on board seemed to be possible.

Rank One Strange Attractors in Periodically Kicked Predator-Prey System with Time-Delay

NASA Astrophysics Data System (ADS)

Yang, Wenjie; Lin, Yiping; Dai, Yunxian; Zhao, Huitao

2016-06-01

This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator-prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator-prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.

Error function attack of chaos synchronization based encryption schemes.

PubMed

Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu

2004-03-01

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.

Experimental study of the dynamics of a ruby laser pumped by a CW argon-ion laser

NASA Technical Reports Server (NTRS)

Afzal, R. S.; Lin, W. P.; Lawandy, N. M.

1989-01-01

A study of the dynamics of a ruby laser pumped by a CW argon-ion laser is presented. The ruby laser is predominantly stable but has two accessible unstable states. One state exhibits chaotic output, while the other results in regular self-pulsing. The conditions needed for instability are discussed and homodyne spectra and temporal maps of the phase-space attractors are obtained. In addition, a numerical simulation of nonlinear beam propagation in ruby is presented that shows that strong deviations from plane-wave behavior exist, and that transverse effects must be incorporated into theoretical models of the instability.

Experimental observation of Lorenz chaos in the Quincke rotor dynamics.

PubMed

Peters, François; Lobry, Laurent; Lemaire, Elisabeth

2005-03-01

In this paper, we report experimental evidence of Lorenz chaos for the Quincke rotor dynamics. We study the angular motion of an insulating cylinder immersed in slightly conducting oil and submitted to a direct current electric field. The simple equations which describe the dynamics of the rotor are shown to be equivalent to the Lorenz equations. In particular, we observe two bifurcations in our experimental system. Above a critical value of the electric field, the cylinder rotates at a constant rate. At a second bifurcation, the system becomes chaotic. The characteristic shape of the experimental first return map provides strong evidence for Lorenz-type chaos.

Experimental observation of Lorenz chaos in the Quincke rotor dynamics

NASA Astrophysics Data System (ADS)

Peters, François; Lobry, Laurent; Lemaire, Elisabeth

2005-03-01

In this paper, we report experimental evidence of Lorenz chaos for the Quincke rotor dynamics. We study the angular motion of an insulating cylinder immersed in slightly conducting oil and submitted to a direct current electric field. The simple equations which describe the dynamics of the rotor are shown to be equivalent to the Lorenz equations. In particular, we observe two bifurcations in our experimental system. Above a critical value of the electric field, the cylinder rotates at a constant rate. At a second bifurcation, the system becomes chaotic. The characteristic shape of the experimental first return map provides strong evidence for Lorenz-type chaos.

A Novel Image Encryption Algorithm Based on DNA Subsequence Operation

PubMed Central

Zhang, Qiang; Xue, Xianglian; Wei, Xiaopeng

2012-01-01

We present a novel image encryption algorithm based on DNA subsequence operation. Different from the traditional DNA encryption methods, our algorithm does not use complex biological operation but just uses the idea of DNA subsequence operations (such as elongation operation, truncation operation, deletion operation, etc.) combining with the logistic chaotic map to scramble the location and the value of pixel points from the image. The experimental results and security analysis show that the proposed algorithm is easy to be implemented, can get good encryption effect, has a wide secret key's space, strong sensitivity to secret key, and has the abilities of resisting exhaustive attack and statistic attack. PMID:23093912

CrowdMapping: A Crowdsourcing-Based Terminology Mapping Method for Medical Data Standardization.

PubMed

Mao, Huajian; Chi, Chenyang; Huang, Boyu; Meng, Haibin; Yu, Jinghui; Zhao, Dongsheng

2017-01-01

Standardized terminology is the prerequisite of data exchange in analysis of clinical processes. However, data from different electronic health record systems are based on idiosyncratic terminology systems, especially when the data is from different hospitals and healthcare organizations. Terminology standardization is necessary for the medical data analysis. We propose a crowdsourcing-based terminology mapping method, CrowdMapping, to standardize the terminology in medical data. CrowdMapping uses a confidential model to determine how terminologies are mapped to a standard system, like ICD-10. The model uses mappings from different health care organizations and evaluates the diversity of the mapping to determine a more sophisticated mapping rule. Further, the CrowdMapping model enables users to rate the mapping result and interact with the model evaluation. CrowdMapping is a work-in-progress system, we present initial results mapping terminologies.

Computations of Chaotic Flows in Micromixers

DTIC Science & Technology

2005-01-01

2005 2. REPORT TYPE 3. DATES COVERED 00-00-2005 to 00-00-2005 4. TITLE AND SUBTITLE Computations of Chaotic Flows in Micromixers 5a. CONTRACT...Std Z39-18 215simulation, computing, and modeling 2005 NRL Review Computations of Chaotic Flows In Micromixers FIGURE 6 Schematic of staggered

Chaos in Atomic Force Microscopy

NASA Astrophysics Data System (ADS)

Hu, Shuiqing; Raman, Arvind

2006-01-01

Chaotic oscillations of microcantilever tips in dynamic atomic force microscopy (AFM) are reported and characterized. Systematic experiments performed using a variety of microcantilevers under a wide range of operating conditions indicate that softer AFM microcantilevers bifurcate from periodic to chaotic oscillations near the transition from the noncontact to the tapping regimes. Careful Lyapunov exponent and noise titration calculations of the tip oscillation data confirm their chaotic nature. AFM images taken by scanning the chaotically oscillating tips over the sample show small, but significant metrology errors at the nanoscale due to this “deterministic” uncertainty.

Simple Chaotic Flow with Circle and Square Equilibrium

NASA Astrophysics Data System (ADS)

Gotthans, Tomas; Sprott, Julien Clinton; Petrzela, Jiri

Simple systems of third-order autonomous nonlinear differential equations can exhibit chaotic behavior. In this paper, we present a new class of chaotic flow with a square-shaped equilibrium. This unique property has apparently not yet been described. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are interesting and important in engineering applications. The mathematical model is accompanied by an electrical circuit implementation, demonstrating structural stability of the strange attractor. The circuit is simulated with PSpice, constructed, and analyzed (measured).

Chaos enhancing tunneling in a coupled Bose-Einstein condensate with a double driving.

PubMed

Rong, Shiguang; Hai, Wenhua; Xie, Qiongtao; Zhu, Qianquan

2009-09-01

We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.

Identical synchronization of chaotic secure communication systems with channel induced coherence resonance

NASA Astrophysics Data System (ADS)

Sepantaie, Marc M.; Namazi, Nader M.; Sepantaie, Amir M.

2016-05-01

This paper is devoted to addressing the synchronization, and detection of random binary data exposed to inherent channel variations existing in Free Space Optical (FSO) communication systems. This task is achieved by utilizing the identical synchronization methodology of Lorenz chaotic communication system, and its synergetic interaction in adversities imposed by the FSO channel. Moreover, the Lorenz system has been analyzed, and revealed to induce Stochastic Resonance (SR) once exposed to Additive White Gaussian Noise (AWGN). In particular, the resiliency of the Lorenz chaotic system, in light of channel adversities, has been attributed to the success of the proposed communication system. Furthermore, this paper advocates the use of Haar wavelet transform for enhanced detection capability of the proposed chaotic communication system, which utilizes Chaotic Parameter Modulation (CPM) technique for means of transmission.

Wavelet threshold method of resolving noise interference in periodic short-impulse signals chaotic detection

NASA Astrophysics Data System (ADS)

Deng, Ke; Zhang, Lu; Luo, Mao-Kang

2010-03-01

The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscillator detection system cannot guarantee the immunity to noises (even white noise). In fact the randomness of noises has a serious or even a destructive effect on the detection results in many cases. To solve this problem, we present a new detecting method based on wavelet threshold processing that can detect the chaotic weak signal accompanied with noise. All theoretical analyses and simulation experiments indicate that the new method reduces the noise interferences to detection significantly, thereby making the corresponding chaotic oscillator that detects the weak signals accompanied with noises more stable and reliable.