TESIS experiment on XUV imaging spectroscopy of the Sun onboard the CORONAS-PHOTON satellite

NASA Astrophysics Data System (ADS)

Kuzin, S. V.; Zhitnik, I. A.; Bogachev, S. A.; Shestov, S. V.; Bugaenko, O. I.; Suhodrev, N. K.; Pertsov, A. A.; Mitrofanov, A. V.; Ignat'ev, A. P.; Slemzin, V. A.

We present a brief description of new complex of space telescopes and spectrographs, TESIS, which will be placed aboard the CORONAS-PHOTON satellite. The complex is intended for high-resolution imaging observation of full Sun in the coronal spectral lines and in the spectral lines of the solar transition region. TESIS will be launched at the end of 2007 - early of 2008. About 25 % of the daily TESIS images will be free for use and for downloading from the TESIS data center that is planned to open 2 months before the TESIS launching at http://www.tesis.lebedev.ru

The good leader.

PubMed

Bottles, K

2001-01-01

What are the traits of successful leaders and can they be applied to those of us in health care? Leaders must deal with conflict to get a group of people to move in the same direction. Successful leaders learn to have difficult conversations that increase understanding and morale and creatively deal with the inevitable interpersonal conflicts present in every organization made up of people. Another useful trait for a leader during uncertain and chaotic times is the ability to see things as they really are, rather than as we wish or believe them to be. Successful leaders are also usually optimists who level with their co-workers.

Stochastic epidemic outbreaks: why epidemics are like lasers

NASA Astrophysics Data System (ADS)

Schwartz, Ira B.; Billings, Lora

2004-05-01

Many diseases, such as childhood diseases, dengue fever, and West Nile virus, appear to oscillate randomly as a function of seasonal environmental or social changes. Such oscillations appear to have a chaotic bursting character, although it is still uncertain how much is due to random fluctuations. Such bursting in the presence of noise is also observed in driven lasers. In this talk, I will show how noise can excite random outbreaks in simple models of seasonally driven outbreaks, as well as lasers. The models for both population dynamics will be shown to share the same class of underlying topology, which plays a major role in the cause of observed stochastic bursting.

Adaptative synchronization in multi-output fractional-order complex dynamical networks and secure communications

NASA Astrophysics Data System (ADS)

Mata-Machuca, Juan L.; Aguilar-López, Ricardo

2018-01-01

This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.

Identification of Targets for Prevention of Peritoneal Catheter Tunnel and Exit-Site Infections in Low Incidence Settings.

PubMed

Santos, Clara; Pérez-Fontán, Miguel; Rodríguez-Carmona, Ana; Calvo-Rodríguez, María; López-Muñiz, Andrés; López-Calviño, Beatriz; García-Falcón, Teresa

2016-01-01

♦ Peritoneal catheter tunnel and exit-site infection (TESI) complicates the clinical course of peritoneal dialysis (PD) patients. Adherence to recommendations for catheter insertion, exit-site care, and management of Staphylococcus aureus (SAu) carriage reduces, but does not abrogate the risk of these infections. ♦ To reappraise the risk profile for TESI in an experienced center with a long-term focus on management of SAu carriage and a low incidence of these infections. ♦ Following a retrospective, observational design, we investigated 665 patients incident on PD. The main study variable was survival to the first episode of TESI. We considered selected demographic, clinical, and technical variables, applying multivariate strategies of analysis. ♦ The overall incidence of TESI was 1 episode/68.5 patient-months. Staphylococcus aureus carriage disclosed at inception of PD (but not if observed sporadically during follow-up) (hazard ratio [HR] 1.53, p = 0.009), PD started shortly after catheter insertion (HR 0.98 per day, p = 0.011), PD after kidney transplant failure (HR 2.18, p = 0.017), lower hemoglobin levels (HR 0.88 per g/dL, p = 0.013) and fast peritoneal transport rates (HR 2.92, p = 0.03) portended an increased risk of TESI. Delaying PD ≥ 30 days after catheter insertion markedly improved the probability of TESI. Carriage of methicillin-resistant SAu since the start of PD was associated with a high incidence of TESI by these bacteria. On the contrary, resistance to mupirocin did not predict such a risk, probably due to the use of an alternative regime in affected patients. ♦ Adherence to current recommendations results in a low incidence of TESI in PD patients. Interventions on specific risk subsets have a potential to bring incidence close to negligible levels. Despite systematic screening and management, SAu carriage is still a predictor of TESI. Antibiotic susceptibility patterns may help to refine stratification of the risk of TESI by these bacteria. Early insertion of the peritoneal catheter should be considered whenever possible, to reduce the risk of later TESI. Copyright © 2016 International Society for Peritoneal Dialysis.

Transforaminal epidural steroid injections followed by mechanical diagnosis and therapy to prevent surgery for lumbar disc herniation.

PubMed

van Helvoirt, Hans; Apeldoorn, Adri T; Ostelo, Raymond W; Knol, Dirk L; Arts, Mark P; Kamper, Steven J; van Tulder, Maurits W

2014-07-01

Prospective cohort study. To report the clinical course of patients with MRI-confirmed lumbar disc herniation-related radicular noncentralizing pain who received transforaminal epidural steroid injections (TESIs) and mechanical diagnosis and therapy (MDT). Noncentralizing symptoms in patients with lumbar disc herniation are associated with poor outcome. Commonly used treatments for these patients include TESIs and MDT. No study has evaluated the outcome of combining both strategies. Consecutive candidates for herniated lumbar disc surgery with noncentralizing chronic pain were eligible. Patients received TESIs followed by MDT. The primary outcomes were pain severity in the leg, disability (Roland-Morris Disability Questionnaire for Sciatica), and global perceived effect (GPE). Outcomes were measured at baseline, discharge, and 12 months. Linear mixed-models and McNemar's tests were used to analyze outcome data. Sixty-nine patients receive TESIs. After TESIs, symptoms were resolved completely in 11 patients (16%). In these patients, symptom resolution was maintained at 12 months. A second subgroup of 32 patients (46%) reported significantly less pain after TESIs and showed centralization with MDT reassessment (significant reductions in leg pain and disability [P < 0.001]) and a satisfaction rate of 90% at 12 months. A third subgroup of 11 patients (16%) reported significantly less pain after TESIs but still showed noncentralization with MDT reassessment (significant reductions in leg pain and disability [P < 0.05] and a satisfaction rate of 50% at 12 months). A fourth subgroup of 15 patients (22%) did not respond on TESIs and received an operative intervention. The results indicate that a course of TESIs followed by MDT may be able to avoid surgery in a substantial proportion of candidates for herniated lumbar disc surgery. Wiley Periodicals, Inc.

High-cadence observations of CME initiation and plasma dynamics in the corona with TESIS on board CORONAS-Photon

NASA Astrophysics Data System (ADS)

Bogachev, Sergey; Kuzin, Sergey; Zhitnik, I. A.; Bugaenko, O. I.; Goncharov, A. L.; Ignatyev, A. P.; Krutov, V. V.; Lomkova, V. M.; Mitrofanov, A. V.; Nasonkina, T. P.; Oparin, S. N.; Petzov, A. A.; Shestov, S. V.; Slemzin, V. A.; Soloviev, V. A.; Suhodrev, N. K.; Shergina, T. A.

The TESIS is an ensemble of space instruments designed in Lebedev Institute of Russian Academy of Sciences for spectroscopic and imaging investigation of the Sun in EUV and soft X-ray spectral range with high spatial, temporal and spectral resolution. From 2009 January, when TESIS was launched onboard the Coronas-Photon satellite, it provided about 200 000 new images and spectra of the Sun, obtained during one of the deepest solar minimum in last century. Because of the wide field of view (4 solar radii) and high sensitivity, TESIS provided high-quality data on the origin and dynamics of eruptive prominences and CMEs in the low and intermediate solar corona. TESIS is also the first EUV instrument which provided high-cadence observations of coronal bright points and solar spicules with temporal resolution of a few seconds. We present first results of TESIS observations and discuss them from a scientific point of view.

Country watch: Nicaragua.

PubMed

Pauw, J

1999-01-01

The Association of Workers for Education, Health and Social Integration (TESIS) works with commercial sex workers to control HIV and sexually transmitted diseases in Nicaragua through free condom distribution and education. Education includes group work, individual counseling, and demonstrations of correct condom use. Condoms are also distributed to the motels frequented by commercial sex workers. When the Condom Social Marketing (CSM) project in Central America started, it sold condoms of the same quality as the ones offered by TESIS; thus the condom donors reduced their donations, and in turn, TESIS lost its normal quota for free condom distribution. Because of this situation, TESIS dealt with a condom promotion scheme at a lower cost for the poorest women. Condom quality did not deteriorate as products only came with simpler packaging. TESIS fills the gap which CSM missed.

Stochastic Epidemic Outbreaks, or Why Epidemics Behave Like Lasers

NASA Astrophysics Data System (ADS)

Schwartz, Ira; Billings, Lora; Bollt, Erik; Carr, Thomas

2004-03-01

Many diseases, such childhood diseases, dengue fever, and West Nile virus, appear to oscillate randomly as a function of seasonal environmental or social changes. Such oscillations appear to have a chaotic bursting character, although it is still uncertain how much is due to random fluctuations. Such bursting in the presence of noise is also observed in driven lasers. In this talk, I will show how noise can excite random outbreaks in simple models of seasonally driven outbreaks, as well as lasers. The models for both population dynamics will be shown to share the same class of underlying topology, which plays a major role in the cause of observed stochastic bursting. New tools for predicting stcohastic outbreaks will be presented.

Robust Adaptive Synchronization of Ring Configured Uncertain Chaotic FitzHugh–Nagumo Neurons under Direction-Dependent Coupling

PubMed Central

Iqbal, Muhammad; Rehan, Muhammad; Hong, Keum-Shik

2018-01-01

This paper exploits the dynamical modeling, behavior analysis, and synchronization of a network of four different FitzHugh–Nagumo (FHN) neurons with unknown parameters linked in a ring configuration under direction-dependent coupling. The main purpose is to investigate a robust adaptive control law for the synchronization of uncertain and perturbed neurons, communicating in a medium of bidirectional coupling. The neurons are assumed to be different and interconnected in a ring structure. The strength of the gap junctions is taken to be different for each link in the network, owing to the inter-neuronal coupling medium properties. Robust adaptive control mechanism based on Lyapunov stability analysis is employed and theoretical criteria are derived to realize the synchronization of the network of four FHN neurons in a ring form with unknown parameters under direction-dependent coupling and disturbances. The proposed scheme for synchronization of dissimilar neurons, under external electrical stimuli, coupled in a ring communication topology, having all parameters unknown, and subject to directional coupling medium and perturbations, is addressed for the first time as per our knowledge. To demonstrate the efficacy of the proposed strategy, simulation results are provided. PMID:29535622

The EUV-observatory TESIS on board Coronas-Photon: scientific goals and initial plan of observations

NASA Astrophysics Data System (ADS)

Bogachev, Sergey

The TESIS a EUV-observatory for solar research from space will be launched in 2008 September on board the satellite Coronas-Photon from cosmodrome Plesetsk. TESIS is a project of Lebedev Physical Institute of Russian Academy of Science with contribution from Space Research Center of Polish Academy of Science (the spectrometer SphinX). The experiment will focus on quasi-monochromatic imaging of the Sun and XUV spectroscopy of solar plasma. The scientific payload of TESIS contains five instruments: (1) Bragg crystal spectroheliometer for Sun monochromatic imaging in the line MgXII 8.42 A, (2) the normal-incidence Herschelian EUV telescopes with a resolution of 1.7 arc sec operated in lines FeXXII 133 A, FeIX 171 A and HeII 304 A, (3) the EUV imaging spectrometer, (4) the wide-field Ritchey-Chretien coronograph and (5) the X-ray spectrometer SphinX. The TESIS will focus on coordinated study of solar activity from the transition region to the outer corona up to 4 solar radii in wide temperature range from 5*104 to 2*107 K. We describe the scientific goals of the TESIS and its initial plan of observations.

Chaos control for the output-constrained system by using adaptive dynamic surface technology and application to the brushless DC motor

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

Luo, Shaohua, E-mail: hua66com@163.com; School of Automation, Chongqing University, Chongqing 400044; Hou, Zhiwei

2015-12-15

In this paper, chaos control is proposed for the output- constrained system with uncertain control gain and time delay and is applied to the brushless DC motor. Using the dynamic surface technology, the controller overcomes the repetitive differentiation of backstepping and boundedness hypothesis of pre-determined control gain by incorporating radial basis function neural network and adaptive technology. The tangent barrier Lyapunov function is employed for time-delay chaotic system to prevent constraint violation. It is proved that the proposed control approach can guarantee asymptotically stable in the sense of uniformly ultimate boundedness without constraint violation. Finally, the effectiveness of the proposedmore » approach is demonstrated on the brushless DC motor example.« less

2011 Army Strategic Planning Guidance

DTIC Science & Technology

2011-03-25

TESI ) of 22,000 Soldiers, the Army’s total force by the end of the mid-term period is programmed to be 520K (AC). We will achieve a more...dwell ratios, extending TESI authority to adequately man deploying units and sustain the All-Volunteer Force, right-sizing the generating force, and... TESI Temporary End-Strength Increase WMD Weapons of Mass Destruction 2011 ARMY STRATEGIC PLANNING GUIDANCE Page 19 2011

Development of Analysis Tools for Certification of Flight Control Laws

DTIC Science & Technology

2009-03-31

In Proc. Conf. on Decision and Control, pages 881-886, Bahamas, 2004. [7] G. Chesi, A. Garulli, A. Tesi , and A. Vicino. LMI-based computation of...Minneapolis, MN, 2006, pp. 117-122. [10] G. Chesi, A. Garulli, A. Tesi . and A. Vicino, "LMI-based computation of optimal quadratic Lyapunov functions...Convex Optimization. Cambridge Univ. Press. Chesi, G., A. Garulli, A. Tesi and A. Vicino (2005). LMI-based computation of optimal quadratic Lyapunov

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.

National Manpower Inventory. Volume 3. Technical Documentation for Software for the Model

DTIC Science & Technology

1985-09-01

Technician APS-96 Search Radar IMA Technician USM-449 (V) & AAI 5500 Series ATE Int Maintenance Level Tech. CO CP-413/ASA-27A SACE TesI Bench IMA...MATE) Test Console IMA Technician ALQ-91/108 DECM IMA Technician ALQ-99 ECM Jammer/Tmilter & ALM-107 TesI Console IMA Technician ALQ-99 ECM Track...Receivers & ALM-109 TesI Console IMA Technician ECM Systems Intermediate Maintenance Technician ASM-347 (GT-1) SACE Programmer/Mainlenanca IMA

Human Signatures for Personnel Detection

DTIC Science & Technology

2010-09-14

work\\ TESIS \\prueba.avi’); switch videoinfo.ImageType case ’truecolor’ video=aviread(’C:\\MATLAB\\R2006a\\work\\ TESIS \\prueba.avi’); case...8217indexed’ video=aviread(’C:\\MATLAB\\R2006a\\work\\ TESIS \\prueba.avi’); video=ind2rgb(video); end 4.1.2 Color to Grayscale Converter The conversion from...algorithm. • Maximum errors for both GTSig and the lattice Boltzmann method were confined to the corners where fthe temperature is ill de ined Numerical

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.

TESIS experiment on EUV imaging spectroscopy of the Sun

NASA Astrophysics Data System (ADS)

Kuzin, S. V.; Bogachev, S. A.; Zhitnik, I. A.; Pertsov, A. A.; Ignatiev, A. P.; Mitrofanov, A. M.; Slemzin, V. A.; Shestov, S. V.; Sukhodrev, N. K.; Bugaenko, O. I.

2009-03-01

TESIS is a set of solar imaging instruments in development by the Lebedev Physical Institute of the Russian Academy of Science, to be launched aboard the Russian spacecraft CORONAS-PHOTON in December 2008. The main goal of TESIS is to provide complex observations of solar active phenomena from the transition region to the inner and outer solar corona with high spatial, spectral and temporal resolution in the EUV and Soft X-ray spectral bands. TESIS includes five unique space instruments: the MgXII Imaging Spectroheliometer (MISH) with spherical bent crystal mirror, for observations of the Sun in the monochromatic MgXII 8.42 Å line; the EUV Spectoheliometer (EUSH) with grazing incidence difraction grating, for the registration of the full solar disc in monochromatic lines of the spectral band 280-330 Å; two Full-disk EUV Telescopes (FET) with multilayer mirrors covering the band 130-136 and 290-320 Å; and the Solar EUV Coronagraph (SEC), based on the Ritchey-Chretien scheme, to observe the inner and outer solar corona from 0.2 to 4 solar radii in spectral band 290-320 Å. TESIS experiment will start at the rising phase of the 24th cycle of solar activity. With the advanced capabilities of its instruments, TESIS will help better understand the physics of solar flares and high-energy phenomena and provide new data on parameters of solar plasma in the temperature range 10-10K. This paper gives a brief description of the experiment, its equipment, and its scientific objectives.

The TESIS experiment on the CORONAS-PHOTON spacecraft

NASA Astrophysics Data System (ADS)

Kuzin, S. V.; Zhitnik, I. A.; Shestov, S. V.; Bogachev, S. A.; Bugaenko, O. I.; Ignat'ev, A. P.; Pertsov, A. A.; Ulyanov, A. S.; Reva, A. A.; Slemzin, V. A.; Sukhodrev, N. K.; Ivanov, Yu. S.; Goncharov, L. A.; Mitrofanov, A. V.; Popov, S. G.; Shergina, T. A.; Solov'ev, V. A.; Oparin, S. N.; Zykov, A. M.

2011-04-01

On February 26, 2009, the first data was obtained in the TESIS experiment on the research of the solar corona using imaging spectroscopy. The TESIS is a part of the scientific equipment of the CORONAS-PHO-TON spacecraft and is designed for imaging the solar corona in soft X-ray and extreme ultraviolet regions of the spectrum with high spatial, spectral, and temporal resolutions at altitudes from the transition region to three solar radii. The article describes the main characteristics of the instrumentation, management features, and operation modes.

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.

Cooperative path planning for multi-USV based on improved artificial bee colony algorithm

NASA Astrophysics Data System (ADS)

Cao, Lu; Chen, Qiwei

2018-03-01

Due to the complex constraints, more uncertain factors and critical real-time demand of path planning for multiple unmanned surface vehicle (multi-USV), an improved artificial bee colony (I-ABC) algorithm were proposed to solve the model of cooperative path planning for multi-USV. First the Voronoi diagram of battle field space is conceived to generate the optimal area of USVs paths. Then the chaotic searching algorithm is used to initialize the collection of paths, which is regard as foods of the ABC algorithm. With the limited data, the initial collection can search the optimal area of paths perfectly. Finally simulations of the multi-USV path planning under various threats have been carried out. Simulation results verify that the I-ABC algorithm can improve the diversity of nectar source and the convergence rate of algorithm. It can increase the adaptability of dynamic battlefield and unexpected threats for USV.

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

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

Teng, L.-W.; Chang, M.-C.; Tseng, Y.-P.

2009-12-11

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation tomore » the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.« less

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

NASA Astrophysics Data System (ADS)

Teng, Lee-Wen; Chang, Mei-Chu; Tseng, Yu-Ping; I, Lin

2009-12-01

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation to the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.

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

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.

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.

Modelling and operation strategies of DLR's large scale thermocline test facility (TESIS)

NASA Astrophysics Data System (ADS)

Odenthal, Christian; Breidenbach, Nils; Bauer, Thomas

2017-06-01

In this work an overview of the TESIS:store thermocline test facility and its current construction status will be given. Based on this, the TESIS:store facility using sensible solid filler material is modelled with a fully transient model, implemented in MATLAB®. Results in terms of the impact of filler site and operation strategies will be presented. While low porosity and small particle diameters for the filler material are beneficial, operation strategy is one key element with potential for optimization. It is shown that plant operators have to ponder between utilization and exergetic efficiency. Different durations of the charging and discharging period enable further potential for optimizations.

Transforaminal epidural steroid injections influence Mechanical Diagnosis and Therapy (MDT) pain response classification in candidates for lumbar herniated disc surgery.

PubMed

van Helvoirt, Hans; Apeldoorn, Adri T; Knol, Dirk L; Arts, Mark P; Kamper, Steven J; van Tulder, Maurits W; Ostelo, Raymond W

2016-04-27

Prospective cohort study. Although lumbar radiculopathy is regarded as a specific diagnosis, the most effective treatment strategy is unclear. Commonly used treatments include transforaminal epidural steroid injections (TESIs) and Mechanical Diagnosis & Therapy (MDT), but no studies have investigated the effectiveness of this combination. MDT differentiates pain centralization (C) from non-centralization (NC), which indicates good vs. poor prognostic validity respectively. The main aims were 1) to determine changes in Mechanical Diagnosis and Therapy (MDT) pain response classifications after transforaminal epidural steroid injections (TESIs) in candidates for lumbar herniated disc surgery and 2) to evaluate differences in short and long term outcomes for patients with different pain response classifications. Candidates for lumbar herniated disc surgery were assessed with a MDT protocol and their pain response classified as centralizing or peripheralizing. For this study,only patients were eligible who showed a peripheralizing pain response at intake. All patients then received TESIs and were reassessed and classified using the MDT protocol, into groups according to pain response (resolved, centralizing, peripheralizing with less pain and peripheralising with severe pain). After receiving targeted treatment based on pain response after TESIs, ranging from advice, MDT or surgery, follow-up assessments were completed at discharge and at 12 months. The primary outcomes were disability (Roland-Morris Disability Questionnaire [RMDQ] for Sciatica), pain severity in leg (visual analogue scale [VAS], 0-100) and global perceived effect (GPE). Linear mixed-models were used to determine between-groups differences in outcome. A total of 77 patients with lumbar disc herniation and peripheralizing symptoms were included. Patients received an average of 2 (SD 0.7) TESIs. After TESIs, 17 patients (22%) were classified as peripheralizing with continuing severe pain.These patients underwent surgery and were not further evaluated. Eleven (14%) patients were classified as resolved, 37 (48%) as centralizing with significant less pain, and 12 (16%) as peripheralizing with significant less pain. None of these patients underwent surgery. Resolved and centralizer subgroups had better outcomes in terms of VAS and RMDQ than the non-operated peripheralizers at discharge and at 12 months. The succes rates (GPE) for the resolved, centralizing, and peripheralizing with less pain patients were 100%, 100% and 33% respectively at short term, and 100%, 92% and 50% respectively at long term. After TESIs, a peripheralizing pain pattern changed to resolved or centralizing in 62% of the patients. For the non-operated patients, those with a centralising pattern after TESIs reported better pain and disability outcomes than those with peripheralizing pattern at short and long term.

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.

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.

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 analysis of a discrete-time ratio-dependent predator-prey model with Allee Effect

NASA Astrophysics Data System (ADS)

Cheng, Lifang; Cao, Hongjun

2016-09-01

A discrete-time predator-prey model with Allee effect is investigated in this paper. We consider the strong and the weak Allee effect (the population growth rate is negative and positive at low population density, respectively). From the stability analysis and the bifurcation diagrams, we get that the model with Allee effect (strong or weak) growth function and the model with logistic growth function have somewhat similar bifurcation structures. If the predator growth rate is smaller than its death rate, two species cannot coexist due to having no interior fixed points. When the predator growth rate is greater than its death rate and other parameters are fixed, the model can have two interior fixed points. One is always unstable, and the stability of the other is determined by the integral step size, which decides the species coexistence or not in some extent. If we increase the value of the integral step size, then the bifurcated period doubled orbits or invariant circle orbits may arise. So the numbers of the prey and the predator deviate from one stable state and then circulate along the period orbits or quasi-period orbits. When the integral step size is increased to a critical value, chaotic orbits may appear with many uncertain period-windows, which means that the numbers of prey and predator will be chaotic. In terms of bifurcation diagrams and phase portraits, we know that the complexity degree of the model with strong Allee effect decreases, which is related to the fact that the persistence of species can be determined by the initial species densities.

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

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.

Treatment of acute sciatica with transforaminal epidural corticosteroids and local anesthetic: design of a randomized controlled trial.

PubMed

Ter Meulen, Bastiaan C; Maas, Esther T; Vyas, Amrita; van der Vegt, Marinus; de Priester, Koo; de Boer, Michiel R; van Tulder, Maurits W; Weinstein, Henry C; Ostelo, Raymond W J G

2017-05-25

Transforaminal epidural injections with steroids (TESI) are used increasingly for patients with sciatica. However there is much debate about their safety and effectiveness. It is important to identify patients that benefit most from TESI and only few trials have yet evaluated the effects in patients with acute sciatica. We describe a prospective, randomized controlled trial (RCT), with the aim to evaluate the hypothesis that TESI plus Levobupivacaine (TESI-plus) added to oral pain medication is more effective compared to pain medication alone or compared to transforaminal injection with a local anesthetic of short duration among patients with acute sciatica. We will recruit a total of 264 patients with sciatica (<8 weeks) caused by a herniated disc, from two clinical sites. Participants are randomly assigned one of three study groups: 1) oral pain medication (control group), 2) oral pain medication and TESI-plus (intervention group one), 3) oral pain medication and transforaminal epidural injection (TEI) with Levobupivaine and saline solution (intervention group two). Primary outcomes are functional status (Roland-Morris Disability Questionnaire), pain intensity for both leg and back, (100 mm visual analogous scale (VAS)), and global perceived recovery (GPR, reported on a 7-point Likert scale, dichotomized into 'recovered' and 'not recovered'). The secondary outcomes are health-related quality of life (EQ5D-5 L) and patient satisfaction (7-point Likert scale). We will also collect information on healthcare utilization and costs, to perform an economic evaluation. All outcomes are measured at three and six weeks, three and six months after randomization. We defined a minimal clinically relevant difference between groups as a difference between both intervention groups and the control group of 20 points for pain (100-point VAS), four points for functional status (24-point RDQ) and a 20% difference on dichotomized GPR (recovered versus not recovered). A clinically relevant outcome in favor of TESI-plus implies that future patients with acute sciatica should be recommended TESI-plus within the first few weeks rather than being treated with pain medication alone in order to relieve pain and improve their functioning. In case of a negative result (no relevant differences in outcome between the three study arms), pain medication will remain the mainstay of treatment in the acute stages of sciatica. Dutch National trial register: NTR4457 (March, 6th, 2014).

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.

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.

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.

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

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.

Nonlinear dynamics analysis of the spur gear system for railway locomotive

NASA Astrophysics Data System (ADS)

Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

2017-02-01

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

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.

Department of Defense In-House RDT and E Activities

DTIC Science & Technology

1976-10-30

BALLISTIC TESTS.FAC AVAL FCR TESIS OF SP ELELTRONIC’ FIl’ CON EQUIP 4 RELATED SYSTEMS E COMPONFNTZ, 35 INSTALLATION: MEDICAL BIOENGINEERINC- R&D LABORATORY...ANALYSIS OF CHEMICAL AND METALLOGRAPHIC EFFECTS, MICROBIOLOGICAL EFFECTS, CLIMATIC ENVIRONMENTAL EFFECTS. TEST AND EVALUATE WARHEADS AND SPECIAL...CCMMUNICATI’N SYST:M INSTRUMENTED DROP ZONES ENGINEERING TEST FACILITY INSTRUMENTATION CALIBRATICN FACILITY SCIENTIFIC COMPUTER CENTER ENVIRONMENTAL TESY

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.

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.

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.

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.

ALMA Observations of Molecular Clouds in Three Group-centered Elliptical Galaxies: NGC 5846, NGC 4636, and NGC 5044

NASA Astrophysics Data System (ADS)

Temi, Pasquale; Amblard, Alexandre; Gitti, Myriam; Brighenti, Fabrizio; Gaspari, Massimo; Mathews, William G.; David, Laurence

2018-05-01

We present new ALMA CO(2–1) observations of two well-studied group-centered elliptical galaxies: NGC 4636 and NGC 5846. In addition, we include a revised analysis of Cycle 0 ALMA observations of the central galaxy in the NGC 5044 group. We find evidence that molecular gas is a common presence in bright group-centered galaxies (BGG). CO line widths are broader than Galactic molecular clouds, and using the reference Milky Way X CO, the total molecular mass ranges from 2.6 × 105 M ⊙ in NGC 4636 to 6.1 × 107 M ⊙ in NGC 5044. Complementary observations using the ALMA Compact Array do not exhibit any detection of a CO diffuse component at the sensitivity level achieved by current exposures. The origin of the detected molecular features is still uncertain, but these ALMA observations suggest that they are the end product of the hot gas cooling process and not the result of merger events. Some of the molecular clouds are associated with dust features as revealed by HST dust extinction maps, suggesting that these clouds formed from dust-enhanced cooling. The global nonlinear condensation may be triggered via the chaotic turbulent field or buoyant uplift. The large virial parameter of the molecular structures and correlation with the warm ({10}3{--}{10}5 {{K}})/hot (≥106) phase velocity dispersion provide evidence that they are unbound giant molecular associations drifting in the turbulent field, consistent with numerical predictions of the chaotic cold accretion process. Alternatively, the observed large CO line widths may be generated by molecular gas flowing out from cloud surfaces due to heating by the local hot gas atmosphere.

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.

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

PubMed Central

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067

From determinism and probability to chaos: chaotic evolution towards philosophy and methodology of chaotic optimization.

PubMed

Pei, Yan

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

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.

Using Chaotic System in Encryption

NASA Astrophysics Data System (ADS)

Findik, Oğuz; Kahramanli, Şirzat

In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.

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.

Reducing the Dynamical Degradation by Bi-Coupling Digital Chaotic Maps

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Liu, Bocheng; Hu, Hanping; Miao, Suoxia

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.

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.

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.

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.

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.

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.

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.

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

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 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.

Current Sheet Structures Observed by the TESIS EUV Telescope during a Flux Rope Eruption on the Sun

NASA Astrophysics Data System (ADS)

Reva, A. A.; Ulyanov, A. S.; Kuzin, S. V.

2016-11-01

We use the TESIS EUV telescope to study the current sheet signatures observed during flux rope eruption. The special feature of the TESIS telescope was its ability to image the solar corona up to a distance of 2 {R}⊙ from the Sun’s center in the Fe 171 Å line. The Fe 171 Å line emission illuminates the magnetic field lines, and the TESIS images reveal the coronal magnetic structure at high altitudes. The analyzed coronal mass ejection (CME) had a core with a spiral—flux rope—structure. The spiral shape indicates that the flux rope radius varied along its length. The flux rope had a complex temperature structure: cold legs (70,000 K, observed in He 304 Å line) and a hotter core (0.7 MK, observed in Fe 171 Å line). Such a structure contradicts the common assumption that the CME core is a cold prominence. When the CME impulsively accelerated, a dark double Y-structure appeared below the flux rope. The Y-structure timing, location, and morphology agree with the previously performed MHD simulations of the current sheet. We interpreted the Y-structure as a hot envelope of the current sheet and hot reconnection outflows. The Y-structure had a thickness of 6.0 Mm. Its length increased over time from 79 Mm to more than 411 Mm.

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.

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.

High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving

NASA Astrophysics Data System (ADS)

Qiu, Junchao; Zhang, Lin; Li, Diyang; Liu, Xingcheng

2016-06-01

Chaotic sequences can be applied to realize multiple user access and improve the system security for a visible light communication (VLC) system. However, since the map patterns of chaotic sequences are usually well known, eavesdroppers can possibly derive the key parameters of chaotic sequences and subsequently retrieve the information. We design an advanced encryption standard (AES) interleaving aided multiple user access scheme to enhance the security of a chaotic code division multiple access-based visible light communication (C-CDMA-VLC) system. We propose to spread the information with chaotic sequences, and then the spread information is interleaved by an AES algorithm and transmitted over VLC channels. Since the computation complexity of performing inverse operations to deinterleave the information is high, the eavesdroppers in a high speed VLC system cannot retrieve the information in real time; thus, the system security will be enhanced. Moreover, we build a mathematical model for the AES-aided VLC system and derive the theoretical information leakage to analyze the system security. The simulations are performed over VLC channels, and the results demonstrate the effectiveness and high security of our presented AES interleaving aided chaotic CDMA-VLC system.

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

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.

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.

Modeling Nucleation and Grain Growth in the Solar Nebula: Initial Progress Report

NASA Technical Reports Server (NTRS)

Nuth, Joseph A.; Paquette, J. A.; Ferguson, F. T.

2010-01-01

The primitive solar nebula was a violent and chaotic environment where high energy collisions, lightning, shocks and magnetic re-connection events rapidly vaporized some fraction of nebular dust, melted larger particles while leaving the largest grains virtually undisturbed. At the same time, some tiny grains containing very easily disturbed noble gas signatures (e.g., small, pre-solar graphite or SiC particles) never experienced this violence, yet can be found directly adjacent to much larger meteoritic components (chondrules or CAIs) that did. Additional components in the matrix of the most primitive carbonaceous chondrites and in some chondritic porous interplanetary dust particles include tiny nebular condensates, aggregates of condensates and partially annealed aggregates. Grains formed in violent transient events in the solar nebula did not come to equilibrium with their surroundings. To understand the formation and textures of these materials as well as their nebular abundances we must rely on Nucleation Theory and kinetic models of grain growth, coagulation and annealing. Such models have been very uncertain in the past: we will discuss the steps we are taking to increase their reliability.

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.

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.

Design of an image encryption scheme based on a multiple chaotic map

NASA Astrophysics Data System (ADS)

Tong, Xiao-Jun

2013-07-01

In order to solve the problem that chaos is degenerated in limited computer precision and Cat map is the small key space, this paper presents a chaotic map based on topological conjugacy and the chaotic characteristics are proved by Devaney definition. In order to produce a large key space, a Cat map named block Cat map is also designed for permutation process based on multiple-dimensional chaotic maps. The image encryption algorithm is based on permutation-substitution, and each key is controlled by different chaotic maps. The entropy analysis, differential analysis, weak-keys analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new image encryption scheme. Through the comparison to the proposed scheme with AES, DES and Logistic encryption methods, we come to the conclusion that the image encryption method solves the problem of low precision of one dimensional chaotic function and has higher speed and higher security.

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.

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.

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).

Experimental realization of a highly secure chaos communication under strong channel noise

NASA Astrophysics Data System (ADS)

Ye, Weiping; Dai, Qionglin; Wang, Shihong; Lu, Huaping; Kuang, Jinyu; Zhao, Zhenfeng; Zhu, Xiangqing; Tang, Guoning; Huang, Ronghuai; Hu, Gang

2004-09-01

A one-way coupled spatiotemporally chaotic map lattice is used to construct cryptosystem. With the combinatorial applications of both chaotic computations and conventional algebraic operations, our system has optimal cryptographic properties much better than the separative applications of known chaotic and conventional methods. We have realized experiments to practice duplex voice secure communications in realistic Wired Public Switched Telephone Network by applying our chaotic system and the system of Advanced Encryption Standard (AES), respectively, for cryptography. Our system can work stably against strong channel noise when AES fails to work.

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.

Multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.; Wang, Qiqi

2018-02-01

Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional sensitivity analysis methods are unable to compute useful gradient information for long-time-averaged quantities in chaotic dynamical systems. Sensitivity analysis with least squares shadowing (LSS) can compute useful gradient information for a number of chaotic systems, including simulations of chaotic vortex shedding and homogeneous isotropic turbulence. However, this gradient information comes at a very high computational cost. This paper presents multiple shooting shadowing (MSS), a more computationally efficient shadowing approach than the original LSS approach. Through an analysis of the convergence rate of MSS, it is shown that MSS can have lower memory usage and run time than LSS.

Future missions studies: Combining Schatten's solar activity prediction model with a chaotic prediction model

NASA Technical Reports Server (NTRS)

Ashrafi, S.

1991-01-01

K. Schatten (1991) recently developed a method for combining his prediction model with our chaotic model. The philosophy behind this combined model and his method of combination is explained. Because the Schatten solar prediction model (KS) uses a dynamo to mimic solar dynamics, accurate prediction is limited to long-term solar behavior (10 to 20 years). The Chaotic prediction model (SA) uses the recently developed techniques of nonlinear dynamics to predict solar activity. It can be used to predict activity only up to the horizon. In theory, the chaotic prediction should be several orders of magnitude better than statistical predictions up to that horizon; beyond the horizon, chaotic predictions would theoretically be just as good as statistical predictions. Therefore, chaos theory puts a fundamental limit on predictability.

Chaos in the brain: imaging via chaoticity of EEG/MEG signals

NASA Astrophysics Data System (ADS)

Kowalik, Zbigniew J.; Elbert, Thomas; Rockstroh, Brigitte; Hoke, Manfried

1995-03-01

Brain electro- (EEG) or magnetoencephalogram (MEG) can be analyzed by using methods of the nonlinear system theory. We show that even for very short and nonstationary time series it is possible to functionally differentiate various brain activities. Usually the analysis assumes that the analyzed signals are both long and stationary, so that the classic spectral methods can be used. Even more convincing results can be obtained under these circumstances when the dimensional analysis or estimation of the Kolmogorov entropy or the Lyapunov exponent are performed. When measuring the spontaneous activity of a human brain the assumption of stationarity is questionable and `static' methods (correlation dimension, entropy, etc.) are then not adequate. In this case `dynamic' methods like pointwise-D2 dimension or chaoticity measures should be applied. Predictability measures in the form of local Lyapunov exponents are capable of revealing directly the chaoticity of a given process, and can practically be applied for functional differentiation of brain activity. We exemplify these in cases of apallic syndrome, tinnitus and schizophrenia. We show that: the average chaoticity in apallic syndrome differentiates brain states both in space and time, chaoticity changes temporally in case of schizophrenia (critical jumps of chaoticity), chaoticity changes locally in space, i.e., in the cortex plane in case of tinnitus.

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.

Synthesis of a fully-integrated digital signal source for communications from chaotic dynamics-based oscillations

NASA Astrophysics Data System (ADS)

Glenn, Chance Michael, Sr.

This work is the conceptualization, derivation, analysis, and fabrication of a fully practical digital signal source designed from a chaotic oscillator. In it we show how a simple electronic circuit based upon the Colpitts oscillator, can be made to produce highly complex signals capable of carrying digital information. We show a direct relationship between the continuous-time chaotic oscillations produced by the circuit and the logistic map, which is discrete-time, one-dimensional map that is a fundamental paradigm for the study of chaotic systems. We demonstrate the direct encoding of binary information into the oscillations of the chaotic circuit. We demonstrate a new concept in power amplification, called syncrodyne amplification , which uses fundamental properties of chaotic oscillators to provide high-efficiency, high gain amplification of standard communication waveforms as well as typical chaotic oscillations. We show modeling results of this system providing nearly 60-dB power gain and 80% PAE for communications waveforms conforming to GMSK modulation. Finally we show results from a fabricated syncrodyne amplifier circuit operating at 2 MHz, providing over 40-dB power gain and 72% PAE, and propose design criteria for an 824--850 MHz circuit utilizing heterojunction bipolar transistors (HBTs), providing the basis for microwave frequency realization.

Using Biochar composts for improving sandy vineyard soils while reducing the risk of

NASA Astrophysics Data System (ADS)

Kammann, Claudia; Mengel, Jonathan; Mohr, Julia; Muskat, Stefan; Schmidt, Hans-Peter; Löhnertz, Otmar

2016-04-01

In recent years, biochar has increasingly been discussed as an option for sustainable environmentalmanagement, combining C sequestration with the aim of soil fertility improvement. Biochar has shownpositive effects in viticulture before (Genesio et al. 2015) which were largely attributed to improved water supply to the plants. However, in fertile temperate soils, the use of pure, untreated biochar does not guarantee economic benefits on the farm level (Ruysschaert et al., 2016). Hence, recent approaches started introducing biochar in management of nutrient-rich agricultural waste, e.g. in compost production (Kammann et al. 2015). Compost is frequently used in German vineyards for humus buildup and as a slow-release organic fertilizer. This, and increasingly mild, precipitation-rich winters, promoting mineralization, increase the risk of unwanted nitrate leaching losses into surface and ground waters during winter. To investigate if biochar pure, or biochar-compost mixtures and -products may have the potential to reduce nitrate leaching, we set up the following experiment: Either 30 or 60 t ha-1 of the following additives were mixed into the top 30 cm of sandy soil in large (120 L) containers, and planted with oneRiesling grapevine (Clone 198-30 GM) per container: Control (no addition), pure woody biochar, pure compost, biochar-compost (produced from the same organic feedstock than the compost, with 20 vol. - % of a woody biochar added), and pure compost plus pure biochar (same mixing ratio as in the former product). Once monthly, containers were exposed to simulated heavy rainfall that caused drainage. Leachates were collected from an outlet at the bottom of the containers, and analyzed for nutrients. The nutrient-rich additives containing compost all improved grape biomass and yield, most markedly pure compost and biochar-compost; same amendments were not significantly different. However,while the addition of the lower amount (30 t ha-1) of compost reduced nitrate leaching compared to the control (where nearly all mineral N was lost), the larger application amount in pure compost caused rising nitrate loss rates, likely due to compost mineralization. Interestingly, this was not the case when biochar was included, either co-composted or mixed into the substrates afterwards. However, after three years, the biochar-compost treatment still showed the highest grape yield of all treatments, while the treatment with biochar mixed in after compost production did not have the same effect. The results suggest that biochar-composts, for example produced from vine making residue and greenwaste, may reduce the risk of nitrate leaching while increasing the soil organic content more permanently than other amendments. Genesio, L., Miglietta, F., Baronti, S., Vaccari, F.P., 2015. Biochar increases vineyard Productivity without affecting grape quality: Results from a four years field experiment in Tuscany. Agriculture, Ecosystems & Environment 201, 20-25. Kammann, C.I., Schmidt, H.-P., Messerschmidt, N., Linsel, S., Steffens, D., Müller, C., Koyro, H.-W., Conte, P., Joseph, S., 2015. Plant growth improvement mediated by nitrate capture in cocomposted biochar. Scientific Reports 5, doi: 10.1038/srep11080. Ruysschaert, G., Nelissen, V., Postma, R., Bruun, E., O'Toole, A., Hammond, J., Rödger, J.-M.,Hylander, L., Kihlberg, T., Zwart, K., Hauggaard-Nielsen, H., Shackley, S., 2016. Field applications of pure biochar in the North Sea region and across Europe, in: Shackley, S.,Ruysschaert, G., Zwart, K., Glaser, B. (Eds.), Biochar in European Soils and Agriculture - Science and Practice. Routhledge, Oxon, UK and New York, USA.

Numerical explorations of R. M. Goodwin's business cycle model.

PubMed

Jakimowicz, Aleksander

2010-01-01

Goodwin's model, which was formulated in , still attracts economists' attention. The model possesses numerous interesting properties that have been discovered only recently due to the development of the chaos theory and the complexity theory. The first numerical explorations of the model were conducted in the early s by Strotz, McAnulty and Naines (1953). They discovered the coexistence of attractors that are well-known today, two properties of chaotic systems: the sensitive dependence on the initial conditions and the sensitive dependence on parameters. The occurrence of periodic and chaotic attractors is dependent on the value of parameters in a system. In case of certain parametric values fractal basin boundaries exist which results in enormous system sensitivity to external noise. If periodic attractors are placed in the neighborhood of the fractal basin boundaries, then even a low external noise can move the trajectory into the region in which the basin's structure is tangled. This leads to a kind of movement that resembles a chaotic movement on a strange attractor. In Goodwin's model, apart from typical chaotic behavior, there exists yet another kind of complex movements - transient chaotic behavior that is caused by the occurrence of invariant chaotic sets that are not attracting. Such sets are represented by chaotic saddles. Some of the latest observation methods of trajectories lying on invariant chaotic sets that are not attracting are straddle methods. This article provides examples of the basin boundary straddle trajectory and the saddle straddle trajectory. These cases were studied by Lorenz and Nusse (2002). I supplement the results they acquired with calculations of capacity dimension and correlation dimension.

Detection of chaotic dynamics in human gait signals from mobile devices

NASA Astrophysics Data System (ADS)

DelMarco, Stephen; Deng, Yunbin

2017-05-01

The ubiquity of mobile devices offers the opportunity to exploit device-generated signal data for biometric identification, health monitoring, and activity recognition. In particular, mobile devices contain an Inertial Measurement Unit (IMU) that produces acceleration and rotational rate information from the IMU accelerometers and gyros. These signals reflect motion properties of the human carrier. It is well-known that the complexity of bio-dynamical systems gives rise to chaotic dynamics. Knowledge of chaotic properties of these systems has shown utility, for example, in detecting abnormal medical conditions and neurological disorders. Chaotic dynamics has been found, in the lab, in bio-dynamical systems data such as electrocardiogram (heart), electroencephalogram (brain), and gait data. In this paper, we investigate the following question: can we detect chaotic dynamics in human gait as measured by IMU acceleration and gyro data from mobile phones? To detect chaotic dynamics, we perform recurrence analysis on real gyro and accelerometer signal data obtained from mobile devices. We apply the delay coordinate embedding approach from Takens' theorem to reconstruct the phase space trajectory of the multi-dimensional gait dynamical system. We use mutual information properties of the signal to estimate the appropriate delay value, and the false nearest neighbor approach to determine the phase space embedding dimension. We use a correlation dimension-based approach together with estimation of the largest Lyapunov exponent to make the chaotic dynamics detection decision. We investigate the ability to detect chaotic dynamics for the different one-dimensional IMU signals, across human subject and walking modes, and as a function of different phone locations on the human carrier.

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

Chaotic interactions of self-replicating RNA.

PubMed

Forst, C V

1996-03-01

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks.

PubMed

Feng, Cun-Fang; Xu, Xin-Jian; Wang, Sheng-Jun; Wang, Ying-Hai

2008-06-01

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.

Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency.

PubMed

Uenohara, Seiji; Mitsui, Takahito; Hirata, Yoshito; Morie, Takashi; Horio, Yoshihiko; Aihara, Kazuyuki

2013-06-01

We experimentally study strange nonchaotic attractors (SNAs) and chaotic attractors by using a nonlinear integrated circuit driven by a quasiperiodic input signal. An SNA is a geometrically strange attractor for which typical orbits have nonpositive Lyapunov exponents. It is a difficult problem to distinguish between SNAs and chaotic attractors experimentally. If a system has an SNA as a unique attractor, the system produces an identical response to a repeated quasiperiodic signal, regardless of the initial conditions, after a certain transient time. Such reproducibility of response outputs is called consistency. On the other hand, if the attractor is chaotic, the consistency is low owing to the sensitive dependence on initial conditions. In this paper, we analyze the experimental data for distinguishing between SNAs and chaotic attractors on the basis of the consistency.

Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems.

PubMed

Namikawa, Jun

2005-08-01

Chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line and a Markov chain with a transition probability matrix. The stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins. It is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of (truncated) power-law distributions if the basin of attraction for each attractor ruin has a zero measure. This result is confirmed by simulation of models exhibiting chaotic itinerancy. Chaotic itinerancy is also shown to be absent in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.

Chaotic Zones around Rotating Small Bodies

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

Lages, José; Shevchenko, Ivan I.; Shepelyansky, Dima L., E-mail: jose.lages@utinam.cnrs.fr

Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumb-bells or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples ofmore » the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.« less

Literalism, perspectivism, chaotic fragmentalism and psychotherapy techniques.

PubMed

Leitner, L M

1982-12-01

Literalism and chaotic fragmentalism have been advanced as two concepts to explain psychopathology while perspectivism has been used to explain psychological health (Landfield, 1980 a). It is hypothesized that, to the extent that they are therapeutic, all therapies move clients toward perspectivism and away from literalism and chaotic fragmentalism. Eight major schools of psychotherapy are discussed in terms of the principles of technique which enable them to change literalism and chaotic fragmentalism. The advantages of a unifying theory permitting diversity of techniques are discussed in relation to the ability of the clinician to be flexible yet not confused. Further, the unifying concepts of literalism, perspectivism, and chaotic fragmentalism are used to understand systematically the strengths and weaknesses of many therapeutic techniques. Finally, the implications of the differences in therapeutic techniques for changing different types of literalisms are discussed.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.

PubMed

Maslennikov, Oleg V; Nekorkin, Vladimir I

2016-07-01

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

Chaotic Experiences and Low-Income Children’s Social-Emotional Development

PubMed Central

Bobbitt, Kaeley C.; Gershoff, Elizabeth T.

2016-01-01

Development in early childhood is increasingly likely to take place in multiple contexts. Continuity and discontinuity in children’s experiences across multiple contexts have important implications for their development. This study examines the extent to which children experience chaos in their homes and in their preschool settings is linked with their social-emotional development over the course of the preschool year. Data from a large, representative sample of low-income preschool children attending Head Start was used to test a series of multi-level models. Children whose experiences of their homes were highly chaotic, regardless of the how chaotic their experiences of their classroom were, decreased in their social-emotional skills over the preschool year. Chaotic experiences in the home environment thus appear to have more influence on children’s development than do chaotic preschool experiences. PMID:28435178

640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser

NASA Astrophysics Data System (ADS)

Zhang, Limeng; Pan, Biwei; Chen, Guangcan; Guo, Lu; Lu, Dan; Zhao, Lingjuan; Wang, Wei

2017-04-01

An ultra-fast physical random number generator is demonstrated utilizing a photonic integrated device based broadband chaotic source with a simple post data processing method. The compact chaotic source is implemented by using a monolithic integrated dual-mode amplified feedback laser (AFL) with self-injection, where a robust chaotic signal with RF frequency coverage of above 50 GHz and flatness of ±3.6 dB is generated. By using 4-least significant bits (LSBs) retaining from the 8-bit digitization of the chaotic waveform, random sequences with a bit-rate up to 640 Gbit/s (160 GS/s × 4 bits) are realized. The generated random bits have passed each of the fifteen NIST statistics tests (NIST SP800-22), indicating its randomness for practical applications.

Solving large scale traveling salesman problems by chaotic neurodynamics.

PubMed

Hasegawa, Mikio; Ikeguch, Tohru; Aihara, Kazuyuki

2002-03-01

We propose a novel approach for solving large scale traveling salesman problems (TSPs) by chaotic dynamics. First, we realize the tabu search on a neural network, by utilizing the refractory effects as the tabu effects. Then, we extend it to a chaotic neural network version. We propose two types of chaotic searching methods, which are based on two different tabu searches. While the first one requires neurons of the order of n2 for an n-city TSP, the second one requires only n neurons. Moreover, an automatic parameter tuning method of our chaotic neural network is presented for easy application to various problems. Last, we show that our method with n neurons is applicable to large TSPs such as an 85,900-city problem and exhibits better performance than the conventional stochastic searches and the tabu searches.

Quantitative Measures of Chaotic Charged Particle Dynamics in the Magnetotail

NASA Astrophysics Data System (ADS)

Holland, D. L.; Martin, R. F., Jr.; Burris, C.

2017-12-01

It has long been noted that the motion of charged particles in magnetotail-like magnetic fields is chaotic, however, efforts to quantify the degree of chaos have had conflicting conclusions. In this paper we re-examine the question by focusing on quantitative measures of chaos. We first examine the percentage of orbits that enter the chaotic region of phase space and the average trapping time of those particles. We then examine the average exponential divergence rate (AEDR) of the chaotic particles between their first and last crossing of the mid-plane. We show that at resonant energies where the underlying phase space has a high degree of symmetry, only a small number of particle enter the chaotic region, but they are trapped for long periods of time and the time asymptotic value of the AEDR is very close to the average value of the AEDR. At the off-resonant energies where the phase space is highly asymmetric, the majority of the particle enter the chaotic region for fairly short periods of time and the time asymptotic value of the AEDR is much smaller than the average value. The root cause is that in the resonant case, the longest-lived orbits tend interact with the current many times and sample the entire chaotic region, whereas in the non-resonant case the longest-lived orbits only interact with the current sheet a small number of times but have very long mirrorings where the motion is nearly regular. Additionally we use an ad-hoc model where we model the current sheet as a Lorentz scattering system with each interaction with the current sheet being considered as a "collision". We find that the average kick per collision is greatest at off-resonant energies. Finally, we propose a chaos parameter as the product of the AEDR times the average chaotic particle trapping time times the percentage of orbits that are chaotic. We find that this takes on peak values at the resonant energies.

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

Information's role in the estimation of chaotic signals

NASA Astrophysics Data System (ADS)

Drake, Daniel Fred

1998-11-01

Researchers have proposed several methods designed to recover chaotic signals from noise-corrupted observations. While the methods vary, their qualitative performance does not: in low levels of noise all methods effectively recover the underlying signal; in high levels of noise no method can recover the underlying signal to any meaningful degree of accuracy. Of the methods proposed to date, all represent sub-optimal estimators. So: Is the inability to recover the signal in high noise levels simply a consequence of estimator sub-optimality? Or is estimator failure actually a manifestation of some intrinsic property of chaos itself? These questions are answered by deriving an optimal estimator for a class of chaotic systems and noting that it, too, fails in high levels of noise. An exact, closed- form expression for the estimator is obtained for a class of chaotic systems whose signals are solutions to a set of linear (but noncausal) difference equations. The existence of this linear description circumvents the difficulties normally encountered when manipulating the nonlinear (but causal) expressions that govern. chaotic behavior. The reason why even the optimal estimator fails to recover underlying chaotic signals in high levels of noise has its roots in information theory. At such noise levels, the mutual information linking the corrupted observations to the underlying signal is essentially nil, reducing the estimator to a simple guessing strategy based solely on a priori statistics. Entropy, long the common bond between information theory and dynamical systems, is actually one aspect of a far more complete characterization of information sources: the rate distortion function. Determining the rate distortion function associated with the class of chaotic systems considered in this work provides bounds on estimator performance in high levels of noise. Finally, a slight modification of the linear description leads to a method of synthesizing on limited precision platforms ``pseudo-chaotic'' sequences that mimic true chaotic behavior to any finite degree of precision and duration. The use of such a technique in spread-spectrum communications is considered.

Chaotic optical time-domain reflectometry using a distributed feedback laser diode modulated by an improved Colpitts oscillator

NASA Astrophysics Data System (ADS)

Li, Jing Xia; Xu, Hang; Liu, Li; Su, Peng Cheng; Zhang, Jian Guo

2015-05-01

We report a chaotic optical time-domain reflectometry for fiber fault location, where a chaotic probe signal is generated by driving a distributed feedback laser diode with an improved Colpitts chaotic oscillator. The results show that the unterminated fiber end, the loose connector, and the mismatch connector can be precisely located. A measurement range of approximately 91 km and a range independent resolution of 6 cm are achieved. This implementation method is easy to integrate and is cost effective, which gives it great potential for commercial applications.

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.

Regular transport dynamics produce chaotic travel times.

PubMed

Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro

2014-06-01

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

Separation of Trend and Chaotic Components of Time Series and Estimation of Their Characteristics by Linear Splines

NASA Astrophysics Data System (ADS)

Kryanev, A. V.; Ivanov, V. V.; Romanova, A. O.; Sevastyanov, L. A.; Udumyan, D. K.

2018-03-01

This paper considers the problem of separating the trend and the chaotic component of chaotic time series in the absence of information on the characteristics of the chaotic component. Such a problem arises in nuclear physics, biomedicine, and many other applied fields. The scheme has two stages. At the first stage, smoothing linear splines with different values of smoothing parameter are used to separate the "trend component." At the second stage, the method of least squares is used to find the unknown variance σ2 of the noise component.

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.

Dynamic analysis of a buckled asymmetric piezoelectric beam for energy harvesting

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

Van Blarigan, Louis, E-mail: louis01@umail.ucsb.edu; Moehlis, Jeff

2016-03-15

A model of a buckled beam energy harvester is analyzed to determine the phenomena behind the transition between high and low power output levels. It is shown that the presence of a chaotic attractor is a sufficient condition to predict high power output, though there are relatively small areas where high output is achieved without a chaotic attractor. The chaotic attractor appears as a product of a period doubling cascade or a boundary crisis. Bifurcation diagrams provide insight into the development of the chaotic region as the input power level is varied, as well as the intermixed periodic windows.

Bluetooth based chaos synchronization using particle swarm optimization and its applications to image encryption.

PubMed

Yau, Her-Terng; Hung, Tzu-Hsiang; Hsieh, Chia-Chun

2012-01-01

This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO) algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption.

Regular transport dynamics produce chaotic travel times

NASA Astrophysics Data System (ADS)

Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F.; Toledo, Benjamín; Valdivia, Juan Alejandro

2014-06-01

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

Bistability and chaos in the Taylor-Green dynamo.

PubMed

Yadav, Rakesh K; Verma, Mahendra K; Wahi, Pankaj

2012-03-01

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

Chaotic Motifs in Gene Regulatory Networks

PubMed Central

Zhang, Zhaoyang; Ye, Weiming; Qian, Yu; Zheng, Zhigang; Huang, Xuhui; Hu, Gang

2012-01-01

Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs. PMID:22792171

Generating Random Numbers by Means of Nonlinear Dynamic Systems

ERIC Educational Resources Information Center

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-01-01

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…

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

Orbital structure in oscillating galactic potentials

NASA Astrophysics Data System (ADS)

Terzić, Balša; Kandrup, Henry E.

2004-01-01

Subjecting a galactic potential to (possibly damped) nearly periodic, time-dependent variations can lead to large numbers of chaotic orbits experiencing systematic changes in energy, and the resulting chaotic phase mixing could play an important role in explaining such phenomena as violent relaxation. This paper focuses on the simplest case of spherically symmetric potentials subjected to strictly periodic driving with the aim of understanding precisely why orbits become chaotic and under what circumstances they will exhibit systematic changes in energy. Four unperturbed potentials V0(r) were considered, each subjected to a time dependence of the form V(r, t) =V0(r)(1 +m0 sinωt). In each case, the orbits divide clearly into regular and chaotic, distinctions which appear absolute. In particular, transitions from regularity to chaos are seemingly impossible. Over finite time intervals, chaotic orbits subdivide into what can be termed `sticky' chaotic orbits, which exhibit no large-scale secular changes in energy and remain trapped in the phase-space region where they started; and `wildly' chaotic orbits, which do exhibit systematic drifts in energy as the orbits diffuse to different phase-space regions. This latter distinction is not absolute, transitions corresponding apparently to orbits penetrating a `leaky' phase-space barrier. The three different orbit types can be identified simply in terms of the frequencies for which their Fourier spectra have the most power. An examination of the statistical properties of orbit ensembles as a function of driving frequency ω allows us to identify the specific resonances that determine orbital structure. Attention focuses also on how, for fixed amplitude m0, such quantities as the mean energy shift, the relative measure of chaotic orbits and the mean value of the largest Lyapunov exponent vary with driving frequency ω and how, for fixed ω, the same quantities depend on m0.

Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations.

PubMed

Kügler, Philipp; Bulelzai, M A K; Erhardt, André H

2017-04-04

Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.

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.

Fault detection technique for wavelength division multiplexing passive optical network using chaotic fiber laser

NASA Astrophysics Data System (ADS)

Xu, Naijun; Yang, Lingzhen; Zhang, Juan; Zhang, Xiangyuan; Wang, Juanfen; Zhang, Zhaoxia; Liu, Xianglian

2014-03-01

We propose a fault localization method for wavelength division multiplexing passive optical network (WDM-PON). A proof-of-concept experiment was demonstrated by utilizing the wavelength tunable chaotic laser generated from an erbium-doped fiber ring laser with a manual tunable fiber Bragg grating (TFBG) filter. The range of the chaotic lasing wavelength can cover the C-band. Basing on the TFBG filter, we can adjust the wavelength of the chaotic laser to match the WDM-PON channel with identical wavelength. We determined the fault location by calculating the cross-correlation between the reference and return signals. Analysis of the characteristics of the wavelength tunable chaotic laser showed that the breakpoint, the loose connector, and the mismatch connector could be precisely located. A dynamic range of approximately 23.8 dB and a spatial resolution of 4 cm, which was independent of the measuring range, were obtained.

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.

A discrete-time chaos synchronization system for electronic locking devices

NASA Astrophysics Data System (ADS)

Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.

2016-11-01

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.

On synchronisation of a class of complex chaotic systems with complex unknown parameters via integral sliding mode control

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed; Karami-Mollaee, Ali

2018-06-01

Chaotic systems demonstrate complex behaviour in their state variables and their parameters, which generate some challenges and consequences. This paper presents a new synchronisation scheme based on integral sliding mode control (ISMC) method on a class of complex chaotic systems with complex unknown parameters. Synchronisation between corresponding states of a class of complex chaotic systems and also convergence of the errors of the system parameters to zero point are studied. The designed feedback control vector and complex unknown parameter vector are analytically achieved based on the Lyapunov stability theory. Moreover, the effectiveness of the proposed methodology is verified by synchronisation of the Chen complex system and the Lorenz complex systems as the leader and the follower chaotic systems, respectively. In conclusion, some numerical simulations related to the synchronisation methodology is given to illustrate the effectiveness of the theoretical discussions.

Simulation and Visualization of Chaos in a Driven Nonlinear Pendulum -- An Aid to Introducing Chaotic Systems in Physics

NASA Astrophysics Data System (ADS)

Akpojotor, Godfrey; Ehwerhemuepha, Louis; Amromanoh, Ogheneriobororue

2013-03-01

The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The results obtained which highlight the hypersensitivity of the pendulum are used to discuss the effectiveness of teaching and learning the physics of chaotic system using Python. This study is one of the many studies under the African Computational Science and Engineering Tour Project (PASET) which is using Python to model, simulate and visualize concepts, laws and phenomena in Science and Engineering to compliment the teaching/learning of theory and experiment.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale

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

Maslennikov, Oleg V.; Nekorkin, Vladimir I.

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basicmore » properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.« less

A one-time pad color image cryptosystem based on SHA-3 and multiple chaotic systems

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Wang, Siwei; Zhang, Yingqian; Luo, Chao

2018-04-01

A novel image encryption algorithm is proposed that combines the SHA-3 hash function and two chaotic systems: the hyper-chaotic Lorenz and Chen systems. First, 384 bit keystream hash values are obtained by applying SHA-3 to plaintext. The sensitivity of the SHA-3 algorithm and chaotic systems ensures the effect of a one-time pad. Second, the color image is expanded into three-dimensional space. During permutation, it undergoes plane-plane displacements in the x, y and z dimensions. During diffusion, we use the adjacent pixel dataset and corresponding chaotic value to encrypt each pixel. Finally, the structure of alternating between permutation and diffusion is applied to enhance the level of security. Furthermore, we design techniques to improve the algorithm's encryption speed. Our experimental simulations show that the proposed cryptosystem achieves excellent encryption performance and can resist brute-force, statistical, and chosen-plaintext attacks.

Chaotic dynamics of controlled electric power systems

NASA Astrophysics Data System (ADS)

Kozlov, V. N.; Trosko, I. U.

2016-12-01

The conditions for appearance of chaotic dynamics of electromagnetic and electromechanical processes in energy systems described by the Park-Gorev bilinear differential equations with account for lags of coordinates and restrictions on control have been formulated. On the basis of classical equations, the parameters of synchronous generators and power lines, at which the chaotic dynamics of energy systems appears, have been found. The qualitative and quantitative characteristics of chaotic processes in energy associations of two types, based on the Hopf theorem, and methods of nonstationary linearization and decompositions are given. The properties of spectral characteristics of chaotic processes have been investigated, and the qualitative similarity of bilinear equations of power systems and Lorentz equations have been found. These results can be used for modernization of the systems of control of energy objects. The qualitative and quantitative characteristics for power energy systems as objects of control and for some laws of control with the feedback have been established.

Terminal Transient Phase of Chaotic Transients

NASA Astrophysics Data System (ADS)

Lilienkamp, Thomas; Parlitz, Ulrich

2018-03-01

Transient chaos in spatially extended systems can be characterized by the length of the transient phase, which typically grows quickly with the system size (supertransients). For a large class of these systems, the chaotic phase terminates abruptly, without any obvious precursors in commonly used observables. Here we investigate transient spatiotemporal chaos in two different models of this class. By probing the state space using perturbed trajectories we show the existence of a "terminal transient phase," which occurs prior to the abrupt collapse of chaotic dynamics. During this phase the impact of perturbations is significantly different from the earlier transient and particular patterns of (non)susceptible regions in state space occur close to the chaotic trajectories. We therefore hypothesize that even without perturbations proper precursors for the collapse of chaotic transients exist, which might be highly relevant for coping with spatiotemporal chaos in cardiac arrhythmias or brain functionality, for example.

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.

The CORONAS-Photon/TESIS experiment on EUV imaging spectroscopy of the Sun

NASA Astrophysics Data System (ADS)

Kuzin, S.; Zhitnik, I.; Bogachev, S.; Bugaenko, O.; Ignat'ev, A.; Mitrofanov, A.; Perzov, A.; Shestov, S.; Slemzin, V.; Suhodrev, N.

The new experiment TESIS is developent for russian CORONAS-Photon mission launch is planned on the end of 2007 The experiment is aimed on the study of activity of the Sun in the phases of minimum rise and maximum of 24 th cycle of Solar activity by the method of XUV imaging spectroscopy The method is based on the registration full-Sun monochromatic images with high spatial and temporal resolution The scientific tasks of the experiment are i Investigation dynamic processes in corona flares CME etc with high spatial up to 1 and temporal up to 1 second resolution ii determination of the main plasma parameters like plasma electron and ion density and temperature differential emission measure etc iii study of the processes of appearance and development large scale long-life magnetic structures in the solar corona study of the fluency of this structures on the global activity of the corona iv study of the mechanisms of energy accumulation and release in the solar flares and mechanisms of transformation of this energy into the heating of the plasma and kinematics energy To get the information for this studies the TESIS will register full-Sun images in narrow spectral intervals and the monochromatic lines of HeII SiXI FeXXI-FeXXIII MgXII ions The instrument includes 5 independent channels 2 telescopes for 304 and 132 A wide-field 2 5 degrees coronograph 280-330A and 8 42 A spectroheliographs The detailed description of the TESIS experiment and the instrument is presented

Chaotic neoclassical separatrix dissipation in parametric drift-wave decay.

PubMed

Kabantsev, A A; Tsidulko, Yu A; Driscoll, C F

2014-02-07

Experiments and theory characterize a parametric decay instability between plasma drift waves when the nonlinear coupling is modified by an electrostatic barrier. Novel mode coupling terms representing enhanced dissipation and mode phase shifts are caused by chaotic separatrix crossings on the wave-ruffled separatrix. Experimental determination of these coupling terms is in broad agreement with new chaotic neoclassical transport analyses.

Melnikov method approach to control of homoclinic/heteroclinic chaos by weak harmonic excitations.

PubMed

Chacón, Ricardo

2006-09-15

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative oscillator systems by weak harmonic excitations is presented, including diverse applications, such as chaotic escape from a potential well, chaotic solitons in Frenkel-Kontorova chains and chaotic-charged particles in the field of an electrostatic wave packet.

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.

Extreme multistability in a memristor-based multi-scroll hyper-chaotic system.

PubMed

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2016-07-01

In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

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.

Widely tunable chaotic fiber laser for WDM-PON detection

NASA Astrophysics Data System (ADS)

Zhang, Juan; Yang, Ling-zhen; Xu, Nai-jun; Wang, Juan-fen; Zhang, Zhao-xia; Liu, Xiang-lian

2014-05-01

A widely tunable high precision chaotic fiber laser is proposed and experimentally demonstrated. A tunable fiber Bragg grating (TFBG) filter is used as a tuning element to determine the turning range from 1533 nm to 1558 nm with a linewidth of 0.5 nm at any wavelength. The wide tuning range is capable of supporting 32 wavelength-division multiplexing (WDM) channels with 100 GHz channel spacing. All single wavelengths are found to be chaotic with 10 GHz bandwidth. The full width at half maximum (FWHM) of the chaotic correlation curve of the different wavelengths is on a picosecond time scale, thereby offering millimeter spatial resolution in WDM detection.

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.

Detecting unstable periodic orbits in chaotic time series using synchronization

NASA Astrophysics Data System (ADS)

Olyaei, Ali Azimi; Wu, Christine; Kinsner, Witold

2017-07-01

An alternative approach of detecting unstable periodic orbits in chaotic time series is proposed using synchronization techniques. A master-slave synchronization scheme is developed, in which the chaotic system drives a system of harmonic oscillators through a proper coupling condition. The proposed scheme is designed so that the power of the coupling signal exhibits notches that drop to zero once the system approaches an unstable orbit yielding an explicit indication of the presence of a periodic motion. The results shows that the proposed approach is particularly suitable in practical situations, where the time series is short and noisy, or it is obtained from high-dimensional chaotic systems.

Dynamic analyses, FPGA implementation and engineering applications of multi-butterfly chaotic attractors generated from generalised Sprott C system

NASA Astrophysics Data System (ADS)

Lai, Qiang; Zhao, Xiao-Wen; Rajagopal, Karthikeyan; Xu, Guanghui; Akgul, Akif; Guleryuz, Emre

2018-01-01

This paper considers the generation of multi-butterfly chaotic attractors from a generalised Sprott C system with multiple non-hyperbolic equilibria. The system is constructed by introducing an additional variable whose derivative has a switching function to the Sprott C system. It is numerically found that the system creates two-, three-, four-, five-butterfly attractors and any other multi-butterfly attractors. First, the dynamic analyses of multi-butterfly chaotic attractors are presented. Secondly, the field programmable gate array implementation, electronic circuit realisation and random number generator are done with the multi-butterfly chaotic attractors.

Parameter estimation for chaotic systems using improved bird swarm algorithm

NASA Astrophysics Data System (ADS)

Xu, Chuangbiao; Yang, Renhuan

2017-12-01

Parameter estimation of chaotic systems is an important problem in nonlinear science and has aroused increasing interest of many research fields, which can be basically reduced to a multidimensional optimization problem. In this paper, an improved boundary bird swarm algorithm is used to estimate the parameters of chaotic systems. This algorithm can combine the good global convergence and robustness of the bird swarm algorithm and the exploitation capability of improved boundary learning strategy. Experiments are conducted on the Lorenz system and the coupling motor system. Numerical simulation results reveal the effectiveness and with desirable performance of IBBSA for parameter estimation of chaotic systems.

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.

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.

A novel grid multiwing chaotic system with only non-hyperbolic equilibria

NASA Astrophysics Data System (ADS)

Zhang, Sen; Zeng, Yicheng; Li, Zhijun; Wang, Mengjiao; Xiong, Le

2018-05-01

The structure of the chaotic attractor of a system is mainly determined by the nonlinear functions in system equations. By using a new saw-tooth wave function and a new stair function, a novel complex grid multiwing chaotic system which belongs to non-Shil'nikov chaotic system with non-hyperbolic equilibrium points is proposed in this paper. It is particularly interesting that the complex grid multiwing attractors are generated by increasing the number of non-hyperbolic equilibrium points, which are different from the traditional methods of realising multiwing attractors by adding the index-2 saddle-focus equilibrium points in double-wing chaotic systems. The basic dynamical properties of the new system, such as dissipativity, phase portraits, the stability of the equilibria, the time-domain waveform, power spectrum, bifurcation diagram, Lyapunov exponents, and so on, are investigated by theoretical analysis and numerical simulations. Furthermore, the corresponding electronic circuit is designed and simulated on the Multisim platform. The Multisim simulation results and the hardware experimental results are in good agreement with the numerical simulations of the same system on Matlab platform, which verify the feasibility of this new grid multiwing chaotic system.

Solar System Dynamics

NASA Technical Reports Server (NTRS)

Wisdom, Jack

2002-01-01

In these 18 years, the research has touched every major dynamical problem in the solar system, including: the effect of chaotic zones on the distribution of asteroids, the delivery of meteorites along chaotic pathways, the chaotic motion of Pluto, the chaotic motion of the outer planets and that of the whole solar system, the delivery of short period comets from the Kuiper belt, the tidal evolution of the Uranian arid Galilean satellites, the chaotic tumbling of Hyperion and other irregular satellites, the large chaotic variations of the obliquity of Mars, the evolution of the Earth-Moon system, and the resonant core- mantle dynamics of Earth and Venus. It has introduced new analytical and numerical tools that are in widespread use. Today, nearly every long-term integration of our solar system, its subsystems, and other solar systems uses algorithms that was invented. This research has all been primarily Supported by this sequence of PGG NASA grants. During this period published major investigations of tidal evolution of the Earth-Moon system and of the passage of the Earth and Venus through non-linear core-mantle resonances were completed. It has published a major innovation in symplectic algorithms: the symplectic corrector. A paper was completed on non-perturbative hydrostatic equilibrium.

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.

Cooling of a magmatic system under thermal chaotic mixing

NASA Astrophysics Data System (ADS)

Petrelli, Maurizio; El Omari, Kamal; Le Guer, Yves; Perugini, Diego

2015-04-01

The cooling of a melt undergoing chaotic advection is studied numerically for a magma with a temperature-dependent viscosity in a 2D cavity with moving boundary. Different statistical mixing and energy indicators are used to characterize the efficiency of cooling by thermal chaotic mixing. We show that different cooling rates can be obtained during the thermal mixing even of a single basaltic magmatic batch undergoing chaotic advection. This process can induce complex temperature patterns inside the magma chamber. The emergence of chaotic dynamics strongly affects the temperature field during time and greatly increases the cooling rates. This mechanism has implications for the lifetime of a magmatic body and may favor the appearance of chemical heterogeneities in igneous systems as a result of different crystallization rates. Results from this study also highlight that even a single magma batch can develop, under chaotic thermal advection, complex thermal and therefore compositional patterns resulting from different cooling rates, which can account for some natural features that, to date, have received unsatisfactory explanations. Among them, the production of magmatic enclaves showing completely different cooling histories compared with the host magma, compositional zoning in mineral phases, and the generation of large-scale compositionally zoning observed in many plutons worldwide.

Synthetic Modeling of Autonomous Learning with a Chaotic Neural Network

NASA Astrophysics Data System (ADS)

Funabashi, Masatoshi

We investigate the possible role of intermittent chaotic dynamics called chaotic itinerancy, in interaction with nonsupervised learnings that reinforce and weaken the neural connection depending on the dynamics itself. We first performed hierarchical stability analysis of the Chaotic Neural Network model (CNN) according to the structure of invariant subspaces. Irregular transition between two attractor ruins with positive maximum Lyapunov exponent was triggered by the blowout bifurcation of the attractor spaces, and was associated with riddled basins structure. We secondly modeled two autonomous learnings, Hebbian learning and spike-timing-dependent plasticity (STDP) rule, and simulated the effect on the chaotic itinerancy state of CNN. Hebbian learning increased the residence time on attractor ruins, and produced novel attractors in the minimum higher-dimensional subspace. It also augmented the neuronal synchrony and established the uniform modularity in chaotic itinerancy. STDP rule reduced the residence time on attractor ruins, and brought a wide range of periodicity in emerged attractors, possibly including strange attractors. Both learning rules selectively destroyed and preserved the specific invariant subspaces, depending on the neuron synchrony of the subspace where the orbits are situated. Computational rationale of the autonomous learning is discussed in connectionist perspective.

A novel image encryption algorithm based on the chaotic system and DNA computing

NASA Astrophysics Data System (ADS)

Chai, Xiuli; Gan, Zhihua; Lu, Yang; Chen, Yiran; Han, Daojun

A novel image encryption algorithm using the chaotic system and deoxyribonucleic acid (DNA) computing is presented. Different from the traditional encryption methods, the permutation and diffusion of our method are manipulated on the 3D DNA matrix. Firstly, a 3D DNA matrix is obtained through bit plane splitting, bit plane recombination, DNA encoding of the plain image. Secondly, 3D DNA level permutation based on position sequence group (3DDNALPBPSG) is introduced, and chaotic sequences generated from the chaotic system are employed to permutate the positions of the elements of the 3D DNA matrix. Thirdly, 3D DNA level diffusion (3DDNALD) is given, the confused 3D DNA matrix is split into sub-blocks, and XOR operation by block is manipulated to the sub-DNA matrix and the key DNA matrix from the chaotic system. At last, by decoding the diffused DNA matrix, we get the cipher image. SHA 256 hash of the plain image is employed to calculate the initial values of the chaotic system to avoid chosen plaintext attack. Experimental results and security analyses show that our scheme is secure against several known attacks, and it can effectively protect the security of the images.

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.

Effects of `Environmental Chemistry' Elective Course Via Technology-Embedded Scientific Inquiry Model on Some Variables

NASA Astrophysics Data System (ADS)

Çalik, Muammer; Özsevgeç, Tuncay; Ebenezer, Jazlin; Artun, Hüseyin; Küçük, Zeynel

2014-06-01

The purpose of this study is to examine the effects of `environmental chemistry' elective course via Technology-Embedded Scientific Inquiry (TESI) model on senior science student teachers' (SSSTs) conceptions of environmental chemistry concepts/issues, attitudes toward chemistry, and technological pedagogical content knowledge (TPACK) levels. Within one group pre-test-post-test design, the study was conducted with 117 SSSTs (68 females and 49 males—aged 21-23 years) enrolled in an `environmental chemistry' elective course in the spring semester of 2011-2012 academic-years. Instruments for data collection comprised of Environmental Chemistry Conceptual Understanding Questionnaire, TPACK survey, and Chemistry Attitudes and Experiences Questionnaire. Significant increases in the SSSTs' conceptions of environmental chemistry concepts/issues, attitudes toward chemistry, and TPACK levels are attributed to the SSSTs learning how to use the innovative technologies in the contexts of the `environmental chemistry' elective course and teaching practicum. The study implies that the TESI model may serve a useful purpose in experimental science courses that use the innovative technologies. However, to generalize feasibility of the TESI model, it should be evaluated with SSSTs in diverse learning contexts.

Improving performance of DS-CDMA systems using chaotic complex Bernoulli spreading codes

NASA Astrophysics Data System (ADS)

Farzan Sabahi, Mohammad; Dehghanfard, Ali

2014-12-01

The most important goal of spreading spectrum communication system is to protect communication signals against interference and exploitation of information by unintended listeners. In fact, low probability of detection and low probability of intercept are two important parameters to increase the performance of the system. In Direct Sequence Code Division Multiple Access (DS-CDMA) systems, these properties are achieved by multiplying the data information in spreading sequences. Chaotic sequences, with their particular properties, have numerous applications in constructing spreading codes. Using one-dimensional Bernoulli chaotic sequence as spreading code is proposed in literature previously. The main feature of this sequence is its negative auto-correlation at lag of 1, which with proper design, leads to increase in efficiency of the communication system based on these codes. On the other hand, employing the complex chaotic sequences as spreading sequence also has been discussed in several papers. In this paper, use of two-dimensional Bernoulli chaotic sequences is proposed as spreading codes. The performance of a multi-user synchronous and asynchronous DS-CDMA system will be evaluated by applying these sequences under Additive White Gaussian Noise (AWGN) and fading channel. Simulation results indicate improvement of the performance in comparison with conventional spreading codes like Gold codes as well as similar complex chaotic spreading sequences. Similar to one-dimensional Bernoulli chaotic sequences, the proposed sequences also have negative auto-correlation. Besides, construction of complex sequences with lower average cross-correlation is possible with the proposed method.

Modeling and Analysis of a Fractional-Order Generalized Memristor-Based Chaotic System and Circuit Implementation

NASA Astrophysics Data System (ADS)

Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin

2017-12-01

Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.

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.

Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control.

PubMed

Wan, Ying; Cao, Jinde; Wen, Guanghui

In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.

Longterm Follow-Up of Patients in CSP 298 ’Treatment of Patients with Acquired Deficiency Syndrome (AIDS) and AIDS Related Complex’.

DTIC Science & Technology

1992-04-01

involving hazardous organisms, the investigator(s) adhered to the CDC-NIH Guide for Biosatety in Microbiological and Biomedical Laboratories. 01 DTIC...wais asse ssed Ib\\ it Chi- be. itijijated for all patienits wiih s~ muptorntati: tiir aSvmpiuitnatie square tesi or Fisher’s exact iesi for diSirete...en S open-label zidco.udine. 52 because of’ the protocol and ’Only 321 patieni, were tesied for ’erun p_24 antigen The pvserentag-~ho- ar-1 he ta 27

Simultaneous Observation of High Temperature Plasma of Solar Corona By TESIS CORONAS-PHOTON and XRT Hinode.

NASA Astrophysics Data System (ADS)

Reva, A.; Kuzin, S.; Bogachev, S.; Shestov, S.

2012-05-01

The Mg XII spectroheliograph is a part of instrumentation complex TESIS (satellite CORONAS-PHOTON). This instrument builds monochromatic images of hot plasma of the solar corona (λ = 8.42 Å, T>5 MK). The Mg XII spectroheliograph observed hot plasma in the non-flaring active-region NOAA 11019 during nine days. We reconstructed DEM of this active region with the help of genetic algorithm (we used data of the Mg XII spectroheliograph, XRT and EIT). Emission measure of the hot component amounts 1 % of the emission measure of the cool component.

Extreme multistability in a memristor-based multi-scroll hyper-chaotic system

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

Yuan, Fang, E-mail: yf210yf@163.com; Wang, Guangyi, E-mail: wanggyi@163.com; Wang, Xiaowei

In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numericalmore » simulations.« less

Frequency-locked chaotic opto-RF oscillator.

PubMed

Thorette, Aurélien; Romanelli, Marco; Brunel, Marc; Vallet, Marc

2016-06-15

A driven opto-RF oscillator, consisting of a dual-frequency laser (DFL) submitted to frequency-shifted feedback, is experimentally and numerically studied in a chaotic regime. Precise control of the reinjection strength and detuning permits isolation of a parameter region of bounded-phase chaos, where the opto-RF oscillator is frequency-locked to the master oscillator, in spite of chaotic phase and intensity oscillations. Robust experimental evidence of this synchronization regime is found, and phase noise spectra allow us to compare phase-locking and bounded-phase chaos regimes. In particular, it is found that the long-term phase stability of the master oscillator is well transferred to the opto-RF oscillator, even in the chaotic regime.

Temperature crossover of decoherence rates in chaotic and regular bath dynamics.

PubMed

Sanz, A S; Elran, Y; Brumer, P

2012-03-01

The effect of chaotic bath dynamics on the decoherence of a quantum system is examined for the vibrational degrees of freedom of a diatomic molecule in a realistic, constant temperature collisional bath. As an example, the specific case of I(2) in liquid xenon is examined as a function of temperature, and the results compared with an integrable xenon bath. A crossover in behavior is found: The integrable bath induces more decoherence at low bath temperatures than does the chaotic bath, whereas the opposite is the case at the higher bath temperatures. These results, verifying a conjecture due to Wilkie, shed light on the differing views of the effect of chaotic dynamics on system decoherence.

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

Entanglement as a signature of quantum chaos.

PubMed

Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C; Hu, Bambi

2004-01-01

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

Synchronization of chaotic systems involving fractional operators of Liouville-Caputo type with variable-order

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.; Valtierra-Rodríguez, M.

2017-12-01

In this paper, we propose a state-observer-based approach to synchronize variable-order fractional (VOF) chaotic systems. In particular, this work is focused on complete synchronization with a so-called unidirectional master-slave topology. The master is described by a dynamical system in state-space representation whereas the slave is described by a state observer. The slave is composed of a master copy and a correction term which in turn is constituted of an estimation error and an appropriate gain that assures the synchronization. The differential equations of the VOF chaotic system are described by the Liouville-Caputo and Atangana-Baleanu-Caputo derivatives. Numerical simulations involving the synchronization of Rössler oscillators, Chua's systems and multi-scrolls are studied. The simulations show that different chaotic behaviors can be obtained if different smooths functions defined in the interval (0 , 1 ] are used as the variable order of the fractional derivatives. Furthermore, simulations show that the VOF chaotic systems can be synchronized.

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.

Chaotic dynamics and its analysis of Hindmarsh-Rose neurons by Shil’nikov approach

NASA Astrophysics Data System (ADS)

Wei, Wei; Zuo, Min

2015-08-01

In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh-Rose (HR) neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results. Project supported by the Beijing Natural Science Foundation, China (Grant No. 4132005), the National Natural Science Foundation of China (Grant No. 61403006), the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions, China (Grant No. YETP1449), and the Project of Scientific and Technological Innovation Platform, China (Grant No. PXM2015_014213_000063).

Chaotic micromixers using two-layer crossing channels to exhibit fast mixing at low Reynolds numbers.

PubMed

Xia, H M; Wan, S Y M; Shu, C; Chew, Y T

2005-07-01

We report two chaotic micromixers that exhibit fast mixing at low Reynolds numbers in this paper. Passive mixers usually use the channel geometry to stir the fluids, and many previously reported designs rely on inertial effects which are only available at moderate Re. In this paper, we propose two chaotic micromixers using two-layer crossing channels. Both numerical and experimental studies show that the mixers are very efficient for fluid manipulation at low Reynolds numbers, such as stretching and splitting, folding and recombination, through which chaotic advection can be generated and the mixing is significantly promoted. More importantly, the generation of chaotic advection does not rely on the fluid inertial forces, so the mixers work well at very low Re. The mixers are benchmarked against a three-dimensional serpentine mixer. Results show that the latter is inefficient at Re = 0.2, while the new design exhibits rapid mixing at Re = 0.2 and at Re of O(10(-2)). The new mixer design will benefit various microfluidic systems.

Chaotic behaviour of the short-term variations in ozone column observed in Arctic

NASA Astrophysics Data System (ADS)

Petkov, Boyan H.; Vitale, Vito; Mazzola, Mauro; Lanconelli, Christian; Lupi, Angelo

2015-09-01

The diurnal variations observed in the ozone column at Ny-Ålesund, Svalbard during different periods of 2009, 2010 and 2011 have been examined to test the hypothesis that they could be a result of a chaotic process. It was found that each of the attractors, reconstructed by applying the time delay technique and corresponding to any of the three time series can be embedded by 6-dimensional space. Recurrence plots, depicted to characterise the attractor features revealed structures typical for a chaotic system. In addition, the two positive Lyapunov exponents found for the three attractors, the fractal Hausdorff dimension presented by the Kaplan-Yorke estimator and the feasibility to predict the short-term ozone column variations within 10-20 h, knowing the past behaviour make the assumption about their chaotic character more realistic. The similarities of the estimated parameters in all three cases allow us to hypothesise that the three time series under study likely present one-dimensional projections of the same chaotic system taken at different time intervals.

Design and Smartphone-Based Implementation of a Chaotic Video Communication Scheme via WAN Remote Transmission

NASA Astrophysics Data System (ADS)

Lin, Zhuosheng; Yu, Simin; Li, Chengqing; Lü, Jinhu; Wang, Qianxue

This paper proposes a chaotic secure video remote communication scheme that can perform on real WAN networks, and implements it on a smartphone hardware platform. First, a joint encryption and compression scheme is designed by embedding a chaotic encryption scheme into the MJPG-Streamer source codes. Then, multiuser smartphone communications between the sender and the receiver are implemented via WAN remote transmission. Finally, the transmitted video data are received with the given IP address and port in an Android smartphone. It should be noted that, this is the first time that chaotic video encryption schemes are implemented on such a hardware platform. The experimental results demonstrate that the technical challenges on hardware implementation of secure video communication are successfully solved, reaching a balance amongst sufficient security level, real-time processing of massive video data, and utilization of available resources in the hardware environment. The proposed scheme can serve as a good application example of chaotic secure communications for smartphone and other mobile facilities in the future.

Experimental demonstration of the real-time online fault monitoring technique for chaos-based passive optical networks

NASA Astrophysics Data System (ADS)

Dou, Xinyu; Yin, Hongxi; Yue, Hehe; Jin, Yu; Shen, Jing; Li, Lin

2015-09-01

In this paper, a real-time online fault monitoring technique for chaos-based passive optical networks (PONs) is proposed and experimentally demonstrated. The fault monitoring is performed by the chaotic communication signal. The proof-of-concept experiments are demonstrated for two PON structures, i.e., wavelength-division-multiplexing (WDM) PON and Ethernet PON (EPON), respectively. For WDM PON, two monitoring approaches are investigated, one deploying a chaotic optical time domain reflectometry (OTDR) for each transmitter, and the other using only one tunable chaotic OTDR. The experimental results show that the faults at beyond 20 km from the OLT can be detected and located. The spatial resolution of the tunable chaotic OTDR is an order of magnitude of centimeter. Meanwhile, the monitoring process can operate in parallel with the chaotic optical secure communications. The proposed technique has benefits of real-time, online, precise fault location, and simple realization, which will significantly reduce the cost of operation, administration and maintenance (OAM) of PON.

The effect of inertia, viscous damping, temperature and normal stress on chaotic behaviour of the rate and state friction model

NASA Astrophysics Data System (ADS)

Sinha, Nitish; Singh, Arun K.; Singh, Trilok N.

2018-04-01

A fundamental understanding of frictional sliding at rock surfaces is of practical importance for nucleation and propagation of earthquakes and rock slope stability. We investigate numerically the effect of different physical parameters such as inertia, viscous damping, temperature and normal stress on the chaotic behaviour of the two state variables rate and state friction (2sRSF) model. In general, a slight variation in any of inertia, viscous damping, temperature and effective normal stress reduces the chaotic behaviour of the sliding system. However, the present study has shown the appearance of chaos for the specific values of normal stress before it disappears again as the normal stress varies further. It is also observed that magnitude of system stiffness at which chaotic motion occurs, is less than the corresponding value of critical stiffness determined by using the linear stability analysis. These results explain the practical observation why chaotic nucleation of an earthquake is a rare phenomenon as reported in literature.

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.

Dynamics of coherent states in regular and chaotic regimes of the non-integrable Dicke model

NASA Astrophysics Data System (ADS)

Lerma-Hernández, S.; Chávez-Carlos, J.; Bastarrachea-Magnani, M. A.; López-del-Carpio, B.; Hirsch, J. G.

2018-04-01

The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time t, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.

On the relevance of chaos for halo stars in the solar neighbourhood II

NASA Astrophysics Data System (ADS)

Maffione, Nicolas P.; Gómez, Facundo A.; Cincotta, Pablo M.; Giordano, Claudia M.; Grand, Robert J. J.; Marinacci, Federico; Pakmor, Rüdiger; Simpson, Christine M.; Springel, Volker; Frenk, Carlos S.

2018-05-01

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

NASA Astrophysics Data System (ADS)

Chavarette, Fábio Roberto; Balthazar, José Manoel; Felix, Jorge L. P.; Rafikov, Marat

2009-05-01

This paper analyzes the non-linear dynamics, with a chaotic behavior of a particular micro-electro-mechanical system. We used a technique of the optimal linear control for reducing the irregular (chaotic) oscillatory movement of the non-linear systems to a periodic orbit. We use the mathematical model of a (MEMS) proposed by Luo and Wang.

Chaotic behavior in Malaysian stock market: A study with recurrence quantification analysis

NASA Astrophysics Data System (ADS)

Niu, Betty Voon Wan; Noorani, Mohd Salmi Md; Jaaman, Saiful Hafizah

2016-11-01

The dynamics of stock market has been questioned for decades. Its behavior appeared random yet some found it behaves as chaos. Up to 5000 daily adjusted closing data of FTSE Bursa Malaysia Kuala Lumpur Composite Index (KLSE) was investigated through recurrence plot and recurrence quantification analysis. Results were compared between stochastic system, chaotic system and deterministic system. Results show that KLSE daily adjusted closing data behaves chaotically.

Chaotic Motions in the Real Fuzzy Electronic Circuits

DTIC Science & Technology

2012-12-30

field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be...Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended ...model. The overall fuzzy model of the system is achieved by fuzzy blending of the linear system models. Consider a continuous-time nonlinear dynamic

Cooling of a Magmatic System Under Thermal Chaotic Mixing

NASA Astrophysics Data System (ADS)

El Omari, Kamal; Le Guer, Yves; Perugini, Diego; Petrelli, Maurizio

2015-07-01

The cooling of a basaltic melt undergoing chaotic advection is studied numerically for a magma with a temperature-dependent viscosity in a two-dimensional (2D) cavity with moving boundary. Different statistical mixing and energy indicators are used to characterize the efficiency of cooling by thermal chaotic mixing. We show that different cooling rates can be obtained during the thermal mixing of a single basaltic magmatic batch undergoing chaotic advection. This process can induce complex temperature patterns inside the magma chamber. The emergence of chaotic dynamics strongly modulates the temperature fields over time and greatly increases the cooling rates. This mechanism has implications for the thermal lifetime of the magmatic body and may favor the appearance of chemical heterogeneities in the igneous system as a result of different crystallization rates. Results from this study also highlight that even a single magma batch can develop, under chaotic thermal advection, complex thermal and therefore compositional patterns resulting from different cooling rates, which can account for some natural features that, to date, have received unsatisfactory explanations, including the production of magmatic enclaves showing completely different cooling histories compared with the host magma, compositional zoning in mineral phases, and the generation of large-scale compositional zoning observed in many plutons worldwide.

Periodic or chaotic bursting dynamics via delayed pitchfork bifurcation in a slow-varying controlled system

NASA Astrophysics Data System (ADS)

Yu, Yue; Zhang, Zhengdi; Han, Xiujing

2018-03-01

In this work, we aim to demonstrate the novel routes to periodic and chaotic bursting, i.e., the different bursting dynamics via delayed pitchfork bifurcations around stable attractors, in the classical controlled Lü system. First, by computing the corresponding characteristic polynomial, we determine where some critical values about bifurcation behaviors appear in the Lü system. Moreover, the transition mechanism among different stable attractors has been introduced including homoclinic-type connections or chaotic attractors. Secondly, taking advantage of the above analytical results, we carry out a study of the mechanism for bursting dynamics in the Lü system with slowly periodic variation of certain control parameter. A distinct delayed supercritical pitchfork bifurcation behavior can be discussed when the control item passes through bifurcation points periodically. This delayed dynamical behavior may terminate at different parameter areas, which leads to different spiking modes around different stable attractors (equilibriums, limit cycles, or chaotic attractors). In particular, the chaotic attractor may appear by Shilnikov connections or chaos boundary crisis, which leads to the occurrence of impressive chaotic bursting oscillations. Our findings enrich the study of bursting dynamics and deepen the understanding of some similar sorts of delayed bursting phenomena. Finally, some numerical simulations are included to illustrate the validity of our study.

Rainfall Prediction of Indian Peninsula: Comparison of Time Series Based Approach and Predictor Based Approach using Machine Learning Techniques

NASA Astrophysics Data System (ADS)

Dash, Y.; Mishra, S. K.; Panigrahi, B. K.

2017-12-01

Prediction of northeast/post monsoon rainfall which occur during October, November and December (OND) over Indian peninsula is a challenging task due to the dynamic nature of uncertain chaotic climate. It is imperative to elucidate this issue by examining performance of different machine leaning (ML) approaches. The prime objective of this research is to compare between a) statistical prediction using historical rainfall observations and global atmosphere-ocean predictors like Sea Surface Temperature (SST) and Sea Level Pressure (SLP) and b) empirical prediction based on a time series analysis of past rainfall data without using any other predictors. Initially, ML techniques have been applied on SST and SLP data (1948-2014) obtained from NCEP/NCAR reanalysis monthly mean provided by the NOAA ESRL PSD. Later, this study investigated the applicability of ML methods using OND rainfall time series for 1948-2014 and forecasted up to 2018. The predicted values of aforementioned methods were verified using observed time series data collected from Indian Institute of Tropical Meteorology and the result revealed good performance of ML algorithms with minimal error scores. Thus, it is found that both statistical and empirical methods are useful for long range climatic projections.

Extracting harmonic signal from a chaotic background with local linear model

NASA Astrophysics Data System (ADS)

Li, Chenlong; Su, Liyun

2017-02-01

In this paper, the problems of blind detection and estimation of harmonic signal in strong chaotic background are analyzed, and new methods by using local linear (LL) model are put forward. The LL model has been exhaustively researched and successfully applied for fitting and forecasting chaotic signal in many chaotic fields. We enlarge the modeling capacity substantially. Firstly, we can predict the short-term chaotic signal and obtain the fitting error based on the LL model. Then we detect the frequencies from the fitting error by periodogram, a property on the fitting error is proposed which has not been addressed before, and this property ensures that the detected frequencies are similar to that of harmonic signal. Secondly, we establish a two-layer LL model to estimate the determinate harmonic signal in strong chaotic background. To estimate this simply and effectively, we develop an efficient backfitting algorithm to select and optimize the parameters that are hard to be exhaustively searched for. In the method, based on sensitivity to initial value of chaos motion, the minimum fitting error criterion is used as the objective function to get the estimation of the parameters of the two-layer LL model. Simulation shows that the two-layer LL model and its estimation technique have appreciable flexibility to model the determinate harmonic signal in different chaotic backgrounds (Lorenz, Henon and Mackey-Glass (M-G) equations). Specifically, the harmonic signal can be extracted well with low SNR and the developed background algorithm satisfies the condition of convergence in repeated 3-5 times.

Unscrambling the Omlette: a New Bubble and Crystal Clustering Mechanism in Chaotically Mixed Magma Flows

NASA Astrophysics Data System (ADS)

Robertson, J.; Metcalfe, G.; Wang, S.; Barnes, S. J.

2014-12-01

The concentration of bubbles, crystals or droplets into small volumes of magma is a key trigger for many interesting magmatic processes. For example, gas slugs driving Strombolian eruptions form from the coalesence of exsolved bubbles within a volcanic conduit, while Ni-Cu-PGE magmatic sulfide deposits require a concentration of dense sulfide droplets from a large volume of magma to form a massive ore body. However the physical mechanism for this clustering remains unresolved - especially since small particles in active magma flows are expected to mostly track flow streamlines rather than clustering. We have uncovered a previously unreported clustering mechanism which is applicable to magmatic flows. This mechanism involves the interaction of particles with two kinds of chaotic flow structure: (a) high-strain regions within the well-mixed chaotic zones of the flow, and (b) unmixed islands of stability within the chaotic flow, known as Kolmogorov-Arnold-Moser (KAM) regions. The first figure shows the difference between chaotic and KAM regions in a chaotic laminar pipe flow. Trapping occurs when particles are scattered from high-strain regions in the chaotic zones and become trapped in the KAM regions, leading to a rapid concentration of particles relative to their original distribution (shown in the second series of figures). Using a combination of these analogue experiments and theoretical analysis we outline the conditions under which this clustering process can occur. We examine the onset of secondary density-related instabilities and the effects of increased particle-particle interaction within the clustered particles, and highlight the impact of particle clustering on the dynamics of magma ascent and emplacement.

Secondary chaotic terrain formation in the higher outflow channels of southern circum-Chryse, Mars

USGS Publications Warehouse

Rodriguez, J.A.P.; Kargel, J.S.; Tanaka, K.L.; Crown, D.A.; Berman, D.C.; Fairen, A.G.; Baker, V.R.; Furfaro, R.; Candelaria, P.; Sasaki, S.

2011-01-01

Higher outflow channel dissection in the martian region of southern circum-Chryse appears to have extended from the Late Hesperian to the Middle Amazonian Epoch. These outflow channels were excavated within the upper 1. km of the cryolithosphere, where no liquid water is expected to have existed during these geologic epochs. In accordance with previous work, our examination of outflow channel floor morphologies suggests the upper crust excavated by the studied outflow channels consisted of a thin (a few tens of meters) layer of dry geologic materials overlying an indurated zone that extends to the bases of the investigated outflow channels (1. km in depth). We find that the floors of these outflow channels contain widespread secondary chaotic terrains (i.e., chaotic terrains produced by the destruction of channel-floor materials). These chaotic terrains occur within the full range of outflow channel dissection and tend to form clusters. Our examination of the geology of these chaotic terrains suggests that their formation did not result in the generation of floods. Nevertheless, despite their much smaller dimensions, these chaotic terrains are comprised of the same basic morphologic elements (e.g., mesas, knobs, and smooth deposits within scarp-bound depressions) as those located in the initiation zones of the outflow channels, which suggests that their formation must have involved the release of ground volatiles. We propose that these chaotic terrains developed not catastrophically but gradually and during multiple episodes of nested surface collapse. In order to explain the formation of secondary chaotic terrains within zones of outflow channel dissection, we propose that the regional Martian cryolithosphere contained widespread lenses of volatiles in liquid form. In this model, channel floor collapse and secondary chaotic terrain formation would have taken place as a consequence of instabilities arising during their exhumation by outflow channel dissection. Within relatively warm upper crustal materials in volcanic settings, or within highly saline crustal materials where cryopegs developed, lenses of volatiles in liquid form within the cryolithosphere could have formed, and/or remained stable.In addition, our numerical simulations suggest that low thermal conductivity, dry fine-grained porous geologic materials just a few tens of meters in thickness (e.g., dunes, sand sheets, some types of regolith materials), could have produced high thermal anomalies resulting in subsurface melting. The existence of a global layer of dry geologic materials overlying the cryolithosphere would suggest that widespread lenses of fluids existed (and may still exist) at shallow depths wherever these materials are fine-grained and porous. The surface ages of the investigated outflow channels and chaotic terrains span a full 500 to 700. Myr. Chaotic terrains similar in dimensions and morphology to secondary chaotic terrains are not observed conspicuously throughout the surface of Mars, suggesting that intra-cryolithospheric fluid lenses may form relatively stable systems. The existence of widespread groundwater lenses at shallow depths of burial has tremendous implications for exobiological studies and future human exploration. We find that the clear geomorphologic anomaly that the chaotic terrains and outflow channels of southern Chryse form within the Martian landscape could have been a consequence of large-scale resurfacing resulting from anomalously extensive subsurface melt in this region of the planet produced by high concentrations of salts within the regional upper crust. Crater count statistics reveal that secondary chaotic terrains and the outflow channels within which they occur have overlapping ages, suggesting that the instabilities leading to their formation rapidly dissipated, perhaps as the thickness of the cryolithosphere was reset following the disruption of the upper crustal thermal structure produced during outflow channel ex

Adaptive feedback synchronization of a unified chaotic system

NASA Astrophysics Data System (ADS)

Lu, Junan; Wu, Xiaoqun; Han, Xiuping; Lü, Jinhu

2004-08-01

This Letter further improves and extends the work of Wang et al. [Phys. Lett. A 312 (2003) 34]. In detailed, the linear feedback synchronization and adaptive feedback synchronization with only one controller for a unified chaotic system are discussed here. It is noticed that this unified system contains the noted Lorenz and Chen systems. Two chaotic synchronization theorems are attained. Also, numerical simulations are given to show the effectiveness of these methods.

A chaotic jerk system with non-hyperbolic equilibrium: Dynamics, effect of time delay and circuit realisation

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Pham, Viet-Thanh; Tahir, Fadhil Rahma; Akgul, Akif; Abdolmohammadi, Hamid Reza; Jafari, Sajad

2018-04-01

The literature on chaos has highlighted several chaotic systems with special features. In this work, a novel chaotic jerk system with non-hyperbolic equilibrium is proposed. The dynamics of this new system is revealed through equilibrium analysis, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, we investigate the time-delay effects on the proposed system. Realisation of such a system is presented to verify its feasibility.

Optical image hiding based on chaotic vibration of deformable moiré grating

NASA Astrophysics Data System (ADS)

Lu, Guangqing; Saunoriene, Loreta; Aleksiene, Sandra; Ragulskis, Minvydas

2018-03-01

Image hiding technique based on chaotic vibration of deformable moiré grating is presented in this paper. The embedded secret digital image is leaked in a form of a pattern of time-averaged moiré fringes when the deformable cover grating vibrates according to a chaotic law of motion with a predefined set of parameters. Computational experiments are used to demonstrate the features and the applicability of the proposed scheme.

A Non-Intrusive Algorithm for Sensitivity Analysis of Chaotic Flow Simulations

NASA Technical Reports Server (NTRS)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2017-01-01

We demonstrate a novel algorithm for computing the sensitivity of statistics in chaotic flow simulations to parameter perturbations. The algorithm is non-intrusive but requires exposing an interface. Based on the principle of shadowing in dynamical systems, this algorithm is designed to reduce the effect of the sampling error in computing sensitivity of statistics in chaotic simulations. We compare the effectiveness of this method to that of the conventional finite difference method.

Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime

NASA Astrophysics Data System (ADS)

Löck, Steffen; Bäcker, Arnd; Ketzmerick, Roland; Schlagheck, Peter

2010-03-01

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given ℏ regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.

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.

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.

An Improved Cuckoo Search Optimization Algorithm for the Problem of Chaotic Systems Parameter Estimation

PubMed Central

Wang, Jun; Zhou, Bihua; Zhou, Shudao

2016-01-01

This paper proposes an improved cuckoo search (ICS) algorithm to establish the parameters of chaotic systems. In order to improve the optimization capability of the basic cuckoo search (CS) algorithm, the orthogonal design and simulated annealing operation are incorporated in the CS algorithm to enhance the exploitation search ability. Then the proposed algorithm is used to establish parameters of the Lorenz chaotic system and Chen chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the algorithm can estimate parameters with high accuracy and reliability. Finally, the results are compared with the CS algorithm, genetic algorithm, and particle swarm optimization algorithm, and the compared results demonstrate the method is energy-efficient and superior. PMID:26880874

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

PubMed

Wang, Rong; Gao, Jin-Yue

2005-09-01

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

Quantifying chaotic dynamics from integrate-and-fire processes

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

Pavlov, A. N.; Saratov State Technical University, Politehnicheskaya Str. 77, 410054 Saratov; Pavlova, O. N.

2015-01-15

Characterizing chaotic dynamics from integrate-and-fire (IF) interspike intervals (ISIs) is relatively easy performed at high firing rates. When the firing rate is low, a correct estimation of Lyapunov exponents (LEs) describing dynamical features of complex oscillations reflected in the IF ISI sequences becomes more complicated. In this work we discuss peculiarities and limitations of quantifying chaotic dynamics from IF point processes. We consider main factors leading to underestimated LEs and demonstrate a way of improving numerical determining of LEs from IF ISI sequences. We show that estimations of the two largest LEs can be performed using around 400 mean periodsmore » of chaotic oscillations in the regime of phase-coherent chaos. Application to real data is discussed.« less

Compound synchronization of four memristor chaotic oscillator systems and secure communication.

PubMed

Sun, Junwei; Shen, Yi; Yin, Quan; Xu, Chengjie

2013-03-01

In this paper, a novel kind of compound synchronization among four chaotic systems is investigated, where the drive systems have been conceptually divided into two categories: scaling drive systems and base drive systems. Firstly, a sufficient condition is obtained to ensure compound synchronization among four memristor chaotic oscillator systems based on the adaptive technique. Secondly, a secure communication scheme via adaptive compound synchronization of four memristor chaotic oscillator systems is presented. The corresponding theoretical proofs and numerical simulations are given to demonstrate the validity and feasibility of the proposed control technique. The unpredictability of scaling drive systems can additionally enhance the security of communication. The transmitted signals can be split into several parts loaded in the drive systems to improve the reliability of communication.

Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2018-01-01

The classical connection between symmetry breaking and the onset of chaos in dynamical systems harks back to the seminal theory of Noether [Transp. Theory Statist. Phys. 1, 186 (1918), 10.1080/00411457108231446]. We study the Lagrangian kinematics of steady 3D Stokes flow through simple cubic and body-centered cubic (bcc) crystalline lattices of close-packed spheres, and uncover an important exception. While breaking of point-group symmetries is a necessary condition for chaotic mixing in both lattices, a further space-group (glide) symmetry of the bcc lattice generates a transition from globally regular to globally chaotic dynamics. This finding provides new insights into chaotic mixing in porous media and has significant implications for understanding the impact of symmetries upon generic dynamical systems.

Chaotic dynamics of a microswimmer in Poiseuille flow.

PubMed

Chacón, Ricardo

2013-11-01

The chaotic dynamics of pointlike, spherical particles in cylindrical Poiseuille flow is theoretically characterized and numerically confirmed when their own intrinsic swimming velocity undergoes temporal fluctuations around an average value. Two dimensionless ratios associated with the three significant temporal scales of the problem are identified that fully determine the chaos scenario. In particular, small but finite periodic fluctuations of swimming speed result in chaotic or regular motion depending on the position and orientation of the microswimmer with respect to the flow center line. Remarkably, the spatial extension of chaotic microswimmers is found to depend crucially on the fluctuations' period and amplitude and to be highly sensitive to the Fourier spectrum of the fluctuations. This has implications for the design of artificial microswimmers.

Characterization of stickiness by means of recurrence.

PubMed

Zou, Yong; Thiel, Marco; Romano, M Carmen; Kurths, Jürgen

2007-12-01

We propose recurrence plots (RPs) to characterize the stickiness of a typical area-preserving map with coexisting chaotic and regular orbits. The difference of the recurrence properties between quasiperiodic and chaotic orbits is revisited, which helps to understand the complex patterns of the corresponding RPs. Moreover, several measures from the recurrence quantification analysis are used to quantify these patterns. Among these measures, the recurrence rate, quantifying the percentage of black points in the plot, is applied to characterize the stickiness of a typical chaotic orbit. The advantage of the recurrence based method in comparison to other standard techniques is that it is possible to distinguish between quasiperiodic and chaotic orbits that are temporarily trapped in a sticky domain, from very short trajectories.

Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system

NASA Astrophysics Data System (ADS)

Zhou, Nanrun; Chen, Weiwei; Yan, Xinyu; Wang, Yunqian

2018-06-01

In order to obtain higher encryption efficiency, a bit-level quantum color image encryption scheme by exploiting quantum cross-exchange operation and a 5D hyper-chaotic system is designed. Additionally, to enhance the scrambling effect, the quantum channel swapping operation is employed to swap the gray values of corresponding pixels. The proposed color image encryption algorithm has larger key space and higher security since the 5D hyper-chaotic system has more complex dynamic behavior, better randomness and unpredictability than those based on low-dimensional hyper-chaotic systems. Simulations and theoretical analyses demonstrate that the presented bit-level quantum color image encryption scheme outperforms its classical counterparts in efficiency and security.

Security Analysis of Some Diffusion Mechanisms Used in Chaotic Ciphers

NASA Astrophysics Data System (ADS)

Zhang, Leo Yu; Zhang, Yushu; Liu, Yuansheng; Yang, Anjia; Chen, Guanrong

As a variant of the substitution-permutation network, the permutation-diffusion structure has received extensive attention in the field of chaotic cryptography over the last three decades. Because of the high implementation speed and nonlinearity over GF(2), the Galois field of two elements, mixing modulo addition/multiplication and Exclusive OR becomes very popular in various designs to achieve the desired diffusion effect. This paper reports that some diffusion mechanisms based on modulo addition/multiplication and Exclusive OR are not resistant to plaintext attacks as claimed. By cracking several recently proposed chaotic ciphers as examples, it is demonstrated that a good understanding of the strength and weakness of these crypto-primitives is crucial for designing more practical chaotic encryption algorithms in the future.

Regular and Chaotic Spatial Distribution of Bose-Einstein Condensed Atoms in a Ratchet Potential

NASA Astrophysics Data System (ADS)

Li, Fei; Xu, Lan; Li, Wenwu

2018-02-01

We study the regular and chaotic spatial distribution of Bose-Einstein condensed atoms with a space-dependent nonlinear interaction in a ratchet potential. There exists in the system a space-dependent atomic current that can be tuned via Feshbach resonance technique. In the presence of the space-dependent atomic current and a weak ratchet potential, the Smale-horseshoe chaos is studied and the Melnikov chaotic criterion is obtained. Numerical simulations show that the ratio between the intensities of optical potentials forming the ratchet potential, the wave vector of the laser producing the ratchet potential or the wave vector of the modulating laser can be chosen as the controlling parameters to result in or avoid chaotic spatial distributional states.

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1991-01-01

A preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity is presented. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. It is shown that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

Evidence of chaotic pattern in solar flux through a reproducible sequence of period-doubling-type bifurcations

NASA Technical Reports Server (NTRS)

Ashrafi, S.; Roszman, L.

1991-01-01

Presented here is a preliminary study of the limits to solar flux intensity prediction, and of whether the general lack of predictability in the solar flux arises from the nonlinear chaotic nature of the Sun's physical activity. Statistical analysis of a chaotic signal can extract only its most gross features, and detailed physical models fail, since even the simplest equations of motion for a nonlinear system can exhibit chaotic behavior. A recent theory by Feigenbaum suggests that nonlinear systems that can be led into chaotic behavior through a sequence of period-doubling bifurcations will exhibit a universal behavior. As the control parameter is increased, the bifurcation points occur in such a way that a proper ratio of these will approach the universal Feigenbaum number. Experimental evidence supporting the applicability of the Feigenbaum scenario to solar flux data is sparse. However, given the hypothesis that the Sun's convection zones are similar to a Rayleigh-Bernard mechanism, we can learn a great deal from the remarkable agreement observed between the prediction by theory (period doubling - a universal route to chaos) and the amplitude decrease of the signal's regular subharmonics. The authors show that period-doubling-type bifurcation is a possible route to a chaotic pattern of solar flux that is distinguishable from the logarithm of its power spectral density. This conclusion is the first positive step toward a reformulation of solar flux by a nonlinear chaotic approach. The ultimate goal of this research is to be able to predict an estimate of the upper and lower bounds for solar flux within its predictable zones. Naturally, it is an important task to identify the time horizons beyond which predictability becomes incompatible with computability.

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

Symmetry breaking: a tool to unveil the topology of chaotic scattering with three degrees of freedom

NASA Astrophysics Data System (ADS)

Jung, Christof; Zapfe, W. P. Karel; Merlo, Olivier; Seligman, T. H.

2010-12-01

We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.

Making chaotic behavior in a damped linear harmonic oscillator

NASA Astrophysics Data System (ADS)

Konishi, Keiji

2001-06-01

The present Letter proposes a simple control method which makes chaotic behavior in a damped linear harmonic oscillator. This method is a modified scheme proposed in paper by Wang and Chen (IEEE CAS-I 47 (2000) 410) which presents an anti-control method for making chaotic behavior in discrete-time linear systems. We provide a systematic procedure to design parameters and sampling period of a feedback controller. Furthermore, we show that our method works well on numerical simulations.

Synthesis of Feedback Controller for Chaotic Systems by Means of Evolutionary Techniques

NASA Astrophysics Data System (ADS)

Senkerik, Roman; Oplatkova, Zuzana; Zelinka, Ivan; Davendra, Donald; Jasek, Roman

2011-06-01

This research deals with a synthesis of control law for three selected discrete chaotic systems by means of analytic programming. The novality of the approach is that a tool for symbolic regression—analytic programming—is used for such kind of difficult problem. The paper consists of the descriptions of analytic programming as well as chaotic systems and used cost function. For experimentation, Self-Organizing Migrating Algorithm (SOMA) with analytic programming was used.

Symmetry breaking: a tool to unveil the topology of chaotic scattering with three degrees of freedom

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

Jung, Christof; Zapfe, W. P. Karel; Seligman, T. H.

2010-12-23

We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.

Chaotic Brillouin optical correlation-domain analysis

NASA Astrophysics Data System (ADS)

Zhang, Jianzhong; Zhang, Mingtao; Zhang, Mingjiang; Liu, Yi; Feng, Changkun; Wang, Yahui; Wang, Yuncai

2018-04-01

We propose and experimentally demonstrate a chaotic Brillouin optical correlation-domain analysis (BOCDA) system for distributed fiber sensing. The utilization of the chaotic laser with low coherent state ensures high spatial resolution. The experimental results demonstrate a 3.92-cm spatial resolution over a 906-m measurement range. The uncertainty in the measurement of the local Brillouin frequency shift is 1.2MHz. The measurement signal-to-noise ratio is given, which is agreement with the theoretical value.

Chaotic structures of nonlinear magnetic fields. I - Theory. II - Numerical results

NASA Technical Reports Server (NTRS)

Lee, Nam C.; Parks, George K.

1992-01-01

A study of the evolutionary properties of nonlinear magnetic fields in flowing MHD plasmas is presented to illustrate that nonlinear magnetic fields may involve chaotic dynamics. It is shown how a suitable transformation of the coupled equations leads to Duffing's form, suggesting that the behavior of the general solution can also be chaotic. Numerical solutions of the nonlinear magnetic field equations that have been cast in the form of Duffing's equation are presented.

Morphological Expressions of Crater Infill Collapse: Model Simulations of Chaotic Terrains on Mars

NASA Astrophysics Data System (ADS)

Roda, Manuel; Marketos, George; Westerweel, Jan; Govers, Rob

2017-10-01

Martian chaotic terrains are characterized by deeply depressed intensively fractured areas that contain a large number of low-strain tilted blocks. Stronger deformation (e.g., higher number of fractures) is generally observed in the rims when compared to the middle regions of the terrains. The distribution and number of fractures and tilted blocks are correlated with the size of the chaotic terrains. Smaller chaotic terrains are characterized by few fractures between undeformed blocks. Larger terrains show an elevated number of fractures uniformly distributed with single blocks. We investigate whether this surface morphology may be a consequence of the collapse of the infill of a crater. We perform numerical simulations with the Discrete Element Method and we evaluate the distribution of fractures within the crater and the influence of the crater size, infill thickness, and collapsing depth on the final morphology. The comparison between model predictions and the morphology of the Martian chaotic terrains shows strong statistical similarities in terms of both number of fractures and correlation between fractures and crater diameters. No or very weak correlation is observed between fractures and the infill thickness or collapsing depth. The strong correspondence between model results and observations suggests that the collapse of an infill layer within a crater is a viable mechanism for the peculiar morphology of the Martian chaotic terrains.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

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

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

Grebogi, C.; Yorke, J.A.

This report discusses the following topics: controlling chaotic dynamical systems; embedding of experimental data; effect of noise on critical exponents of crises; transition to chaotic scattering; and distribution of floaters on a fluid surface. (LSP)

Exponential H(infinity) synchronization of general discrete-time chaotic neural networks with or without time delays.

PubMed

Qi, Donglian; Liu, Meiqin; Qiu, Meikang; Zhang, Senlin

2010-08-01

This brief studies exponential H(infinity) synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H(infinity) control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H(infinity) norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H(infinity) synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.

On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

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

Kengne, Jacques; Kenmogne, Fabien

2014-12-15

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by usingmore » time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.« less

Is the normal heart rate ``chaotic'' due to respiration?

NASA Astrophysics Data System (ADS)

Wessel, Niels; Riedl, Maik; Kurths, Jürgen

2009-06-01

The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: "Is the normal heart rate `chaotic' due to respiration?"

Alteration of chaotic advection in blood flow around partial blockage zone: Role of hematocrit concentration

NASA Astrophysics Data System (ADS)

Maiti, Soumyabrata; Chaudhury, Kaustav; DasGupta, Debabrata; Chakraborty, Suman

2013-01-01

Spatial distributions of particles carried by blood exhibit complex filamentary pattern under the combined effects of geometrical irregularities of the blood vessels and pulsating pumping by the heart. This signifies the existence of so called chaotic advection. In the present article, we argue that the understanding of such pathologically triggered chaotic advection is incomplete without giving due consideration to a major constituent of blood: abundant presence of red blood cells quantified by the hematocrit (HCT) concentration. We show that the hematocrit concentration in blood cells can alter the filamentary structures of the spatial distribution of advected particles in an intriguing manner. Our results reveal that there primarily are two major impacts of HCT concentrations towards dictating the chaotic dynamics of blood flow: changing the zone of influence of chaotic mixing and determining the enhancement of residence time of the advected particles away from the wall. This, in turn, may alter the extent of activation of platelets or other reactive biological entities, bearing immense consequence towards dictating the biophysical mechanisms behind possible life-threatening diseases originating in the circulatory system.

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.

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.

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

NASA Technical Reports Server (NTRS)

Deissler, Robert G.

1996-01-01

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform

NASA Astrophysics Data System (ADS)

Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun

2018-07-01

Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.

Emergent patterns in interacting neuronal sub-populations

NASA Astrophysics Data System (ADS)

Kamal, Neeraj Kumar; Sinha, Sudeshna

2015-05-01

We investigate an ensemble of coupled model neurons, consisting of groups of varying sizes and intrinsic dynamics, ranging from periodic to chaotic, where the inter-group coupling interaction is effectively like a dynamic signal from a different sub-population. We observe that the minority group can significantly influence the majority group. For instance, when a small chaotic group is coupled to a large periodic group, the chaotic group de-synchronizes. However, counter-intuitively, when a small periodic group couples strongly to a large chaotic group, it leads to complete synchronization in the majority chaotic population, which also spikes at the frequency of the small periodic group. It then appears that the small group of periodic neurons can act like a pacemaker for the whole network. Further, we report the existence of varied clustering patterns, ranging from sets of synchronized clusters to anti-phase clusters, governed by the interplay of the relative sizes and dynamics of the sub-populations. So these results have relevance in understanding how a group can influence the synchrony of another group of dynamically different elements, reminiscent of event-related synchronization/de-synchronization in complex networks.

Linking Chaotic Advection with Subsurface Biogeochemical Processes

NASA Astrophysics Data System (ADS)

Mays, D. C.; Freedman, V. L.; White, S. K.; Fang, Y.; Neupauer, R.

2017-12-01

This work investigates the extent to which groundwater flow kinematics drive subsurface biogeochemical processes. In terms of groundwater flow kinematics, we consider chaotic advection, whose essential ingredient is stretching and folding of plumes. Chaotic advection is appealing within the context of groundwater remediation because it has been shown to optimize plume spreading in the laminar flows characteristic of aquifers. In terms of subsurface biogeochemical processes, we consider an existing model for microbially-mediated reduction of relatively mobile uranium(VI) to relatively immobile uranium(IV) following injection of acetate into a floodplain aquifer beneath a former uranium mill in Rifle, Colorado. This model has been implemented in the reactive transport code eSTOMP, the massively parallel version of STOMP (Subsurface Transport Over Multiple Phases). This presentation will report preliminary numerical simulations in which the hydraulic boundary conditions in the eSTOMP model are manipulated to simulate chaotic advection resulting from engineered injection and extraction of water through a manifold of wells surrounding the plume of injected acetate. This approach provides an avenue to simulate the impact of chaotic advection within the existing framework of the eSTOMP code.

Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows

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

Ottino, J.M.

1991-05-01

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of microstructures'' whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context ofmore » the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.« less

Chaotic examination

NASA Astrophysics Data System (ADS)

Bildirici, Melike; Sonustun, Fulya Ozaksoy; Sonustun, Bahri

2018-01-01

In the regards of chaos theory, new concepts such as complexity, determinism, quantum mechanics, relativity, multiple equilibrium, complexity, (continuously) instability, nonlinearity, heterogeneous agents, irregularity were widely questioned in economics. It is noticed that linear models are insufficient for analyzing unpredictable, irregular and noncyclical oscillations of economies, and for predicting bubbles, financial crisis, business cycles in financial markets. Therefore, economists gave great consequence to use appropriate tools for modelling non-linear dynamical structures and chaotic behaviors of the economies especially in macro and the financial economy. In this paper, we aim to model the chaotic structure of exchange rates (USD-TL and EUR-TL). To determine non-linear patterns of the selected time series, daily returns of the exchange rates were tested by BDS during the period from January 01, 2002 to May 11, 2017 which covers after the era of the 2001 financial crisis. After specifying the non-linear structure of the selected time series, it was aimed to examine the chaotic characteristic for the selected time period by Lyapunov Exponents. The findings verify the existence of the chaotic structure of the exchange rate returns in the analyzed time period.

Design and FPGA Implementation of a Universal Chaotic Signal Generator Based on the Verilog HDL Fixed-Point Algorithm and State Machine Control

NASA Astrophysics Data System (ADS)

Qiu, Mo; Yu, Simin; Wen, Yuqiong; Lü, Jinhu; He, Jianbin; Lin, Zhuosheng

In this paper, a novel design methodology and its FPGA hardware implementation for a universal chaotic signal generator is proposed via the Verilog HDL fixed-point algorithm and state machine control. According to continuous-time or discrete-time chaotic equations, a Verilog HDL fixed-point algorithm and its corresponding digital system are first designed. In the FPGA hardware platform, each operation step of Verilog HDL fixed-point algorithm is then controlled by a state machine. The generality of this method is that, for any given chaotic equation, it can be decomposed into four basic operation procedures, i.e. nonlinear function calculation, iterative sequence operation, iterative values right shifting and ceiling, and chaotic iterative sequences output, each of which corresponds to only a state via state machine control. Compared with the Verilog HDL floating-point algorithm, the Verilog HDL fixed-point algorithm can save the FPGA hardware resources and improve the operation efficiency. FPGA-based hardware experimental results validate the feasibility and reliability of the proposed approach.

Computing with Chaos

NASA Astrophysics Data System (ADS)

Murali, K.; Sinah, Sudeshna; Ditto, William

2004-03-01

Recently there has been a new theoretical direction in harnessing the richness of spatially extended chaotic systems, namely the exploitation of coupled chaotic elements to do flexible computations [1]. The aim of this presentation is to demonstrate the use a single chaotic element to emulate different logic gates and perform different arithmetic tasks. Additionally we demonstrate that the elements can be controlled to switch easily between the different operational roles. Such a computing unit may then allow a more dynamic computer architecture and serve as ingredients of a general-purpose device more flexible than statically wired hardware. The theoretical scheme for flexible implementation of all these fundamental logical operations utilizing low dimensional chaos [1] will be reviewed along with a specific realization of the theory in a chaotic circuit [2]. Results will also be presented from experiments done on leech neurons. [1] Sinha, S., Munakata, T. and Ditto, W.L., Phys. Rev. E 65 036216 [2] "Experimental realization of the fundamental NOR Gate using a chaotic circuit," K. Murali, Sudeshna Sinha and William L. Ditto Phys. Rev. E 68, 016205 (2003).

Chaotic oscillator containing memcapacitor and meminductor and its dimensionality reduction analysis.

PubMed

Yuan, Fang; Wang, Guangyi; Wang, Xiaowei

2017-03-01

In this paper, smooth curve models of meminductor and memcapacitor are designed, which are generalized from a memristor. Based on these models, a new five-dimensional chaotic oscillator that contains a meminductor and memcapacitor is proposed. By dimensionality reducing, this five-dimensional system can be transformed into a three-dimensional system. The main work of this paper is to give the comparisons between the five-dimensional system and its dimensionality reduction model. To investigate dynamics behaviors of the two systems, equilibrium points and stabilities are analyzed. And the bifurcation diagrams and Lyapunov exponent spectrums are used to explore their properties. In addition, digital signal processing technologies are used to realize this chaotic oscillator, and chaotic sequences are generated by the experimental device, which can be used in encryption applications.

Maximizing the security of chaotic optical communications.

PubMed

Hou, T T; Yi, L L; Yang, X L; Ke, J X; Hu, Y; Yang, Q; Zhou, P; Hu, W S

2016-10-03

The practical application of chaotic optical communications has been limited by two aspects: the difficulty in concealing the time delay - a critical security parameter in feedback chaotic systems, and the difficulty of significantly enlarging the key space without complicating the implementation. Here we propose an architecture to break the above limits. By introducing a frequency-dependent group delay module with frequency tuning resolution of 1 MHz into the chaotic feedback loop, we demonstrate excellent time delay concealment effect, and an additional huge key space of 10⁴⁸ can be achieved at the same time. The effectiveness is proved by both numerical simulation and experiment. Besides, the proposed scheme is compatible with the existing commercial optical communication systems, thus pave the way for high-speed secure optical communications.

Parameter Estimation of Fractional-Order Chaotic Systems by Using Quantum Parallel Particle Swarm Optimization Algorithm

PubMed Central

Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng

2015-01-01

Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158

Desktop chaotic systems: Intuition and visualization

NASA Technical Reports Server (NTRS)

Bright, Michelle M.; Melcher, Kevin J.; Qammar, Helen K.; Hartley, Tom T.

1993-01-01

This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.

Transversal homoclinic orbits in a transiently chaotic neural network.

PubMed

Chen, Shyan-Shiou; Shih, Chih-Wen

2002-09-01

We study the existence of snap-back repellers, hence the existence of transversal homoclinic orbits in a discrete-time neural network. Chaotic behaviors for the network system in the sense of Li and Yorke or Marotto can then be concluded. The result is established by analyzing the structures of the system and allocating suitable parameters in constructing the fixed points and their pre-images for the system. The investigation provides a theoretical confirmation on the scenario of transient chaos for the system. All the parameter conditions for the theory can be examined numerically. The numerical ranges for the parameters which yield chaotic dynamics and convergent dynamics provide significant information in the annealing process in solving combinatorial optimization problems using this transiently chaotic neural network. (c) 2002 American Institute of Physics.

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.

Human brain detects short-time nonlinear predictability in the temporal fine structure of deterministic chaotic sounds

NASA Astrophysics Data System (ADS)

Itoh, Kosuke; Nakada, Tsutomu

2013-04-01

Deterministic nonlinear dynamical processes are ubiquitous in nature. Chaotic sounds generated by such processes may appear irregular and random in waveform, but these sounds are mathematically distinguished from random stochastic sounds in that they contain deterministic short-time predictability in their temporal fine structures. We show that the human brain distinguishes deterministic chaotic sounds from spectrally matched stochastic sounds in neural processing and perception. Deterministic chaotic sounds, even without being attended to, elicited greater cerebral cortical responses than the surrogate control sounds after about 150 ms in latency after sound onset. Listeners also clearly discriminated these sounds in perception. The results support the hypothesis that the human auditory system is sensitive to the subtle short-time predictability embedded in the temporal fine structure of sounds.

Dynamic analysis, circuit implementation and passive control of a novel four-dimensional chaotic system with multiscroll attractor and multiple coexisting attractors

NASA Astrophysics Data System (ADS)

Lai, Bang-Cheng; He, Jian-Jun

2018-03-01

In this paper, we construct a novel 4D autonomous chaotic system with four cross-product nonlinear terms and five equilibria. The multiple coexisting attractors and the multiscroll attractor of the system are numerically investigated. Research results show that the system has various types of multiple attractors, including three strange attractors with a limit cycle, three limit cycles, two strange attractors with a pair of limit cycles, two coexisting strange attractors. By using the passive control theory, a controller is designed for controlling the chaos of the system. Both analytical and numerical studies verify that the designed controller can suppress chaotic motion and stabilise the system at the origin. Moreover, an electronic circuit is presented for implementing the chaotic system.

Chaotic dynamics of large-scale double-diffusive convection in a porous medium

NASA Astrophysics Data System (ADS)

Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

2018-02-01

We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

Competitions hatch butterfly attractors in foreign exchange markets

NASA Astrophysics Data System (ADS)

Jin, Yu Ying

2005-03-01

Chaos in foreign exchange markets is a common issue of concern in the study of economic dynamics. In this work, we mainly investigate the competition effect on chaos in foreign exchange markets. As one of the main economic structures in the globalization process, competition between two target exchange rates with the same base currency forms a simple competitive exchange rate relation, where each exchange rate follows the chaotic model of De Grauwe (Exchange Rate Theory-Chaotic Models of Foreign Exchange Markets, Blackwell, Oxford, Cambridge, MA, 1993). The main discovery is, while each exchange rate is in its non-chaotic parameter regions, the effect of competition will “hatch” butterfly-like chaotic attractors in the competitive market. The positive Lyapunov exponent in the market explains the reason why chaos occurs.

Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Wu, Wei; Cui, Bao-Tong

2007-07-01

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

Mixing by Unstirring: Hyperuniform Dispersion of Interacting Particles upon Chaotic Advection

NASA Astrophysics Data System (ADS)

Weijs, Joost H.; Bartolo, Denis

2017-07-01

We show how to achieve both fast and hyperuniform dispersions of particles in viscous fluids. To do so, we first extend the concept of critical random organization to chaotic drives. We show how palindromic sequences of chaotic advection cause microscopic particles to effectively interact at long range, thereby inhibiting critical self-organization. Based on this understanding we go around this limitation and design sequences of stirring and unstirring which simultaneously optimize the speed of particle spreading and the homogeneity of the resulting dispersions.

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.

Dynamic Long-Term Anticipation of Chaotic States

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

Voss, Henning U.

2001-07-02

Introducing a short time delay into the coupling of two synchronizing chaotic systems, it was shown recently that the driven system may anticipate the driving system in real time. Augmenting the phase space of the driven system, we accomplish anticipation times that are multiples of the coupling delay time and exceed characteristic time scales of the chaotic dynamics. The stability properties of the associated anticipatory synchronization manifold in certain cases turn out to be the same as for identically synchronizing oscillators.

Transient statistics in stabilizing periodic orbits

NASA Astrophysics Data System (ADS)

Meucci, R.; Gadomski, W.; Ciofini, M.; Arecchi, F. T.

1995-11-01

The statistics of chaotic and periodic transient time intervals preceding the stabilization of a given periodic orbit have been experimentally studied in a CO2 laser with modulated losses, subjected to a small subharmonic perturbation. As predicted by the theory, an exponential tail has been found in the probability distribution of chaotic transients. Furthermore, a fine periodic structure in the distributions of the periodic transients, resulting from the interaction of the control signal and the local structure of the chaotic attractor, has been revealed.

Recent developments in chaotic dynamics

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

Ott, E.

1994-02-01

Before the relatively recent wide acceptance of the existence of chaotic dynamics, many physicists and engineers were under the impression that simple systems could necessarily only display simple solutions. This feeling had been unintentionally reinforced by conventional college courses which emphasize linear dynamics (partly because that is the only case with nice general solutions). More recently, physical experiments and numerical examples have abundantly demonstrated how wrong this feeling is. A brief review of chaotic dynamics is presented. Topics discussed include basic concepts, recent developments, and applications.

Firefly algorithm with chaos

NASA Astrophysics Data System (ADS)

Gandomi, A. H.; Yang, X.-S.; Talatahari, S.; Alavi, A. H.

2013-01-01

A recently developed metaheuristic optimization algorithm, firefly algorithm (FA), mimics the social behavior of fireflies based on the flashing and attraction characteristics of fireflies. In the present study, we will introduce chaos into FA so as to increase its global search mobility for robust global optimization. Detailed studies are carried out on benchmark problems with different chaotic maps. Here, 12 different chaotic maps are utilized to tune the attractive movement of the fireflies in the algorithm. The results show that some chaotic FAs can clearly outperform the standard FA.

Transition of chaotic motion to a limit cycle by intervention of economic policy: an empirical analysis in agriculture.

PubMed

Sakai, Kenshi; Managi, Shunsuke; Vitanov, Nikolay K; Demura, Katsuhiko

2007-04-01

This paper investigates the transition of dynamics observed in an actual real agricultural economic dataset. Lyapunov spectrum analysis is conducted on the data to distinguish deterministic chaos and the limit cycle. Chaotic and periodic oscillation were identified before and after the second oil crisis, respectively. The statitonarity of the time series is investigated using recurrence plots. This shows that government intervention might reduce market instability by removing a chaotic market's long-term unpredictability.

Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers

NASA Astrophysics Data System (ADS)

Li, Huanan; Suwunnarat, Suwun; Fleischmann, Ragnar; Schanz, Holger; Kottos, Tsampikos

2017-01-01

We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γCPA and energy ECPA, for which a CPA occurs, are expressed in terms of the eigenmodes of the isolated cavity—thus carrying over the information about the chaotic nature of the target—and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.

Using chaotic artificial neural networks to model memory in the brain

NASA Astrophysics Data System (ADS)

Aram, Zainab; Jafari, Sajad; Ma, Jun; Sprott, Julien C.; Zendehrouh, Sareh; Pham, Viet-Thanh

2017-03-01

In the current study, a novel model for human memory is proposed based on the chaotic dynamics of artificial neural networks. This new model explains a biological fact about memory which is not yet explained by any other model: There are theories that the brain normally works in a chaotic mode, while during attention it shows ordered behavior. This model uses the periodic windows observed in a previously proposed model for the brain to store and then recollect the information.

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.

Experimental Control of a Fast Chaotic Time-Delay Opto-Electronic Device

DTIC Science & Technology

2003-01-01

chaotic sources such as the erbium-doped Þber laser. The basic idea is to use the message as a driving signal for the chaotic system. The message...47 x 3.10 Block diagram of feedback loop. Light from the interferometer is con- verted into an electrical signal by the photodiode (PD). All...a time delay of τD. Finally, the electrical signal is converted back into light by the laser diode (LD). . . . . . . . . . . . . . . . . 48 3.11 Setup

Stability analysis of piecewise non-linear systems and its application to chaotic synchronisation with intermittent control

NASA Astrophysics Data System (ADS)

Wang, Qingzhi; Tan, Guanzheng; He, Yong; Wu, Min

2017-10-01

This paper considers a stability analysis issue of piecewise non-linear systems and applies it to intermittent synchronisation of chaotic systems. First, based on piecewise Lyapunov function methods, more general and less conservative stability criteria of piecewise non-linear systems in periodic and aperiodic cases are presented, respectively. Next, intermittent synchronisation conditions of chaotic systems are derived which extend existing results. Finally, Chua's circuit is taken as an example to verify the validity of our methods.

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 robustness of complex heterogeneous gene expression networks.

PubMed

Gómez-Gardeñes, Jesús; Moreno, Yamir; Floría, Luis M

2005-04-01

We analyze a continuous gene expression model on the underlying topology of a complex heterogeneous network. Numerical simulations aimed at studying the chaotic and periodic dynamics of the model are performed. The results clearly indicate that there is a region in which the dynamical and structural complexity of the system avoid chaotic attractors. However, contrary to what has been reported for Random Boolean Networks, the chaotic phase cannot be completely suppressed, which has important bearings on network robustness and gene expression modeling.

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.

Antiphase synchronization in coupled chaotic oscillators.

PubMed

Liu, Weiqing; Xiao, Jinghua; Qian, Xiaolan; Yang, Junzhong

2006-05-01

Anti-phase synchronization (AS) in coupled chaotic oscillators is investigated. The necessary condition for AS is given and the stability of AS is studied. Results are demonstrated with numerical simulations and electronic circuits.

A Route to Chaotic Behavior of Single Neuron Exposed to External Electromagnetic Radiation.

PubMed

Feng, Peihua; Wu, Ying; Zhang, Jiazhong

2017-01-01

Non-linear behaviors of a single neuron described by Fitzhugh-Nagumo (FHN) neuron model, with external electromagnetic radiation considered, is investigated. It is discovered that with external electromagnetic radiation in form of a cosine function, the mode selection of membrane potential occurs among periodic, quasi-periodic, and chaotic motions as increasing the frequency of external transmembrane current, which is selected as a sinusoidal function. When the frequency is small or large enough, periodic, and quasi-periodic motions are captured alternatively. Otherwise, when frequency is in interval 0.778 < ω < 2.208, chaotic motion characterizes the main behavior type. The mechanism of mode transition from quasi-periodic to chaotic motion is also observed when varying the amplitude of external electromagnetic radiation. The frequency apparently plays a more important role in determining the system behavior.

A Route to Chaotic Behavior of Single Neuron Exposed to External Electromagnetic Radiation

PubMed Central

Feng, Peihua; Wu, Ying; Zhang, Jiazhong

2017-01-01

Non-linear behaviors of a single neuron described by Fitzhugh-Nagumo (FHN) neuron model, with external electromagnetic radiation considered, is investigated. It is discovered that with external electromagnetic radiation in form of a cosine function, the mode selection of membrane potential occurs among periodic, quasi-periodic, and chaotic motions as increasing the frequency of external transmembrane current, which is selected as a sinusoidal function. When the frequency is small or large enough, periodic, and quasi-periodic motions are captured alternatively. Otherwise, when frequency is in interval 0.778 < ω < 2.208, chaotic motion characterizes the main behavior type. The mechanism of mode transition from quasi-periodic to chaotic motion is also observed when varying the amplitude of external electromagnetic radiation. The frequency apparently plays a more important role in determining the system behavior. PMID:29089882

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-06-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems

NASA Astrophysics Data System (ADS)

Sun, Jun-Wei; Shen, Yi; Zhang, Guo-Dong; Wang, Yan-Feng; Cui, Guang-Zhao

2013-04-01

According to the Lyapunov stability theorem, a new general hybrid projective complete dislocated synchronization scheme with non-derivative and derivative coupling based on parameter identification is proposed under the framework of drive-response systems. Every state variable of the response system equals the summation of the hybrid drive systems in the previous hybrid synchronization. However, every state variable of the drive system equals the summation of the hybrid response systems while evolving with time in our method. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-derivative and derivative coupling, and parameter identification are included as its special item. The Lorenz chaotic system, Rössler chaotic system, memristor chaotic oscillator system, and hyperchaotic Lü system are discussed to show the effectiveness of the proposed methods.

Design and implementation of grid multi-scroll fractional-order chaotic attractors

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

Chen, Liping, E-mail: lip-chenhut@126.com; Pan, Wei; Wu, Ranchao

2016-08-15

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most.more » Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.« less

Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme

NASA Astrophysics Data System (ADS)

Khanzadeh, Alireza; Pourgholi, Mahdi

2016-08-01

In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-04-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

A new approach of optimal control for a class of continuous-time chaotic systems by an online ADP algorithm

NASA Astrophysics Data System (ADS)

Song, Rui-Zhuo; Xiao, Wen-Dong; Wei, Qing-Lai

2014-05-01

We develop an online adaptive dynamic programming (ADP) based optimal control scheme for continuous-time chaotic systems. The idea is to use the ADP algorithm to obtain the optimal control input that makes the performance index function reach an optimum. The expression of the performance index function for the chaotic system is first presented. The online ADP algorithm is presented to achieve optimal control. In the ADP structure, neural networks are used to construct a critic network and an action network, which can obtain an approximate performance index function and the control input, respectively. It is proven that the critic parameter error dynamics and the closed-loop chaotic systems are uniformly ultimately bounded exponentially. Our simulation results illustrate the performance of the established optimal control method.

Modelling and prediction for chaotic fir laser attractor using rational function neural network.

PubMed

Cho, S

2001-02-01

Many real-world systems such as irregular ECG signal, volatility of currency exchange rate and heated fluid reaction exhibit highly complex nonlinear characteristic known as chaos. These chaotic systems cannot be retreated satisfactorily using linear system theory due to its high dimensionality and irregularity. This research focuses on prediction and modelling of chaotic FIR (Far InfraRed) laser system for which the underlying equations are not given. This paper proposed a method for prediction and modelling a chaotic FIR laser time series using rational function neural network. Three network architectures, TDNN (Time Delayed Neural Network), RBF (radial basis function) network and the RF (rational function) network, are also presented. Comparisons between these networks performance show the improvements introduced by the RF network in terms of a decrement in network complexity and better ability of predictability.

Amplification through chaotic synchronization in spatially extended beam-plasma systems

NASA Astrophysics Data System (ADS)

Moskalenko, Olga I.; Frolov, Nikita S.; Koronovskii, Alexey A.; Hramov, Alexander E.

2017-12-01

In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.

Chaotic Mixing in Magmatic Systems: a new experiment

NASA Astrophysics Data System (ADS)

de Campos, C. P.; Perugini, D.; Dingwell, D. B.; Poli, G.; Ertel-Ingrisch, W.; Hess, K.

2007-12-01

Previous studies on magma mixing systems have evidenced that mixing processes could be controlled by chaotic dynamics. These processes are thought to be the source of fractal structures propagating within natural magmatic systems, from meter to the micrometer length scale (Perugini et al., 2006. EPSL, 234: 669-680 and references therein). We have developed a device for experimental studies of chaotic mixing dynamics in silicate melts at high temperatures (up to 1700°C). This device has been inspired by the journal bearing or eccentric cylinder geometry for viscous fluids for the study of chaotic mixing in slow flows (Swanson and Ottino, 1990. J. Fluid Mech., 213:227-249). This geometry is thought to be an ideal system for chaotic studies because a) it is experimentally accessible/feasible for silicate rheologies and b) it is subject to an analytical solution for the stream function. In the journal bearing system the flow region, is confined in the torus between the centers of the two cylinders. Their central axes are parallel but not coincident, i. e. the cylinders are eccentric. In order to generate chaos in a flow, the streamlines must be time dependent, resulting in alternating movements between the two cylinders. This means that at least one of the cylinders has alternating rotation directions. The dimension of this new experimental device follows the required main dimensionless numbers for a chaotic flow. Our first experimental goal is to characterize the mixing process in a prototypical system (haplogranite-haplobasalt)under variable mixing protocols. muenchen.de/

Symmetric encryption algorithms using chaotic and non-chaotic generators: A review

PubMed Central

Radwan, Ahmed G.; AbdElHaleem, Sherif H.; Abd-El-Hafiz, Salwa K.

2015-01-01

This paper summarizes the symmetric image encryption results of 27 different algorithms, which include substitution-only, permutation-only or both phases. The cores of these algorithms are based on several discrete chaotic maps (Arnold’s cat map and a combination of three generalized maps), one continuous chaotic system (Lorenz) and two non-chaotic generators (fractals and chess-based algorithms). Each algorithm has been analyzed by the correlation coefficients between pixels (horizontal, vertical and diagonal), differential attack measures, Mean Square Error (MSE), entropy, sensitivity analyses and the 15 standard tests of the National Institute of Standards and Technology (NIST) SP-800-22 statistical suite. The analyzed algorithms include a set of new image encryption algorithms based on non-chaotic generators, either using substitution only (using fractals) and permutation only (chess-based) or both. Moreover, two different permutation scenarios are presented where the permutation-phase has or does not have a relationship with the input image through an ON/OFF switch. Different encryption-key lengths and complexities are provided from short to long key to persist brute-force attacks. In addition, sensitivities of those different techniques to a one bit change in the input parameters of the substitution key as well as the permutation key are assessed. Finally, a comparative discussion of this work versus many recent research with respect to the used generators, type of encryption, and analyses is presented to highlight the strengths and added contribution of this paper. PMID:26966561

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh—Rose neuron model

NASA Astrophysics Data System (ADS)

Jia, Bing

2014-03-01

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh—Rose (HR) neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two-dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the deterministic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in different two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops

NASA Astrophysics Data System (ADS)

Rahman, Aminur; Jordan, Ian; Blackmore, Denis

2018-01-01

It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.

Hypothesis on the Origin of Chaotic Pulse Train in Dart Leader

NASA Astrophysics Data System (ADS)

Pu, Y.; Qie, X.; Sun, Z.; Jiang, R.; Liu, M.; Zhang, H.

2017-12-01

The origin of chaotic pulse train (CPT) during the dart leader propagation remains debatable. Based on previous observations, the `chaotic' dart leader is featured by chaotic electric fields, large charge transfer and high energetic radiation. In some cases, the cause of CPT was attributed to the concurrent branches or upward connecting leader. In this presentation, after carefully examining the simultaneous optical, electrical and VHF location data of triggered lightning in SHATLE and some results in other literature, we found the close relationship between the upper luminous leader segment and CPT. It is hypothesized that the CPT originates from the luminous corona zone around the upper leader channel beyond the leader tip. The fast, sufficient supply of negative charge from the cloud can result in a net negative charge layer around the ionized channel surface. Then new diffuse discharge can make a corona zone outside the channel and radiates in a chaotic way. The cloud charge reservoir and the speed of charge transfer, which can be indicated by the speed of the leader, are determinative to the generation of CPT. Using VHF location technique, we also estimated the speed evolution of the leader and link it with electric field change.

Extreme multistability analysis of memristor-based chaotic system and its application in image decryption

NASA Astrophysics Data System (ADS)

Li, Chuang; Min, Fuhong; Jin, Qiusen; Ma, Hanyuan

2017-12-01

An active charge-controlled memristive Chua's circuit is implemented, and its basic properties are analyzed. Firstly, with the system trajectory starting from an equilibrium point, the dynamic behavior of multiple coexisting attractors depending on the memristor initial value and the system parameter is studied, which shows the coexisting behaviors of point, period, chaos, and quasic-period. Secondly, with the system motion starting from a non-equilibrium point, the dynamics of extreme multistability in a wide initial value domain are easily conformed by new analytical methods. Furthermore, the simulation results indicate that some strange chaotic attractors like multi-wing type and multi-scroll type are observed when the observed signals are extended from voltage and current to power and energy, respectively. Specially, when different initial conditions are taken, the coexisting strange chaotic attractors between the power and energy signals are exhibited. Finally, the chaotic sequences of the new system are used for encrypting color image to protect image information security. The encryption performance is analyzed by statistic histogram, correlation, key spaces and key sensitivity. Simulation results show that the new memristive chaotic system has high security in color image encryption.

Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops.

PubMed

Rahman, Aminur; Jordan, Ian; Blackmore, Denis

2018-01-01

It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behaviour. This behaviour can be used to design analogues of more complex logic families and some properties can be exploited for electronics applications. Some of these circuits have been modelled as systems of ordinary differential equations. However, as the number of components in newer circuits increases so does the complexity. This renders continuous dynamical systems models impractical and necessitates new modelling techniques. In recent years, some discrete dynamical models have been developed using various simplifying assumptions. To create a robust modelling framework for chaotic logical circuits, we developed both deterministic and stochastic discrete dynamical models, which exploit the natural recurrence behaviour, for two chaotic NOR gates and a chaotic set/reset flip-flop. This work presents a complete applied mathematical investigation of logical circuits. Experiments on our own designs of the above circuits are modelled and the models are rigorously analysed and simulated showing surprisingly close qualitative agreement with the experiments. Furthermore, the models are designed to accommodate dynamics of similarly designed circuits. This will allow researchers to develop ever more complex chaotic logical circuits with a simple modelling framework.

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.

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

NASA Technical Reports Server (NTRS)

Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.

1989-01-01

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

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.

Synchronization in node of complex networks consist of complex chaotic system

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

Wei, Qiang, E-mail: qiangweibeihua@163.com; Digital Images Processing Institute of Beihua University, BeiHua University, Jilin, 132011, Jilin; Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024

2014-07-15

A new synchronization method is investigated for node of complex networks consists of complex chaotic system. When complex networks realize synchronization, different component of complex state variable synchronize up to different scaling complex function by a designed complex feedback controller. This paper change synchronization scaling function from real field to complex field for synchronization in node of complex networks with complex chaotic system. Synchronization in constant delay and time-varying coupling delay complex networks are investigated, respectively. Numerical simulations are provided to show the effectiveness of the proposed method.

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.

Chaotic itinerancy in the oscillator neural network without Lyapunov functions.

PubMed

Uchiyama, Satoki; Fujisaka, Hirokazu

2004-09-01

Chaotic itinerancy (CI), which is defined as an incessant spontaneous switching phenomenon among attractor ruins in deterministic dynamical systems without Lyapunov functions, is numerically studied in the case of an oscillator neural network model. The model is the pseudoinverse-matrix version of the previous model [S. Uchiyama and H. Fujisaka, Phys. Rev. E 65, 061912 (2002)] that was studied theoretically with the aid of statistical neurodynamics. It is found that CI in neural nets can be understood as the intermittent dynamics of weakly destabilized chaotic retrieval solutions. Copyright 2004 American Institute of Physics

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 advection in a 2-D mixed convection flow

NASA Astrophysics Data System (ADS)

Tangborn, Andrew V.; Silevitch, Daniel M.; Howes, Tony

1995-06-01

Two-dimensional numerical simulations of particle advection in a channel flow with spatially periodic heating have been carried out. The velocity field is found to be periodic above a critical Rayleigh number of around 18 000 and a Reynolds number of 10. Particle motion becomes chaotic in the lower half plane almost immediately after this critical value is surpassed, as characterized by the power spectral density and Poincaré section of the flow. As the Rayleigh number is increased further, particle motion in the entire domain becomes chaotic.

Chaotic terrain of Mars - A tectonic interpretation from Mariner 6 imagery

NASA Technical Reports Server (NTRS)

Wilson, R. C.; Harp, E. L.; Picard, M. D.; Ward, S. H.

1973-01-01

Sharp et al. (1971) define chaotic terrain as an irregular jumble of topographic forms covering a certain area within Pyrrhae Regio and adjacent regions centered at about 10 deg S., 35 deg W. This area is covered by Mariner 6 television imagery. An analysis of fracture patterns in the Martian surface from high-resolution Mariner 6 imagery suggests that the lineaments observed in both the chaotic terrain and the cratered plateau areas in Pyrrhae Regio are tectonic fractures resulting from stresses within the Martian crust.

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

Munoz, Pablo R.; Rempel, Erico L.; Barroso, Joaquim J.

We study the chaotic dynamics of the Pierce diode, a simple spatially extended system for collisionless bounded plasmas, focusing on the concept of edge of chaos, the boundary that separates transient from asymptotic dynamics. We fully characterize an interior crisis at the end of a periodic window, thereby showing direct evidence of the collision between a chaotic attractor, a chaotic saddle, and the edge of chaos, formed by a period-3 unstable periodic orbit and its stable manifold. The edge of chaos persists after the interior crisis, when the global attractor of the system increases its size in the phase space.

ASTEROIDS: Living in the Kingdom of Chaos

NASA Astrophysics Data System (ADS)

Morbidelli, A.

2000-10-01

The existence of chaotic regions in the main asteroid belt, related with the lowest-order mean-motion and secular resonances, has long been known. However, only in the last decade have semi-analytic theories allowed a proper understanding of the chaotic behavior observed in numerical simulations which accurately incorporate the entire planetary system. The most spectacular result has been the discovery that the asteroids in some of these resonance may collide with the Sun on typical time scales of a few million year, their eccentricities being pumped to unity during their chaotic evolution. But the asteroid belt is not simply divided into violent chaotic zones and regular regions. It has been shown that the belt is criss-crossed by a large number of high-order mean-motion resonances with Jupiter or Mars, as well as by `three-body resonances' with Jupiter and Saturn. All these weak resonances cause the slow chaotic drift of the `proper' eccentricities and inclinations. The traces left by this evolution are visible, for example, in the structure of the Eos and Themis asteroid families. Weak chaos may also explain the anomalous dispersion of the eccentricities and inclinations observed in the Flora ``clan." Moreover, due to slow increases in their eccentricities, many asteroids start to cross the orbit of Mars, over a wide range of semimajor axes. The improved knowledge of the asteroid belt's chaotic structure provides, for the first time, an opportunity to build detailed quantitative models of the origin and the orbital distribution of Near-Earth Asteroids and meteorites. In turn, these models seem to imply that the semimajor axes of main-belt asteroids must also slowly evolve with time. For asteroids larger than about 20 km this is due mainly to encounters with Ceres, Pallas, and Vesta, while for smaller bodies the so-called Yarkovsky effect should dominate. Everything moves chaotically in the asteroid belt.

Chaotic dynamics in nanoscale NbO2 Mott memristors for analogue computing

NASA Astrophysics Data System (ADS)

Kumar, Suhas; Strachan, John Paul; Williams, R. Stanley

2017-08-01

At present, machine learning systems use simplified neuron models that lack the rich nonlinear phenomena observed in biological systems, which display spatio-temporal cooperative dynamics. There is evidence that neurons operate in a regime called the edge of chaos that may be central to complexity, learning efficiency, adaptability and analogue (non-Boolean) computation in brains. Neural networks have exhibited enhanced computational complexity when operated at the edge of chaos, and networks of chaotic elements have been proposed for solving combinatorial or global optimization problems. Thus, a source of controllable chaotic behaviour that can be incorporated into a neural-inspired circuit may be an essential component of future computational systems. Such chaotic elements have been simulated using elaborate transistor circuits that simulate known equations of chaos, but an experimental realization of chaotic dynamics from a single scalable electronic device has been lacking. Here we describe niobium dioxide (NbO2) Mott memristors each less than 100 nanometres across that exhibit both a nonlinear-transport-driven current-controlled negative differential resistance and a Mott-transition-driven temperature-controlled negative differential resistance. Mott materials have a temperature-dependent metal-insulator transition that acts as an electronic switch, which introduces a history-dependent resistance into the device. We incorporate these memristors into a relaxation oscillator and observe a tunable range of periodic and chaotic self-oscillations. We show that the nonlinear current transport coupled with thermal fluctuations at the nanoscale generates chaotic oscillations. Such memristors could be useful in certain types of neural-inspired computation by introducing a pseudo-random signal that prevents global synchronization and could also assist in finding a global minimum during a constrained search. We specifically demonstrate that incorporating such memristors into the hardware of a Hopfield computing network can greatly improve the efficiency and accuracy of converging to a solution for computationally difficult problems.

Chaotic trajectories in the standard map. The concept of anti-integrability

NASA Astrophysics Data System (ADS)

Aubry, Serge; Abramovici, Gilles

1990-07-01

A rigorous proof is given in the standard map (associated with a Frenkel-Kontorowa model) for the existence of chaotic trajectories with unbounded momenta for large enough coupling constant k > k0. These chaotic trajectories (with finite entropy per site) are coded by integer sequences { mi} such that the sequence bi = |m i+1 + m i-1-2m i| be bounded by some integer b. The bound k0 in k depends on b and can be lowered for coding sequences { mi} fulfilling more restrictive conditions. The obtained chaotic trajectories correspond to stationary configurations of the Frenkel-Kontorowa model with a finite (non-zero) photon gap (called gap parameter in dimensionless units). This property implies that the trajectory (or the configuration { ui}) can be uniquely continued as a uniformly continuous function of the model parameter k in some neighborhood of the initial configuration. A non-zero gap parameter implies that the Lyapunov coefficient is strictly positive (when it is defined). In addition, the existence of dilating and contracting manifolds is proven for these chaotic trajectories. “Exotic” trajectories such as ballistic trajectories are also proven to exist as a consequence of these theorems. The concept of anti-integrability emerges from these theorems. In the anti-integrable limit which can be only defined for a discrete time dynamical system, the coordinates of the trajectory at time i do not depend on the coordinates at time i - 1. Thus, at this singular limit, the existence of chaotic trajectories is trivial and the dynamical system reduces to a Bernoulli shift. It is well known that the KAM tori of symplectic dynamical originates by continuity from the invariant tori which exists in the integrible limit (under certain conditions). In a similar way, it appears that the chaotic trajectories of dynamical systems originate by continuity from those which exists at the anti-integrable limits (also under certain conditions).

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.

Heating of the quiet solar corona from measurements of the FET/TESIS instrument on-board the KORONAS-FOTON satellite

NASA Astrophysics Data System (ADS)

Rybák, J.; Gömöry, P.; Benz, A.; Bogachev, P.; Brajša, R.

2010-12-01

The paper presents the first results of the observations of time evolution of the quiet solar corona brightenings obtained due to very rapid photography of the corona with full-disk EUV telescopes of the FET/TESIS instrument onboard the KORONA FOTON satellite. The measurements were performed simultaneously in the emission of the Fe IX / X 17.1 and Fe VIII 13.1 spectral lines with 10 second temporal cadence and spatial scale of 1.7 arc seconds within one hour. This test observation, carried out on 15 July 2009, was analyzed in order to determine whether this type of observation can be used to identify individual microevents in the solar corona heating that are above the tresholds of spatial and temporal resolutions of the observations of non-active regions in the solar atmosphere. For this purpose, a simple method was used involving cross-correlation of the plasma emission time evolution at different temperatures, each time from observations of identical elements. The results obtained are confronted with the expected observable manifestations of the corona heating via nanoflares. TESIS is a set of instruments for the Sun photography developed in the Lebedev Physics Institute of the Russian Academy of Sciences that was launched into orbit in January 2009.

Breakout Reconnection Observed by the TESIS EUV Telescope

NASA Astrophysics Data System (ADS)

Reva, A. A.; Ulyanov, A. S.; Shestov, S. V.; Kuzin, S. V.

2016-01-01

We present experimental evidence of the coronal mass ejection (CME) breakout reconnection, observed by the TESIS EUV telescope. The telescope could observe solar corona up to 2 R⊙ from the Sun center in the Fe 171 Å line. Starting from 2009 April 8, TESIS observed an active region (AR) that had a quadrupolar structure with an X-point 0.5 R⊙ above photosphere. A magnetic field reconstructed from the Michelson Doppler Imager data also has a multipolar structure with an X-point above the AR. At 21:45 UT on April 9, the loops near the X-point started to move away from each other with a velocity of ≈7 km s-1. At 01:15 UT on April 10, a bright stripe appeared between the loops, and the flux in the GOES 0.5-4 Å channel increased. We interpret the loops’ sideways motion and the bright stripe as evidence of the breakout reconnection. At 01:45 UT, the loops below the X-point started to slowly move up. At 15:10 UT, the CME started to accelerate impulsively, while at the same time a flare arcade formed below the CME. After 15:50 UT, the CME moved with constant velocity. The CME evolution precisely followed the breakout model scenario.

The Chaotic Terrains of Mercury: A History of Large-Scale Crustal Devolatilization

NASA Astrophysics Data System (ADS)

Rodriguez, J. A. P.; Domingue, D. L.; Berman, D. C.; Kargel, J. S.; Baker, V. R.; Teodoro, L. F.; Banks, M.; Leonard, G.

2018-05-01

Approximately 400 million years after the Caloris basin impact, extensive collapse formed Mercury's chaotic terrains. Collapse likely resulted from regionally elevated heat flow devolatilizing crustal materials along NE and NW extensional faults.

Shunting inhibitory cellular neural networks with chaotic external inputs

NASA Astrophysics Data System (ADS)

Akhmet, M. U.; Fen, M. O.

2013-06-01

Taking advantage of external inputs, it is shown that shunting inhibitory cellular neural networks behave chaotically. The analysis is based on the Li-Yorke definition of chaos. Appropriate illustrations which support the theoretical results are depicted.

A new class of asymptotically non-chaotic vacuum singularities

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

Klinger, Paul, E-mail: paul.klinger@univie.ac.at

2015-12-15

The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some ofmore » them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.« less

A Simple Snap Oscillator with Coexisting Attractors, Its Time-Delayed Form, Physical Realization, and Communication Designs

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Jafari, Sajad; Akgul, Akif; Karthikeyan, Anitha; Çiçek, Serdar; Shekofteh, Yasser

2018-05-01

In this paper, we report a novel chaotic snap oscillator with one nonlinear function. Dynamic analysis of the system shows the existence of bistability. To study the time delay effects on the proposed snap oscillator, we introduce multiple time delay in the fourth state equation. Investigation of dynamical properties of the time-delayed system shows that the snap oscillator exhibits the same multistable properties as the nondelayed system. The new multistable hyperjerk chaotic system has been tested in chaos shift keying and symmetric choc shift keying modulated communication designs for engineering applications. It has been determined that the symmetric chaos shift keying modulated communication system implemented with the new chaotic system is more successful than the chaos shift keying modulation for secure communication. Also, circuit implementation of the chaotic snap oscillator with tangent function is carried out showing its feasibility.

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 Wave Chaotic Study of Quantum Graphs with Microwave Networks

NASA Astrophysics Data System (ADS)

Fu, Ziyuan

Quantum graphs provide a setting to test the hypothesis that all ray-chaotic systems show universal wave chaotic properties. I study the quantum graphs with a wave chaotic approach. Here, an experimental setup consisting of a microwave coaxial cable network is used to simulate quantum graphs. Some basic features and the distributions of impedance statistics are analyzed from experimental data on an ensemble of tetrahedral networks. The random coupling model (RCM) is applied in an attempt to uncover the universal statistical properties of the system. Deviations from RCM predictions have been observed in that the statistics of diagonal and off-diagonal impedance elements are different. Waves trapped due to multiple reflections on bonds between nodes in the graph most likely cause the deviations from universal behavior in the finite-size realization of a quantum graph. In addition, I have done some investigations on the Random Coupling Model, which are useful for further research.

Nonlinear modeling of chaotic time series: Theory and applications

NASA Astrophysics Data System (ADS)

Casdagli, M.; Eubank, S.; Farmer, J. D.; Gibson, J.; Desjardins, D.; Hunter, N.; Theiler, J.

We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.

Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

PubMed

Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul

2012-09-01

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

Lagrangian coherent structures at the onset of hyperchaos in the two-dimensional Navier-Stokes equations.

PubMed

Miranda, Rodrigo A; Rempel, Erico L; Chian, Abraham C-L; Seehafer, Norbert; Toledo, Benjamin A; Muñoz, Pablo R

2013-09-01

We study a transition to hyperchaos in the two-dimensional incompressible Navier-Stokes equations with periodic boundary conditions and an external forcing term. Bifurcation diagrams are constructed by varying the Reynolds number, and a transition to hyperchaos (HC) is identified. Before the onset of HC, there is coexistence of two chaotic attractors and a hyperchaotic saddle. After the transition to HC, the two chaotic attractors merge with the hyperchaotic saddle, generating random switching between chaos and hyperchaos, which is responsible for intermittent bursts in the time series of energy and enstrophy. The chaotic mixing properties of the flow are characterized by detecting Lagrangian coherent structures. After the transition to HC, the flow displays complex Lagrangian patterns and an increase in the level of Lagrangian chaoticity during the bursty periods that can be predicted statistically by the hyperchaotic saddle prior to HC transition.

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.

Evolution of secondary whirls in thermoconvective vortices: Strengthening, weakening, and disappearance in the route to chaos

NASA Astrophysics Data System (ADS)

Castaño, D.; Navarro, M. C.; Herrero, H.

2016-01-01

The appearance, evolution, and disappearance of periodic and quasiperiodic dynamics of fluid flows in a cylindrical annulus locally heated from below are analyzed using nonlinear simulations. The results reveal a route of the transition from a steady axisymmetric vertical vortex to a chaotic flow. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic flow regimes. A scenario similar to the Ruelle-Takens-Newhouse scenario is verified in this convective flow. In the transition to chaos we find the appearance of subvortices embedded in the primary axisymmetric vortex, flows where the subvortical structure strengthens and weakens, that almost disappears before reforming again, leading to a more disorganized flow to a final chaotic regime. Results are remarkable as they connect to observations describing formation, weakening, and virtual disappearance before revival of subvortices in some atmospheric swirls such as dust devils.

Experimental study of firing death in a network of chaotic FitzHugh-Nagumo neurons

NASA Astrophysics Data System (ADS)

Ciszak, Marzena; Euzzor, Stefano; Arecchi, F. Tito; Meucci, Riccardo

2013-02-01

The FitzHugh-Nagumo neurons driven by a periodic forcing undergo a period-doubling route to chaos and a transition to mixed-mode oscillations. When coupled, their dynamics tend to be synchronized. We show that the chaotically spiking neurons change their internal dynamics to subthreshold oscillations, the phenomenon referred to as firing death. These dynamical changes are observed below the critical coupling strength at which the transition to full chaotic synchronization occurs. Moreover, we find various dynamical regimes in the subthreshold oscillations, namely, regular, quasiperiodic, and chaotic states. We show numerically that these dynamical states may coexist with large-amplitude spiking regimes and that this coexistence is characterized by riddled basins of attraction. The reported results are obtained for neurons implemented in the electronic circuits as well as for the model equations. Finally, we comment on the possible scenarios where the coupling-induced firing death could play an important role in biological systems.

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.

Chaos in the sunspot cycle - Analysis and prediction

NASA Technical Reports Server (NTRS)

Mundt, Michael D.; Maguire, W. Bruce, II; Chase, Robert R. P.

1991-01-01

The variability of solar activity over long time scales, given semiquantitatively by measurements of sunspot numbers, is examined as a nonlinear dynamical system. First, a discussion of the data set used and the techniques utilized to reduce the noise and capture the long-term dynamics inherent in the data is presented. Subsequently, an attractor is reconstructed from the data set using the method of time delays. The reconstructed attractor is then used to determine both the dimension of the underlying system and also the largest Lyapunov exponent, which together indicate that the sunspot cycle is indeed chaotic and also low dimensional. In addition, recent techniques of exploiting chaotic dynamics to provide accurate, short-term predictions are utilized in order to improve upon current forecasting methods and also to place theoretical limits on predictability extent. The results are compared to chaotic solar-dynamo models as a possible physically motivated source of this chaotic behavior.

Chimeras and clusters in networks of hyperbolic chaotic oscillators

NASA Astrophysics Data System (ADS)

Cano, A. V.; Cosenza, M. G.

2017-03-01

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

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.

Applying elliptic curve cryptography to a chaotic synchronisation system: neural-network-based approach

NASA Astrophysics Data System (ADS)

Hsiao, Feng-Hsiag

2017-10-01

In order to obtain double encryption via elliptic curve cryptography (ECC) and chaotic synchronisation, this study presents a design methodology for neural-network (NN)-based secure communications in multiple time-delay chaotic systems. ECC is an asymmetric encryption and its strength is based on the difficulty of solving the elliptic curve discrete logarithm problem which is a much harder problem than factoring integers. Because it is much harder, we can get away with fewer bits to provide the same level of security. To enhance the strength of the cryptosystem, we conduct double encryption that combines chaotic synchronisation with ECC. According to the improved genetic algorithm, a fuzzy controller is synthesised to realise the exponential synchronisation and achieves optimal H∞ performance by minimising the disturbances attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of the proposed approach.

An investigation of chaotic Kolmogorov flows

NASA Technical Reports Server (NTRS)

Platt, N.; Sirovich, L.; Fitzmaurice, N.

1990-01-01

A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

NASA Astrophysics Data System (ADS)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

LONG-LIVED CHAOTIC ORBITAL EVOLUTION OF EXOPLANETS IN MEAN MOTION RESONANCES WITH MUTUAL INCLINATIONS

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

Barnes, Rory; Deitrick, Russell; Quinn, Thomas R.

2015-03-10

We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.°9. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364, and HD 60532 systems may be in chaotically evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1, and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs aftermore » several gigayears, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that (1) approximate methods for identifying unstable orbital architectures may have limited applicability, (2) the observed close-in exoplanets may be produced during epochs of high eccentricit induced by inclined resonances, (3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, (4) systems with resonances may be systematically younger than those without, (5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and (6) potentially habitable planets may have dramatically different climatic evolution than Earth. The Gaia spacecraft is capable of discovering giant planets in these types of orbits.« less

Characterization of normality of chaotic systems including prediction and detection of anomalies

NASA Astrophysics Data System (ADS)

Engler, Joseph John

Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.

Forecasting natural hazards, performance of scientists, ethics, and the need for transparency

PubMed Central

Guzzetti, Fausto

2016-01-01

Landslides are one of several natural hazards. As other natural hazards, landslides are difficult to predict, and their forecasts are uncertain. The uncertainty depends on the poor understanding of the phenomena that control the slope failures, and on the inherent complexity and chaotic nature of the landslides. This is similar to other natural hazards, including hurricanes, earthquakes, volcanic eruptions, floods, and droughts. Due to the severe impact of landslides on the population, the environment, and the economy, forecasting landslides is of scientific interest and of societal relevance, and scientists attempting to forecast landslides face known and new problems intrinsic to the multifaceted interactions between science, decision-making, and the society. The problems include deciding on the authority and reliability of individual scientists and groups of scientists, and evaluating the performances of individual scientists, research teams, and their institutions. Related problems lay in the increasing subordination of research scientists to politics and decision-makers, and in the conceptual and operational models currently used to organize and pay for research, based on apparently objective criteria and metrics, considering science as any other human endeavor, and favoring science that produces results of direct and immediate application. The paper argues that the consequences of these problems have not been considered fully. PMID:27695154

Forecasting natural hazards, performance of scientists, ethics, and the need for transparency.

PubMed

Guzzetti, Fausto

2016-10-20

Landslides are one of several natural hazards. As other natural hazards, landslides are difficult to predict, and their forecasts are uncertain. The uncertainty depends on the poor understanding of the phenomena that control the slope failures, and on the inherent complexity and chaotic nature of the landslides. This is similar to other natural hazards, including hurricanes, earthquakes, volcanic eruptions, floods, and droughts. Due to the severe impact of landslides on the population, the environment, and the economy, forecasting landslides is of scientific interest and of societal relevance, and scientists attempting to forecast landslides face known and new problems intrinsic to the multifaceted interactions between science, decision-making, and the society. The problems include deciding on the authority and reliability of individual scientists and groups of scientists, and evaluating the performances of individual scientists, research teams, and their institutions. Related problems lay in the increasing subordination of research scientists to politics and decision-makers, and in the conceptual and operational models currently used to organize and pay for research, based on apparently objective criteria and metrics, considering science as any other human endeavor, and favoring science that produces results of direct and immediate application. The paper argues that the consequences of these problems have not been considered fully.

Role of strategic planning in engineering management

NASA Technical Reports Server (NTRS)

Krishen, Kumar

1993-01-01

Today, more than ever before, engineers are faced with uncertain and sometimes chaotic environments in which to function. The traditional roles of an engineer to design, develop, and streamline a manufacturing process for a product are still valued and relevant. However, the need for an engineer to participate in the process of identifying the product to be developed, the schedule and resources required, and the goal of satisfying the customer, has become paramount to achieving the success of the enterprise. When we include these endeavors in the functions of an engineer, management of 'engineering' takes on a new dimension. In this paper, the ramifications of the changing and increased functions of an engineer and consequent impacts on engineering management are explored. The basic principles which should be invoked in order to embrace the new environment for engineering management are outlined. The ultimate finding of this study is that the enterprise strategic plan should be developed in such a way as to allow engineering management to encompass the full spectrum of the responsibilities of engineers. A consequence of this is that the fundamental elements of the strategic process can best be implemented through a project team or group approach. The paper thus concentrates on three areas: evolving environment, strategic plan, and ways to achieve enterprise success.

Devaney chaos plus shadowing implies distributional chaos.

PubMed

Li, Jian; Li, Jie; Tu, Siming

2016-09-01

We explore connections among the regional proximal relation, the asymptotic relation, and the distal relation for a topological dynamical system with the shadowing property and show that if a Devaney chaotic system has the shadowing property then it is distributionally chaotic.

Generation of wideband chaos with suppressed time-delay signature by delayed self-interference.

PubMed

Wang, Anbang; Yang, Yibiao; Wang, Bingjie; Zhang, Beibei; Li, Lei; Wang, Yuncai

2013-04-08

We demonstrate experimentally and numerically a method using the incoherent delayed self-interference (DSI) of chaotic light from a semiconductor laser with optical feedback to generate wideband chaotic signal. The results show that, the DSI can eliminate the domination of laser relaxation oscillation existing in the chaotic laser light and therefore flatten and widen the power spectrum. Furthermore, the DSI depresses the time-delay signature induced by external cavity modes and improves the symmetry of probability distribution by more than one magnitude. We also experimentally show that this DSI signal is beneficial to the random number generation.

Deterministic chaotic dynamics of Raba River flow (Polish Carpathian Mountains)

NASA Astrophysics Data System (ADS)

Kędra, Mariola

2014-02-01

Is the underlying dynamics of river flow random or deterministic? If it is deterministic, is it deterministic chaotic? This issue is still controversial. The application of several independent methods, techniques and tools for studying daily river flow data gives consistent, reliable and clear-cut results to the question. The outcomes point out that the investigated discharge dynamics is not random but deterministic. Moreover, the results completely confirm the nonlinear deterministic chaotic nature of the studied process. The research was conducted on daily discharge from two selected gauging stations of the mountain river in southern Poland, the Raba River.

Chaos and ion heating in a slow shock

NASA Technical Reports Server (NTRS)

Lin, Y.; Lee, L. C.

1991-01-01

An ion heating mechanism is proposed of slow shocks, which is associated with the chaotic motion of particles in the downstream wave field. For a coherent electromagnetic wave propagating along the downstream magnetic field, corresponding to switch-off shocks, the particle motions are not chaotic. For an oblique wave, the interaction between the particles and the wave field may lead to chaotic particle motions. Such particles may be greatly thermalized within one wavelength after they are incident into the downstream wave field. The results can be used to explain the existence of the critical intermediate Mach number observed in the hybrid simulations.

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.

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.

On adaptive modified projective synchronization of a supply chain management system

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2017-12-01

In this paper, the synchronization problem of a chaotic supply chain management system is studied. A novel adaptive modified projective synchronization method is introduced to control the behaviour of the leader supply chain system by a follower chaotic system and to adjust the leader system parameters until the measurable errors of the system parameters converge to zero. The stability evaluation and convergence analysis are carried out by the Lyapanov stability theorem. The proposed synchronization and antisynchronization techniques are studied for identical supply chain chaotic systems. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical discussions.

Robust control for fractional variable-order chaotic systems with non-singular kernel

NASA Astrophysics Data System (ADS)

Zuñiga-Aguilar, C. J.; Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Romero-Ugalde, H. M.

2018-01-01

This paper investigates the chaos control for a class of variable-order fractional chaotic systems using robust control strategy. The variable-order fractional models of the non-autonomous biological system, the King Cobra chaotic system, the Halvorsen's attractor and the Burke-Shaw system, have been derived using the fractional-order derivative with Mittag-Leffler in the Liouville-Caputo sense. The fractional differential equations and the control law were solved using the Adams-Bashforth-Moulton algorithm. To test the control stability efficiency, different statistical indicators were introduced. Finally, simulation results demonstrate the effectiveness of the proposed robust control.

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.

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

PubMed Central

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

Some new surprises in chaos.

PubMed

Bunimovich, Leonid A; Vela-Arevalo, Luz V

2015-09-01

"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

Path Planning for Robot based on Chaotic Artificial Potential Field Method

NASA Astrophysics Data System (ADS)

Zhang, Cheng

2018-03-01

Robot path planning in unknown environments is one of the hot research topics in the field of robot control. Aiming at the shortcomings of traditional artificial potential field methods, we propose a new path planning for Robot based on chaotic artificial potential field method. The path planning adopts the potential function as the objective function and introduces the robot direction of movement as the control variables, which combines the improved artificial potential field method with chaotic optimization algorithm. Simulations have been carried out and the results demonstrate that the superior practicality and high efficiency of the proposed method.

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.

Finite-time stabilization of chaotic gyros based on a homogeneous supertwisting-like algorithm

NASA Astrophysics Data System (ADS)

Khamsuwan, Pitcha; Sangpet, Teerawat; Kuntanapreeda, Suwat

2018-01-01

This paper presents a finite-time stabilization scheme for nonlinear chaotic gyros. The scheme utilizes a supertwisting-like continuous control algorithm for the systems of dimension more than one with a Lipschitz disturbance. The algorithm yields finite-time convergence similar to that produces by discontinuous sliding mode control algorithms. To design the controller, the nonlinearities in the gyro are treated as a disturbance in the system. Thanks to the dissipativeness of chaotic systems, the nonlinearities also possess the Lipschitz property. Numerical results are provided to illustrate the effectiveness of the scheme.

On a chaotic potential at the surface of a compensated semiconductor under conditions of the self-assembly of electrically active defects

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

Bondarenko, V. B., E-mail: enter@spbstu.ru; Filimonov, A. V.

2015-09-15

Natural irregularities of the electric potential on the surface of a semiconductor under conditions of the partial self-assembly of electrically active defects, i.e., on the formation of donor–acceptor pairs in depletion layers, are studied. The amplitude and character of the spatial distribution of the chaotic potential on the surface of a semiconductor in the cases of localized and delocalized states are determined. The dependence of the amplitude of the chaotic potential on the degree of compensation of the semiconductor is obtained.

Effect of Noise on the Relaxation to an Invariant Probability Measure of Nonhyperbolic Chaotic Attractors

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

Anishchenko, Vadim S.; Vadivasova, Tatjana E.; Kopeikin, Andrey S.

2001-07-30

We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixing is presented which is associated with the dynamics of the instantaneous phase of chaotic trajectories. This also explains why the noncoherent regime is robust against the presence of external noise.

Applied Chaos: From Oxymoron to Reality.

NASA Astrophysics Data System (ADS)

Ditto, William

1996-11-01

The rapidly emerging field of chaotic dynamics has presented the applied scientist with intriguing new tools to understand and manipulate systems that behave chaotically. An overview will be presented which will answer the questions: What is Chaos? and What can you do with Chaos? Examples of recent applications of chaos theory to the physical and biological sciences will be presented covering applications that range from encryption in communications to control of chaotically beating human hearts. Part A of program listing

Mars: Fretted and chaotic terrains

NASA Technical Reports Server (NTRS)

Sharp, R. P.

1973-01-01

Fretted Martian terrain is characterized by smooth, flat, lowland areas separated from a cratered upland by abrupt escarpments of complex planimetric configuration and a maximum estimated height approaching 1 to 2 km. It is the product of some unusual erosive or abstractive process that has created steep escarpments. Chaotic terrain differs from fretted terrain in having a rough floor topography featuring a haphazard jumble of large angular blocks, and by arc-shaped slump blocks on its bounding escarpments. Its existence has now been confirmed by Mariner 9 pictures, and the characteristics, location, and areal extent of chaotic terrain have been more accurately and completely defined.

Evidence for fast dynamo action in a chaotic web

NASA Technical Reports Server (NTRS)

Gilbert, A. D.; Childress, S.

1990-01-01

The evolution of a magnetic field in a chaotic web is studied. The model flow possessing the web is closely related to the nearly integrable ABC flow with A = B and C much less than 1. The magnetic diffusivity is taken to be zero and the field is followed using the Cauchy solution. It is found that the flow folds the magnetic field constructively, in the sense that the average magnetic field in a chaotic region grows exponentially in time. This is suggestive of fast dynamo action, although the effect of diffusion of the strong streamwise magnetic field remains to be assessed.

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.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method.

PubMed

Wang, Yu; Li, Feng-Ming; Wang, Yi-Ze

2015-06-01

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

Application of chaotic attractor analysis in crack assessment of plates

NASA Astrophysics Data System (ADS)

Jalili, Sina; Daneshmehr, A. R.

2018-03-01

Part-through crack presence with limited length is one of the prevalent defects in plate structures. However, this type of damage has only a slight effect on the dynamic response of the structures. In this paper the modified line spring method (MLSM) is used to develop a nonlinear multi-degree of freedom model of part through cracked rectangular plate and chaotic interrogation is implemented to assess crack-induced degradation in the nonlinear model. After a convergence study of the proposed model in time series domain in which the plate subjected to Lorenz-type chaotic excitation, the tuning of interrogation is conducted by crossing the Lyapunov exponents' spectrums of the nonlinear model of the plate and chaotic signal. In this research nonlinear prediction error (NPE) is proposed as a damage sensitive feature which deals with the chaotic attractor of the excited system response. It is found that there are ranges of tuning parameter that result in higher damage sensitivity of the NPE. Damage characteristics such as: length, angle, location and depth of crack are considered as parameters to be varied to scrutinize the response of the plates. Results show that NPE generally has significantly higher sensitivity in comparison with conventional frequency-based methods; however this property has different levels for various boundary conditions.

Biologically inspired rate control of chaos.

PubMed

Olde Scheper, Tjeerd V

2017-10-01

The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.

Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model

NASA Astrophysics Data System (ADS)

Pathak, Jaideep; Wikner, Alexander; Fussell, Rebeckah; Chandra, Sarthak; Hunt, Brian R.; Girvan, Michelle; Ott, Edward

2018-04-01

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the mechanistic processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus, we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone.

Quantification of scaling exponents and dynamical complexity of microwave refractivity in a tropical climate

NASA Astrophysics Data System (ADS)

Fuwape, Ibiyinka A.; Ogunjo, Samuel T.

2016-12-01

Radio refractivity index is used to quantify the effect of atmospheric parameters in communication systems. Scaling and dynamical complexities of radio refractivity across different climatic zones of Nigeria have been studied. Scaling property of the radio refractivity across Nigeria was estimated from the Hurst Exponent obtained using two different scaling methods namely: The Rescaled Range (R/S) and the detrended fluctuation analysis(DFA). The delay vector variance (DVV), Largest Lyapunov Exponent (λ1) and Correlation Dimension (D2) methods were used to investigate nonlinearity and the results confirm the presence of deterministic nonlinear profile in the radio refractivity time series. The recurrence quantification analysis (RQA) was used to quantify the degree of chaoticity in the radio refractivity across the different climatic zones. RQA was found to be a good measure for identifying unique fingerprint and signature of chaotic time series data. Microwave radio refractivity was found to be persistent and chaotic in all the study locations. The dynamics of radio refractivity increases in complexity and chaoticity from the Coastal region towards the Sahelian climate. The design, development and deployment of robust and reliable microwave communication link in the region will be greatly affected by the chaotic nature of radio refractivity in the region.

In Situ Self Assembly of Nanocomposites: Competition of Chaotic Advection and Interfacial Effects as Observed by X-Ray Diffreaction

PubMed Central

Ratnaweera, Dilru R.; Mahesha, Chaitra; Zumbrunnen, David A.; Perahia, Dvora

2015-01-01

The effects of chaotic advection on the in situ assembly of a hierarchal nanocomposite of Poly Amide 6, (nylon 6 or PA6) and platelet shape nanoparticles (NPs) were studied. The assemblies were formed by chaotic advection, where melts of pristine PA6 and a mixture of PA6 with NPs were segregated into discrete layers and extruded into film in a continuous process. The process assembles the nanocomposite into alternating pristine-polymer and oriented NP/polymer layers. The structure of these hierarchal assemblies was probed by X-rays as a processing parameter, N, was varied. This parameter provides a measure of the extent of in situ structuring by chaotic advection. We found that all assemblies are semi-crystalline at room temperature. Increasing N impacts the ratio of α to γ crystalline forms. The effects of the chaotic advection vary with the concentration of the NPs. For nanocomposites with lower NP concentrations the amount of the γ crystalline form increased with N. However, at higher NP concentrations, interfacial effects of the NP play a significant role in determining the structure, where the NPs oriented along the melt flow direction and the polymer chains oriented perpendicular to the NP surfaces. PMID:28347015

Effect of Parametric Dichotomic Markov Noise on the Properties of Chaotic Transitions in Dynamical Systems

NASA Astrophysics Data System (ADS)

Gac, J. M.; Żebrowski, J. J.

A chaotic transition occurs when a continuous change of one of the parameters of the system causes a discontinuous change in the properties of the chaotic attractor of the system. Such phenomena are present in many dynamical systems, in which a chaotic behavior occurs. The best known of these transitions are: the period-doubling bifurcation cascade, intermittency and crises. The effect of dichotomous Markov noise (DMN) on the properties of systems with chaotic transitions is discussed. DMN is a very simple two-valued stochastic process, with constant transition rates between the two states. In spite of its simplicity, this kind of noise is a very powerful tool to describe various phenomena present in many physical, chemical or biological systems. Many interesting phenomena induced by DMN are known. However, there is no research on the effect of this kind of noise on intermittency or crises. We present the change of the mean laminar phase length and of laminar phase length distribution caused by DMN modulating the parameters of a system with intermittency and the modification of the mean life time on the pre-crisis attractor in the case of a boundary crisis. The results obtained analytically are compared with numerical simulations for several simple dynamical systems.

Evidence for Chaotic Edge Turbulence in the Alcator C-Mod Tokamak

NASA Astrophysics Data System (ADS)

Zhu, Ziyan; White, Anne; Carter, Troy; Terry, Jim; Baek, Seung Gyou

2017-10-01

Turbulence greatly reduces the confinement time of magnetic-confined plasmas; understanding the nature of this turbulence and the associated transport is therefore of great importance. This research seeks to establish whether turbulent fluctuations in Alcator C-Mod are chaotic or stochastic. Stochastic fluctuations may lead to a random walk diffusive transport, whereas a diffusive description is unlikely to be valid for chaotic fluctuations since it lives in restricted areas of phase space (e.g., on attractors). Analysis of the time series obtained with the O-mode reflectometer and the gas puff imaging (GPI) systems reveals that the turbulent density fluctuations in C-Mod are chaotic. Supporting evidence for this conclusion includes the observation of an exponential power spectra (which is associated with Lorentzian-shaped pulses in the time series), the population of the corresponding Bandt-Pompe (BP) probability distribution, and the location of the signal on the Complexity-Entropy plane (C-H plane). These analysis techniques will be briefly introduced along with a discussion of the analysis results. The classification of edge turbulence as chaotic opens the door for further work to understand the underlying process and the impact on turbulent transport. Supported by USDoE awards DE-FC02-99ER54512 and DE-FC02-07ER54918:011.

Theory of chaos regularization of tunneling in chaotic quantum dots.

PubMed

Lee, Ming-Jer; Antonsen, Thomas M; Ott, Edward; Pecora, Louis M

2012-11-01

Recent numerical experiments of Pecora et al. [Phys. Rev. E 83, 065201 (2011)] have investigated tunneling between two-dimensional symmetric double wells separated by a tunneling barrier. The wells were bounded by hard walls and by the potential barrier which was created by a step increase from the zero potential within a well to a uniform barrier potential within the barrier region, which is a situation potentially realizable in the context of quantum dots. Numerical results for the splitting of energy levels between symmetric and antisymmetric eigenstates were calculated. It was found that the splittings vary erratically from state to state, and the statistics of these variations were studied for different well shapes with the fluctuation levels being much less in chaotic wells than in comparable nonchaotic wells. Here we develop a quantitative theory for the statistics of the energy level splittings for chaotic wells. Our theory is based on the random plane wave hypothesis of Berry. While the fluctuation statistics are very different for chaotic and nonchaotic well dynamics, we show that the mean splittings of differently shaped wells, including integrable and chaotic wells, are the same if their well areas and barrier parameters are the same. We also consider the case of tunneling from a single well into a region with outgoing quantum waves.

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

NASA Astrophysics Data System (ADS)

Abramov, R. V.

2011-12-01

Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger chaotic system would result in general increase of chaos at the slow variables.

Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays

PubMed Central

Suzuki, Yoko; Lu, Mingyang; Ben-Jacob, Eshel; Onuchic, José N.

2016-01-01

Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer. PMID:26876008

Chimeralike states in a network of oscillators under attractive and repulsive global coupling.

PubMed

Mishra, Arindam; Hens, Chittaranjan; Bose, Mridul; Roy, Prodyot K; Dana, Syamal K

2015-12-01

We report chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify the existence of two types of chimeralike states in a bistable Liénard system; in one type, both the coherent and the incoherent populations are in chaotic states (which we refer to as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular small oscillation. We find a metastable state in a parameter regime of the Liénard system where the coherent and noncoherent states migrate in time from one to another subpopulation. The relative size of the incoherent subpopulation, in the chimeralike states, remains almost stable with increasing size of the network. The generality of the coupling configuration in the origin of the chimeralike states is tested, using a second example of bistable system, the van der Pol-Duffing oscillator where the chimeralike states emerge as weakly chaotic in the coherent subpopulation and chaotic in the incoherent subpopulation. Furthermore, we apply the coupling, in a simplified form, to form a network of the chaotic Rössler system where both the noncoherent and the coherent subpopulations show chaotic dynamics.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method

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

Wang, Yu; Wang, Yi-Ze; Li, Feng-Ming, E-mail: fmli@bjut.edu.cn

2015-06-15

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two bucklingmore » cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.« less

Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays

NASA Astrophysics Data System (ADS)

Suzuki, Yoko; Lu, Mingyang; Ben-Jacob, Eshel; Onuchic, José N.

2016-02-01

Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer.

Performance Comparison of the European Storm Surge Models and Chaotic Model in Forecasting Extreme Storm Surges

NASA Astrophysics Data System (ADS)

Siek, M. B.; Solomatine, D. P.

2009-04-01

Storm surge modeling has rapidly developed considerably over the past 30 years. A number of significant advances on operational storm surge models have been implemented and tested, consisting of: refining computational grids, calibrating the model, using a better numerical scheme (i.e. more realistic model physics for air-sea interaction), implementing data assimilation and ensemble model forecasts. This paper addresses the performance comparison between the existing European storm surge models and the recently developed methods of nonlinear dynamics and chaos theory in forecasting storm surge dynamics. The chaotic model is built using adaptive local models based on the dynamical neighbours in the reconstructed phase space of observed time series data. The comparison focused on the model accuracy in forecasting a recently extreme storm surge in the North Sea on November 9th, 2007 that hit the coastlines of several European countries. The combination of a high tide, north-westerly winds exceeding 50 mph and low pressure produced an exceptional storm tide. The tidal level was exceeded 3 meters above normal sea levels. Flood warnings were issued for the east coast of Britain and the entire Dutch coast. The Maeslant barrier's two arc-shaped steel doors in the Europe's biggest port of Rotterdam was closed for the first time since its construction in 1997 due to this storm surge. In comparison to the chaotic model performance, the forecast data from several European physically-based storm surge models were provided from: BSH Germany, DMI Denmark, DNMI Norway, KNMI Netherlands and MUMM Belgium. The performance comparison was made over testing datasets for two periods/conditions: non-stormy period (1-Sep-2007 till 14-Oct-2007) and stormy period (15-Oct-2007 till 20-Nov-2007). A scalar chaotic model with optimized parameters was developed by utilizing an hourly training dataset of observations (11-Sep-2005 till 31-Aug-2007). The comparison results indicated the chaotic model yields better forecasts than the existing European storm surge models. The best performance of European storm surge models for non-storm and storm conditions was achieved by KNMI (with Kalman filter data assimilation) and BSH with errors of 8.95cm and 10.92cm, respectively. Whereas the chaotic model can provide 6 and 48 hours forecasts with errors of 3.10cm and 8.55cm for non-storm condition and 5.04cm and 15.21cm for storm condition, respectively. The chaotic model can provide better forecasts primarily due to the fact that the chaotic model forecasting are estimated by local models which model and identify the similar development of storm surges in the past. In practice, the chaotic model can serve as a reliable and accurate model to support decision-makers in operational ship navigation and flood forecasting.

The complexity of proving chaoticity and the Church-Turing thesis

NASA Astrophysics Data System (ADS)

Calude, Cristian S.; Calude, Elena; Svozil, Karl

2010-09-01

Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.

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.

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.

Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation

NASA Astrophysics Data System (ADS)

Hailong, Zhang; Enrong, Wang; Fuhong, Min; Ning, Zhang

2016-03-01

The magneto-rheological damper (MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom (2-DOF) MR suspension system was established first, by employing the modified Bouc-Wen force-velocity (F-v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface. The largest Lyapunov exponent (LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density (PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy (K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system. Projects supported by the National Natural Science Foundation of China (Grant Nos. 51475246, 51277098, and 51075215), the Research Innovation Program for College Graduates of Jiangsu Province China (Grant No. KYLX15 0725), and the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20131402).

Chaotic characteristics enhanced by impeller of perturbed six-bent-bladed turbine in stirred tank

NASA Astrophysics Data System (ADS)

Luan, Deyu; Zhang, Shengfeng; Lu, Jianping; Zhang, Xiaoguang

The fundamental way of improving the mixing efficiency is to induce the chaotic flow in a stirred vessel. The impeller form plays an important role for changing the structure of flow field and realizing chaotic mixing. Based on the velocity time series acquired by the experiment of particle image velocimetry (PIV), with the software Matlab, the macro-instability (MI), largest Lyapunov exponent (LLE), and Kolmogorov entropy in the water stirred tank is investigated respectively with the impeller of perturbed six-bent-bladed turbine (6PBT). The results show that the MI characteristics are obvious and two peak values of MI frequency are observed at the speed N = 60 rpm. With the increasing speed (more than 100 rpm), the peak characteristics of MI frequency disappear and a multi-scale wavelet structure of characterizing the chaotic flow field appears. Moreover, under the speed N = 60 rpm, the LLE is less than 0 and Kolmogorov entropy is 0, which means that the flow field is in the periodic moving state. As the speed is increased to more than 100 rpm, the LLE and Kolmogorov entropy are all more than 0, which indicates that the flow field goes into the chaotic mixing. When the speed reaches up to about 210 rpm, both of the LLE and Kolmogorov entropy achieve the optimum values, which will result in an excellent chaos with the highest mixing efficient. So it is feasible that the MI frequency, the LLE and the Kolmogorov entropy can be used to analyze the flow field characteristics in a stirred tank. The research results promote the understanding of the chaotic mixing mechanism and provide a theoretical reference for the development of new type impeller.

Particle Diffusion in Chaotic Magnetic Fields Generated by Asymmetric Current Configurations

NASA Astrophysics Data System (ADS)

Ram, A. K.; Dasgupta, B.

2008-12-01

The observed cross-field diffusion of charged particles in cosmic rays is assumed to be due to the chaotic nature of the interplanetary/intergalactic magnetic fields. Among the classic works on this subject have been those of Parker [1] and Jokipii [2]. Parker considered the passage of cosmic ray particles and energetic solar particles in a large scale magnetic field containing small scale irregularities. In the context of cosmic ray propagation, Jokipii considered a small fluctuating component, added on to a uniform magnetic field, to study the spatial transport of particles. In these studies the irregular component of the magnetic field is prescribed in an ad hoc fashion. In contrast, we consider asymmetric, nonlinear, steady-state magnetic fields, in three spatial dimensions, generated by currents flowing in circular loops and straight lines [3]. These magnetic fields are completely deterministic and, for certain range of parameters, chaotic. We will present analytical and numerical studies on the spatial characteristics of these fields. The motion of charged particles in the nonlinear and chaotic magnetic fields is determined using the Lorentz equation. A particle moving in a deterministic chaotic magnetic field superposed on a uniform background magnetic field is found to undergo spatial transport. This shows that chaotic magnetic fields generated by simple current configurations can produce cross-field diffusion. A detailed analysis of particle motion and diffusion along with application to space plasmas will be presented. [1] E.N. Parker, Planet. Space Sci. 13, 9 (1965). [2] J.R. Jokipii, Astrophys. J. 146, 480 (1966), and J.R. Jokipii, Astrophys. J. 149, 405 (1967). [3] A.K. Ram and B. Dasgupta, Eos Trans. AGU 87 (52), Fall Meet. Suppl. Abstract NG31B-1593 (2006); and Eos Trans. AGU 88 (52), Fall Meet. Suppl. Abstract NG21B-0522 (2007).

Chaotic advection and heat transfer in two similar 2-D periodic flows and in their corresponding 3-D periodic flows

NASA Astrophysics Data System (ADS)

Vinsard, G.; Dufour, S.; Saatdjian, E.; Mota, J. P. B.

2016-03-01

Chaotic advection can effectively enhance the heat transfer rate between a boundary and fluids with high Prandtl number. These fluids are usually highly viscous and thus turbulent agitation is not a viable solution since the energy required to mix the fluid would be prohibitive. Here, we analyze previously obtained results on chaotic advection and heat transfer in two similar 2-D periodic flows and on their corresponding 3-D periodic flows when an axial velocity component is superposed. The two flows studied are the flow between eccentric rotating cylinders and the flow between confocal ellipses. For both of these flows the analysis is simplified because the Stokes equations can be solved analytically to obtain a closed form solution. For both 2-D periodic flows, we show that chaotic heat transfer is enhanced by the displacement of the saddle point location during one period. Furthermore, the enhancement by chaotic advection in the elliptical geometry is approximately double that obtained in the cylindrical geometry because there are two saddle points instead of one. We also explain why, for high eccentricity ratios, there is no heat transfer enhancement in the cylindrical geometry. When an axial velocity component is added to both of these flows so that they become 3-D, previous work has shown that there is an optimum modulation frequency for which chaotic advection and heat transfer enhancement is a maximum. Here we show that the optimum modulation frequency can be derived from results without an axial flow. We also explain by physical arguments other previously unanswered questions in the published data.

Coexistence and chaos in complex ecologies [rapid communication

NASA Astrophysics Data System (ADS)

Sprott, J. C.; Vano, J. A.; Wildenberg, J. C.; Anderson, M. B.; Noel, J. K.

2005-02-01

Many complex dynamical systems in ecology, economics, neurology, and elsewhere, in which agents compete for limited resources, exhibit apparently chaotic fluctuations. This Letter proposes a purely deterministic mechanism for evolving robustly but weakly chaotic systems that exhibit adaptation, self-organization, sporadic volatility, and punctuated equilibria.

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.

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems.

PubMed

Lithwick, Yoram; Wu, Yanqin

2014-09-02

In the inner solar system, the planets' orbits evolve chaotically, driven primarily by secular chaos. Mercury has a particularly chaotic orbit and is in danger of being lost within a few billion years. Just as secular chaos is reorganizing the solar system today, so it has likely helped organize it in the past. We suggest that extrasolar planetary systems are also organized to a large extent by secular chaos. A hot Jupiter could be the end state of a secularly chaotic planetary system reminiscent of the solar system. However, in the case of the hot Jupiter, the innermost planet was Jupiter (rather than Mercury) sized, and its chaotic evolution was terminated when it was tidally captured by its star. In this contribution, we review our recent work elucidating the physics of secular chaos and applying it to Mercury and to hot Jupiters. We also present results comparing the inclinations of hot Jupiters thus produced with observations.

Generation of 2N + 1-scroll existence in new three-dimensional chaos systems.

PubMed

Liu, Yue; Guan, Jian; Ma, Chunyang; Guo, Shuxu

2016-08-01

We propose a systematic methodology for creating 2N + 1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a12a21 = 0, while the Chua system satisfies a12a21 > 0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2N + 1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2N + 1-scroll attractors. Finally, to explore the potential use in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1-, 3-, 5-, and 7-scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

PubMed

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

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.

Nonlinear modeling of chaotic time series: Theory and applications

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

Casdagli, M.; Eubank, S.; Farmer, J.D.

1990-01-01

We review recent developments in the modeling and prediction of nonlinear time series. In some cases apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifyingmore » and quantifying low-dimensional chaotic behavior. During the past few years methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics and human speech. 162 refs., 13 figs.« less

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation

NASA Astrophysics Data System (ADS)

Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

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

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.

Kin-Aggregations Explain Chaotic Genetic Patchiness, a Commonly Observed Genetic Pattern, in a Marine Fish.

PubMed

Selwyn, Jason D; Hogan, J Derek; Downey-Wall, Alan M; Gurski, Lauren M; Portnoy, David S; Heath, Daniel D

2016-01-01

The phenomenon of chaotic genetic patchiness is a pattern commonly seen in marine organisms, particularly those with demersal adults and pelagic larvae. This pattern is usually associated with sweepstakes recruitment and variable reproductive success. Here we investigate the biological underpinnings of this pattern in a species of marine goby Coryphopterus personatus. We find that populations of this species show tell-tale signs of chaotic genetic patchiness including: small, but significant, differences in genetic structure over short distances; a non-equilibrium or "chaotic" pattern of differentiation among locations in space; and within locus, within population deviations from the expectations of Hardy-Weinberg equilibrium (HWE). We show that despite having a pelagic larval stage, and a wide distribution across Caribbean coral reefs, this species forms groups of highly related individuals at small spatial scales (<10 metres). These spatially clustered family groups cause the observed deviations from HWE and local population differentiation, a finding that is rarely demonstrated, but could be more common than previously thought.

Noise induced stabilization of chaotic free-running laser diode

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

Virte, Martin, E-mail: mvirte@b-phot.org

In this paper, we investigate theoretically the stabilization of a free-running vertical-cavity surface-emitting laser exhibiting polarization chaos dynamics. We report the existence of a boundary isolating the chaotic attractor on one side and a steady-state on the other side and identify the unstable periodic orbit playing the role of separatrix. In addition, we highlight a small range of parameters where the chaotic attractor passes through this boundary, and therefore where chaos only appears as a transient behaviour. Then, including the effect of spontaneous emission noise in the laser, we demonstrate that, for realistic levels of noise, the system is systematicallymore » pushed over the separating solution. As a result, we show that the chaotic dynamics cannot be sustained unless the steady-state on the other side of the separatrix becomes unstable. Finally, we link the stability of this steady-state to a small value of the birefringence in the laser cavity and discuss the significance of this result on future experimental work.« less

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.

Large memory capacity in chaotic artificial neural networks: a view of the anti-integrable limit.

PubMed

Lin, Wei; Chen, Guanrong

2009-08-01

In the literature, it was reported that the chaotic artificial neural network model with sinusoidal activation functions possesses a large memory capacity as well as a remarkable ability of retrieving the stored patterns, better than the conventional chaotic model with only monotonic activation functions such as sigmoidal functions. This paper, from the viewpoint of the anti-integrable limit, elucidates the mechanism inducing the superiority of the model with periodic activation functions that includes sinusoidal functions. Particularly, by virtue of the anti-integrable limit technique, this paper shows that any finite-dimensional neural network model with periodic activation functions and properly selected parameters has much more abundant chaotic dynamics that truly determine the model's memory capacity and pattern-retrieval ability. To some extent, this paper mathematically and numerically demonstrates that an appropriate choice of the activation functions and control scheme can lead to a large memory capacity and better pattern-retrieval ability of the artificial neural network models.

Modelling chaotic vibrations using NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1993-01-01

Due to the unavailability and, later, prohibitive cost of the computational power required, many phenomena in nonlinear dynamic systems have in the past been addressed in terms of linear systems. Linear systems respond to periodic inputs with periodic outputs, and may be characterized in the time domain or in the frequency domain as convenient. Reduction to the frequency domain is frequently desireable to reduce the amount of computation required for solution. Nonlinear systems are only soluble in the time domain, and may exhibit a time history which is extremely sensitive to initial conditions. Such systems are termed chaotic. Dynamic buckling, aeroelasticity, fatigue analysis, control systems and electromechanical actuators are among the areas where chaotic vibrations have been observed. Direct transient analysis over a long time period presents a ready means of simulating the behavior of self-excited or externally excited nonlinear systems for a range of experimental parameters, either to characterize chaotic behavior for development of load spectra, or to define its envelope and preclude its occurrence.

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation.

PubMed

Ballard, Christopher C; Esty, C Clark; Egolf, David A

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems

PubMed Central

Lithwick, Yoram; Wu, Yanqin

2014-01-01

In the inner solar system, the planets’ orbits evolve chaotically, driven primarily by secular chaos. Mercury has a particularly chaotic orbit and is in danger of being lost within a few billion years. Just as secular chaos is reorganizing the solar system today, so it has likely helped organize it in the past. We suggest that extrasolar planetary systems are also organized to a large extent by secular chaos. A hot Jupiter could be the end state of a secularly chaotic planetary system reminiscent of the solar system. However, in the case of the hot Jupiter, the innermost planet was Jupiter (rather than Mercury) sized, and its chaotic evolution was terminated when it was tidally captured by its star. In this contribution, we review our recent work elucidating the physics of secular chaos and applying it to Mercury and to hot Jupiters. We also present results comparing the inclinations of hot Jupiters thus produced with observations. PMID:24367108

Efficient topological chaos embedded in the blinking vortex system.

PubMed

Kin, Eiko; Sakajo, Takashi

2005-06-01

We consider the particle mixing in the plane by two vortex points appearing one after the other, called the blinking vortex system. Mathematical and numerical studies of the system reveal that the chaotic particle mixing, i.e., the chaotic advection, is observed due to the homoclinic chaos, but the mixing region is restricted locally in the neighborhood of the vortex points. The present article shows that it is possible to realize a global and efficient chaotic advection in the blinking vortex system with the help of the Thurston-Nielsen theory, which classifies periodic orbits for homeomorphisms in the plane into three types: periodic, reducible, and pseudo-Anosov (pA). It is mathematically shown that periodic orbits of pA type generate a complicated dynamics, which is called topological chaos. We show that the combination of the local chaotic mixing due to the topological chaos and the dipole-like return orbits realize an efficient and global particle mixing in the blinking vortex system.

Nonlinear filtering techniques for noisy geophysical data: Using big data to predict the future

NASA Astrophysics Data System (ADS)

Moore, J. M.

2014-12-01

Chaos is ubiquitous in physical systems. Within the Earth sciences it is readily evident in seismology, groundwater flows and drilling data. Models and workflows have been applied successfully to understand and even to predict chaotic systems in other scientific fields, including electrical engineering, neurology and oceanography. Unfortunately, the high levels of noise characteristic of our planet's chaotic processes often render these frameworks ineffective. This contribution presents techniques for the reduction of noise associated with measurements of nonlinear systems. Our ultimate aim is to develop data assimilation techniques for forward models that describe chaotic observations, such as episodic tremor and slip (ETS) events in fault zones. A series of nonlinear filters are presented and evaluated using classical chaotic systems. To investigate whether the filters can successfully mitigate the effect of noise typical of Earth science, they are applied to sunspot data. The filtered data can be used successfully to forecast sunspot evolution for up to eight years (see figure).

An Exploratory Study of the Butterfly Effect Using Agent-Based Modeling

NASA Technical Reports Server (NTRS)

Khasawneh, Mahmoud T.; Zhang, Jun; Shearer, Nevan E. N.; Rodriquez-Velasquez, Elkin; Bowling, Shannon R.

2010-01-01

This paper provides insights about the behavior of chaotic complex systems, and the sensitive dependence of the system on the initial starting conditions. How much does a small change in the initial conditions of a complex system affect it in the long term? Do complex systems exhibit what is called the "Butterfly Effect"? This paper uses an agent-based modeling approach to address these questions. An existing model from NetLogo library was extended in order to compare chaotic complex systems with near-identical initial conditions. Results show that small changes in initial starting conditions can have a huge impact on the behavior of chaotic complex systems. The term the "butterfly effect" is attributed to the work of Edward Lorenz [1]. It is used to describe the sensitive dependence of the behavior of chaotic complex systems on the initial conditions of these systems. The metaphor refers to the notion that a butterfly flapping its wings somewhere may cause extreme changes in the ecological system's behavior in the future, such as a hurricane.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

NASA Astrophysics Data System (ADS)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Secure Communication Based on a Hybrid of Chaos and Ica Encryptions

NASA Astrophysics Data System (ADS)

Chen, Wei Ching; Yuan, John

Chaos and independent component analysis (ICA) encryptions are two novel schemes for secure communications. In this paper, a new scheme combining chaos and ICA techniques is proposed to enhance the security level during communication. In this scheme, a master chaotic system is embedded at the transmitter. The message signal is mixed with a chaotic signal and a Gaussian white noise into two mixed signals and then transmitted to the receiver through the public channels. A signal for synchronization is transmitted through another public channel to the receiver where a slave chaotic system is embedded to reproduce the chaotic signal. A modified ICA is used to recover the message signal at the receiver. Since only two of the three transmitted signals contain the information of message signal, a hacker would not be able to retrieve the message signal by using ICA even though all the transmitted signals are intercepted. Spectrum analyses are used to prove that the message signal can be securely hidden under this scheme.

Experimental phase synchronization detection in non-phase coherent chaotic systems by using the discrete complex wavelet approach

NASA Astrophysics Data System (ADS)

Ferreira, Maria Teodora; Follmann, Rosangela; Domingues, Margarete O.; Macau, Elbert E. N.; Kiss, István Z.

2017-08-01

Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with non-phase-coherent chaotic systems without state space reconstruction or pre-processing. The method correctly predicts the phase synchronization for a chemical experiment with three locally coupled, non-phase-coherent chaotic processes. The impact of different time-scales is demonstrated on the synchronization process that outlines the advantages of DCWA for analysis of experimental data.

The Lyman Alpha Imaging-Monitor Experiment (LAIME) for TESIS/CORONAS-PHOTON

NASA Astrophysics Data System (ADS)

Damé, L.; Koutchmy, S.; Kuzin, S.; Lamy, P.; Malherbe, J.-M.; Noëns, J.-C.

LAIME the Lyman Alpha Imaging-Monitor Experiment is a remarkably simple no mechanisms and compact 100x100x400 mm full Sun imager to be flown with TESIS on the CORONAS-PHOTON mission launch expected before mid-2008 As such it will be the only true chromospheric imager to be flown in the next years supporting TESIS EUV-XUV imaging SDO and the Belgian LYRA Lyman Alpha flux monitor on the ESA PROBA-2 microsatellite launch expected in September 2007 We will give a short description of this unique O60 mm aperture imaging telescope dedicated to the investigating of the magnetic sources of solar variability in the UV and chromospheric and coronal disruptive events rapid waves Moreton waves disparitions brusques of prominences filaments eruptions and CMEs onset The resolution pixel is 2 7 arcsec the field of view 1 4 solar radius and the acquisition cadence could be as high as 1 image minute The back thinned E2V CCD in the focal plane is using frame transfer to avoid shutter and mechanisms Further more the double Lyman Alpha filtering allows a 40 AA FWHM bandwidth and excellent rejection yet providing a vacuum seal design of the telescope MgF2 entrance window Structural stability of the telescope focal length 1 m is preserved by a 4-INVAR bars design with Aluminium compensation in a large pm 10 o around 20 o

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.

Chua's Equation was Proved to BE Chaotic in Two Years, Lorenz Equation in Thirty Six Years

NASA Astrophysics Data System (ADS)

Muthuswamy, Bharathwaj

2013-01-01

Although there are probably more publications on Chua's circuit than any other chaotic circuit, a tutorial with a historical emphasis is still lacking. Hence the goal of this chapter is to provide such a tutorial. This chapter will prove useful for a novice who is looking to understand the basics behind chaotic circuits without too much technical details. The chapter also includes a cookbook approach to a rigorous proof of chaos in piecewise-linear systems. The proof is a summary of the original piecewise-linear proof of chaos in Chua's circuit. The chapter concludes with a discussion of circuits derived from Chua's circuit.

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.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

PubMed

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-15

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

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.

Experimental Demonstration of Coherent Control in Quantum Chaotic Systems

NASA Astrophysics Data System (ADS)

Bitter, M.; Milner, V.

2017-01-01

We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization of the molecular angular momentum, a characteristic feature of the chaotic quantum kicked rotor. By changing the phases of the rotational states in the initially prepared coherent wave packet, we control the rotational distribution of the final localized state and its total energy. We demonstrate the anticipated sensitivity of control to the exact parameters of the kicking field, as well as its disappearance in the classical regime of excitation.

Paramagnetic colloids: Chaotic routes to clusters and molecules

NASA Astrophysics Data System (ADS)

Abdi, Hamed; Soheilian, Rasam; Erb, Randall M.; Maloney, Craig E.

2018-03-01

We present computer simulations and experiments on dilute suspensions of superparamagnetic particles subject to rotating magnetic fields. We focus on chains of four particles and their decay routes to stable structures. At low rates, the chains track the external field. At intermediate rates, the chains break up but perform a periodic (albeit complex) motion. At sufficiently high rates, the chains generally undergo chaotic motion at short times and decay to either closely packed clusters or more dispersed, colloidal molecules at long times. We show that the transition out of the chaotic states can be described as a Poisson process in both simulation and experiment.

A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

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

Castro-Ramírez, Joel, E-mail: ingcastro.7@gmail.com; Martínez-Guerra, Rafael, E-mail: rguerra@ctrl.cinvestav.mx; Cruz-Victoria, Juan Crescenciano, E-mail: juancrescenciano.cruz@uptlax.edu.mx

2015-10-15

This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.

Local and nonlocal parallel heat transport in general magnetic fields

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

Del-Castillo-Negrete, Diego B; Chacon, Luis

2011-01-01

A novel approach for the study of parallel transport in magnetized plasmas is presented. The method avoids numerical pollution issues of grid-based formulations and applies to integrable and chaotic magnetic fields with local or nonlocal parallel closures. In weakly chaotic fields, the method gives the fractal structure of the devil's staircase radial temperature profile. In fully chaotic fields, the temperature exhibits self-similar spatiotemporal evolution with a stretched-exponential scaling function for local closures and an algebraically decaying one for nonlocal closures. It is shown that, for both closures, the effective radial heat transport is incompatible with the quasilinear diffusion model.

Persistent stability of a chaotic system

NASA Astrophysics Data System (ADS)

Huber, Greg; Pradas, Marc; Pumir, Alain; Wilkinson, Michael

2018-02-01

We report that trajectories of a one-dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time, despite the fact that the system is chaotic. We provide a detailed quantitative description of this effect by developing the large-deviation theory for fluctuations of the finite-time Lyapunov exponent of this system. Specifically, the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods. The system has 'generic' instability properties, and we consider the broader implications of our observation of long-term stability in chaotic systems.

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.

Preliminary chaotic model of snapover on high voltage solar cells

NASA Technical Reports Server (NTRS)

Mackey, Willie R.

1995-01-01

High voltage power systems in space will interact with the space plasma in a variety of ways. One of these, snapover, is characterized by sudden enlargement of the current collection area across normally insulating surfaces generating enhanced electron current collection. Power drain on solar array power systems results from this enhanced current collection. Optical observations of the snapover phenomena in the laboratory indicates a functional relation between glow area and bia potential as a consequence of the fold/cusp bifurcation in chaos theory. Successful characterizations of snapover as a chaotic phenomena may provide a means of snapover prevention and control through chaotic synchronization.

Effect of collision duration on the chaotic dynamics of a ball bouncing on a vertically vibrating plate

NASA Astrophysics Data System (ADS)

Jiang, Z. H.; Liang, Z. J.; Wu, A. C.; Zheng, R. H.

2018-03-01

Experiments have been performed to study the chaotic dynamics of a ball bouncing on a vertically vibrating plate. The velocity dependence of collision duration and coefficient of restitution is determined, and phase portraits of chaotic structures for the flight time and the relative collision velocities are obtained. Numerical calculations are carried out to examine the effects of velocity-dependent collision duration on the ball dynamics. It is revealed that when the collision is instantaneous, sticking solutions are always observed, whereas when the collision duration is taken into account, sticking solutions are destroyed and thereby chaos behaviors are induced.

Chaotic Ising-like dynamics in traffic signals

PubMed Central

Suzuki, Hideyuki; Imura, Jun-ichi; Aihara, Kazuyuki

2013-01-01

The green and red lights of a traffic signal can be viewed as the up and down states of an Ising spin. Moreover, traffic signals in a city interact with each other, if they are controlled in a decentralised way. In this paper, a simple model of such interacting signals on a finite-size two-dimensional lattice is shown to have Ising-like dynamics that undergoes a ferromagnetic phase transition. Probabilistic behaviour of the model is realised by chaotic billiard dynamics that arises from coupled non-chaotic elements. This purely deterministic model is expected to serve as a starting point for considering statistical mechanics of traffic signals. PMID:23350034

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison

NASA Astrophysics Data System (ADS)

Kumar, Santosh; Dietz, Barbara; Guhr, Thomas; Richter, Achim

2017-12-01

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

Working Towards Führer: A Chaotic View

NASA Astrophysics Data System (ADS)

Cakar, Ulas

Leadership is a concept that has been discussed since the beginning of history. Even though there have been many theories in the field accepting leadership's role in bringing order, chaotic aspects of leadership are generally neglected. This chapter aims to examine the leadership beyond an orderly interpretation of universe. For this purpose, Third Reich period and leadership during this period will be examined. Ian Kershaw's "Working Towards Führer" concept provides a unique understanding of leadership concept. It goes beyond the dualist depiction of Third Reich, it does not state Adolf Hitler as an all powerful dictator, or a weak one. Rather, he expresses that due to the conditions in the Third Reich, Adolf Hitler was both of this. This complex situation can be understood deeper when it is examined through the lens of chaos theory. This study contributes to the field by being the first in using chaos theory for examining "Working Towards Führer" concept and its development. Seemingly orderly nature of synchronization process and its vortex will be shown. Adolf Hitler's storm spot position in the chaotic system and its dynamics are explained. War's entropic power and its effect on the downfall of the system is crucial in understanding this unique chaotic system. The chaotic pattern of "Working Towards Führer" offers an opportunity to analyze the complexities of the leadership concept.

Polynomiography and Chaos

NASA Astrophysics Data System (ADS)

Kalantari, Bahman

Polynomiography is the algorithmic visualization of iterative systems for computing roots of a complex polynomial. It is well known that iterations of a rational function in the complex plane result in chaotic behavior near its Julia set. In one scheme of computing polynomiography for a given polynomial p(z), we select an individual member from the Basic Family, an infinite fundamental family of rational iteration functions that in particular include Newton's. Polynomiography is an excellent means for observing, understanding, and comparing chaotic behavior for variety of iterative systems. Other iterative schemes in polynomiography are possible and result in chaotic behavior of different kinds. In another scheme, the Basic Family is collectively applied to p(z) and the iterates for any seed in the Voronoi cell of a root converge to that root. Polynomiography reveals chaotic behavior of another kind near the boundary of the Voronoi diagram of the roots. We also describe a novel Newton-Ellipsoid iterative system with its own chaos and exhibit images demonstrating polynomiographies of chaotic behavior of different kinds. Finally, we consider chaos for the more general case of polynomiography of complex analytic functions. On the one hand polynomiography is a powerful medium capable of demonstrating chaos in different forms, it is educationally instructive to students and researchers, also it gives rise to numerous research problems. On the other hand, it is a medium resulting in images with enormous aesthetic appeal to general audiences.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

NASA Astrophysics Data System (ADS)

Mallory, Kristina; van Gorder, Robert A.

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

Chaos and generalised multistability in a mesoscopic model of the electroencephalogram

NASA Astrophysics Data System (ADS)

Dafilis, Mathew P.; Frascoli, Federico; Cadusch, Peter J.; Liley, David T. J.

2009-06-01

We present evidence for chaos and generalised multistability in a mesoscopic model of the electroencephalogram (EEG). Two limit cycle attractors and one chaotic attractor were found to coexist in a two-dimensional plane of the ten-dimensional volume of initial conditions. The chaotic attractor was found to have a moderate value of the largest Lyapunov exponent (3.4 s -1 base e) with an associated Kaplan-Yorke (Lyapunov) dimension of 2.086. There are two different limit cycles appearing in conjunction with this particular chaotic attractor: one multiperiodic low amplitude limit cycle whose largest spectral peak is within the alpha band (8-13 Hz) of the EEG; and another multiperiodic large-amplitude limit cycle which may correspond to epilepsy. The cause of the coexistence of these structures is explained with a one-parameter bifurcation analysis. Each attractor has a basin of differing complexity: the large-amplitude limit cycle has a basin relatively uncomplicated in its structure while the small-amplitude limit cycle and chaotic attractor each have much more finely structured basins of attraction, but none of the basin boundaries appear to be fractal. The basins of attraction for the chaotic and small-amplitude limit cycle dynamics apparently reside within each other. We briefly discuss the implications of these findings in the context of theoretical attempts to understand the dynamics of brain function and behaviour.

Lyapunov exponents from CHUA's circuit time series using artificial neural networks

NASA Technical Reports Server (NTRS)

Gonzalez, J. Jesus; Espinosa, Ismael E.; Fuentes, Alberto M.

1995-01-01

In this paper we present the general problem of identifying if a nonlinear dynamic system has a chaotic behavior. If the answer is positive the system will be sensitive to small perturbations in the initial conditions which will imply that there is a chaotic attractor in its state space. A particular problem would be that of identifying a chaotic oscillator. We present an example of three well known different chaotic oscillators where we have knowledge of the equations that govern the dynamical systems and from there we can obtain the corresponding time series. In a similar example we assume that we only know the time series and, finally, in another example we have to take measurements in the Chua's circuit to obtain sample points of the time series. With the knowledge about the time series the phase plane portraits are plotted and from them, by visual inspection, it is concluded whether or not the system is chaotic. This method has the problem of uncertainty and subjectivity and for that reason a different approach is needed. A quantitative approach is the computation of the Lyapunov exponents. We describe several methods for obtaining them and apply a little known method of artificial neural networks to the different examples mentioned above. We end the paper discussing the importance of the Lyapunov exponents in the interpretation of the dynamic behavior of biological neurons and biological neural networks.

THE ASTEROID BELT AS A RELIC FROM A CHAOTIC EARLY SOLAR SYSTEM

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

Izidoro, André; Raymond, Sean N.; Pierens, Arnaud

The orbital structure of the asteroid belt holds a record of the solar system’s dynamical history. The current belt only contains ∼10{sup −3} Earth masses yet the asteroids’ orbits are dynamically excited, with a large spread in eccentricity and inclination. In the context of models of terrestrial planet formation, the belt may have been excited by Jupiter’s orbital migration. The terrestrial planets can also be reproduced without invoking a migrating Jupiter; however, as it requires a severe mass deficit beyond Earth’s orbit, this model systematically under-excites the asteroid belt. Here we show that the orbits of the asteroids may havemore » been excited to their current state if Jupiter’s and Saturn’s early orbits were chaotic. Stochastic variations in the gas giants’ orbits cause resonances to continually jump across the main belt and excite the asteroids’ orbits on a timescale of tens of millions of years. While hydrodynamical simulations show that the gas giants were likely in mean motion resonance at the end of the gaseous disk phase, small perturbations could have driven them into a chaotic but stable state. The gas giants’ current orbits were achieved later, during an instability in the outer solar system. Although it is well known that the present-day solar system exhibits chaotic behavior, our results suggest that the early solar system may also have been chaotic.« less

El Mejoramiento de la Efectividad del Personal de las Diferentes Unidades del Ejrcito de Guatemala Involucradas en la Integracin de Contingentes Desplegados en Diferentes Misiones de Paz de la Organizacin de las Naciones Unidas (Improving the Effectiveness of Guatemalan Army Units that Provide Soldiers to Units Deployed in United Nations Peace Missions)

DTIC Science & Technology

2017-06-09

del Ejército de EE.UU. Colegio de Comando y Estado Mayor en el cumplimiento parcial de los requisitos para el grado de MAESTRÍA EN CIENCIAS Y...Rev. 8-98) Prescribed by ANSI Std. Z39.18 iii MAESTRÍA EN CIENCIAS Y ARTES MILITARES PAGINA DE APROBACIÓN DE LA TESIS Name of Candidate: Major... Ciencias Militares. A mi honorable comité de tesis, Doctor Edwin Roldán, Coronel Francisco Rivera Pérez del Ejército de Guatemala y al Mayor Rafael

Chaotic Homes and School Achievement: A Twin Study

ERIC Educational Resources Information Center

Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Jaffee, Sara R.; Plomin, Robert

2011-01-01

Background: Chaotic homes predict poor school performance. Given that it is known that genes affect both children's experience of household chaos and their school achievement, to what extent is the relationship between high levels of noise and environmental confusion in the home, and children's school performance, mediated by heritable child…

A Unit on Deterministic Chaos for Student Teachers

ERIC Educational Resources Information Center

Stavrou, D.; Assimopoulos, S.; Skordoulis, C.

2013-01-01

A unit aiming to introduce pre-service teachers of primary education to the limited predictability of deterministic chaotic systems is presented. The unit is based on a commercial chaotic pendulum system connected with a data acquisition interface. The capabilities and difficulties in understanding the notion of limited predictability of 18…

Chaotic attractors in tumor growth and decay: a differential equation model.

PubMed

Harney, Michael; Yim, Wen-sau

2015-01-01

Tumorigenesis can be modeled as a system of chaotic nonlinear differential equations. A simulation of the system is realized by converting the differential equations to difference equations. The results of the simulation show that an increase in glucose in the presence of low oxygen levels decreases tumor growth.

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.

How to Generate Chaos at Home.

ERIC Educational Resources Information Center

Smith, Douglas

1992-01-01

Describes an electronic circuit that can function as a prototype for chaotic systems. Specific applied voltages produce chaotic signals that can be viewed with an oscilloscope or be made audible with a home stereo system. Provides directions for assembly with typical costs, mathematical basis of chaos theory, and experimental extensions. (JJK)

A Novel Type of Chaotic Attractor for Quadratic Systems Without Equilibriums

NASA Astrophysics Data System (ADS)

Dantsev, Danylo

In this paper, a new chaotic dynamic system without equilibriums is presented. A conducted research of the qualitative properties of the discovered system reveals a noncompliance between the bifurcation behavior of the system and the Feigenbaum-Sharkovskii-Magnitsky theory. Additional research of known systems confirms the discrepancy.

Learning in a Chaotic Environment

ERIC Educational Resources Information Center

Goldman, Ellen; Plack, Margaret; Roche, Colleen; Smith, Jeffrey; Turley, Catherine

2009-01-01

Purpose: The purpose of this study is to understand how, when, and why emergency medicine residents learn while working in the chaotic environment of a hospital emergency room. Design/methodology/approach: This research used a qualitative interview methodology with thematic data analysis that was verified with the entire population of learners.…

Nonlinear Analysis of Two-phase Circumferential Motion in the Ablation Circumstance

NASA Astrophysics Data System (ADS)

Xiao-liang, Xu; Hai-ming, Huang; Zi-mao, Zhang

2010-05-01

In aerospace craft reentry and solid rocket propellant nozzle, thermal chemistry ablation is a complex process coupling with convection, heat transfer, mass transfer and chemical reaction. Based on discrete vortex method (DVM), thermal chemical ablation model and particle kinetic model, a computational module dealing with the two-phase circumferential motion in ablation circumstance is designed, the ablation velocity and circumferential field can be thus calculated. The calculated nonlinear time series are analyzed in chaotic identification method: relative chaotic characters such as correlation dimension and the maximum Lyapunov exponent are calculated, fractal dimension of vortex bulbs and particles distributions are also obtained, thus the nonlinear ablation process can be judged as a spatiotemporal chaotic process.

Experimental demonstration of chaotic scattering of microwaves

NASA Astrophysics Data System (ADS)

Doron, E.; Smilansky, U.; Frenkel, A.

1990-12-01

Reflection of microwaves from a cavity is measured in a frequency domain where the underlying classical chaotic scattering leaves a clear mark on the wave dynamics. We check the hypothesis that the fluctuations of the S matrix can be described in terms of parameters characterizing the chaotic classical scatteirng. Absorption of energy in the cavity walls is shown to significantly affect the results, and is linked to time-domain properties of the scattering in a general way. We also show that features whose origin is entirely due to wave dynamics (e.g., the enhancement of the Wigner time delay due to time-reversal symmetry) coexist with other features which characterize the underlying classical dynamics.

Multiobjective synchronization of coupled systems

NASA Astrophysics Data System (ADS)

Tang, Yang; Wang, Zidong; Wong, W. K.; Kurths, Jürgen; Fang, Jian-an

2011-06-01

In this paper, multiobjective synchronization of chaotic systems is investigated by especially simultaneously minimizing optimization of control cost and convergence speed. The coupling form and coupling strength are optimized by an improved multiobjective evolutionary approach that includes a hybrid chromosome representation. The hybrid encoding scheme combines binary representation with real number representation. The constraints on the coupling form are also considered by converting the multiobjective synchronization into a multiobjective constraint problem. In addition, the performances of the adaptive learning method and non-dominated sorting genetic algorithm-II as well as the effectiveness and contributions of the proposed approach are analyzed and validated through the Rössler system in a chaotic or hyperchaotic regime and delayed chaotic neural networks.

Quantum-classical correspondence in the vicinity of periodic orbits

NASA Astrophysics Data System (ADS)

Kumari, Meenu; Ghose, Shohini

2018-05-01

Quantum-classical correspondence in chaotic systems is a long-standing problem. We describe a method to quantify Bohr's correspondence principle and calculate the size of quantum numbers for which we can expect to observe quantum-classical correspondence near periodic orbits of Floquet systems. Our method shows how the stability of classical periodic orbits affects quantum dynamics. We demonstrate our method by analyzing quantum-classical correspondence in the quantum kicked top (QKT), which exhibits both regular and chaotic behavior. We use our correspondence conditions to identify signatures of classical bifurcations even in a deep quantum regime. Our method can be used to explain the breakdown of quantum-classical correspondence in chaotic systems.

Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.

2017-11-01

This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow.

Quantum synchronization of chaotic oscillator behaviors among coupled BEC-optomechanical systems

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2017-03-01

We consider and theoretically analyze a Bose-Einstein condensate (BEC) trapped inside an optomechanical system consisting of single-mode optical cavity with a moving end mirror. The BEC is formally analogous to a mirror driven by radiation pressure with strong nonlinear coupling. Such a nonlinear enhancement can make the oscillator display chaotic behavior. By establishing proper oscillator couplings, we find that this chaotic motion can be synchronized with other oscillators, even an oscillator network. We also discuss the scheme feasibility by analyzing recent experiment parameters. Our results provide a promising platform for the quantum signal transmission and quantum logic control, and they are of potential applications in quantum information processing and quantum networks.

Chaotic evolution of arms races

NASA Astrophysics Data System (ADS)

Tomochi, Masaki; Kono, Mitsuo

1998-12-01

A new set of model equations is proposed to describe the evolution of the arms race, by extending Richardson's model with special emphases that (1) power dependent defensive reaction or historical enmity could be a motive force to promote armaments, (2) a deterrent would suppress the growth of armaments, and (3) the defense reaction of one nation against the other nation depends nonlinearly on the difference in armaments between two. The set of equations is numerically solved to exhibit stationary, periodic, and chaotic behavior depending on the combinations of parameters involved. The chaotic evolution is realized when the economic situation of each country involved in the arms race is quite different, which is often observed in the real world.

Chaotic coordinates for the Large Helical Device

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

Hudson, S. R., E-mail: shudson@pppl.gov; Suzuki, Y.

The theory of quadratic-flux-minimizing (QFM) surfaces is reviewed, and numerical techniques that allow high-order QFM surfaces to be efficiently constructed for experimentally relevant, non-integrable magnetic fields are described. As a practical example, the chaotic edge of the magnetic field in the Large Helical Device (LHD) is examined. A precise technique for finding the boundary surface is implemented, the hierarchy of partial barriers associated with the near-critical cantori is constructed, and a coordinate system, which we call chaotic coordinates, that is based on a selection of QFM surfaces is constructed that simplifies the description of the magnetic field, so that fluxmore » surfaces become “straight” and islands become “square.”.« less

A Spatiotemporal-Chaos-Based Encryption Having Overall Properties Considerably Better than Advanced Encryption Standard

NASA Astrophysics Data System (ADS)

Wang, Shi-Hong; Ye, Wei-Ping; Lü, Hua-Ping; Kuang, Jin-Yu; Li, Jing-Hua; Luo, Yun-Lun; Hu, Gang

2003-07-01

Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties of high security, fast encryption (decryption) speed, and robustness against noise disturbances in communication channel. The overall features of this spatiotemporal-chaos-based cryptosystem are better than chaotic cryptosystems known so far, and also than currently used conventional cryptosystems, such as the Advanced Encryption Standard (AES). The project supported by National Natural Science Foundation of China under Grant No. 10175010 and the Special Funds for Major State Basic Research Projects under Grant No. G2000077304

Design and implementation of EP-based PID controller for chaos synchronization of Rikitake circuit systems.

PubMed

Hou, Yi-You

2017-09-01

This article addresses an evolutionary programming (EP) algorithm technique-based and proportional-integral-derivative (PID) control methods are established to guarantee synchronization of the master and slave Rikitake chaotic systems. For PID synchronous control, the evolutionary programming (EP) algorithm is used to find the optimal PID controller parameters k p , k i , k d by integrated absolute error (IAE) method for the convergence conditions. In order to verify the system performance, the basic electronic components containing operational amplifiers (OPAs), resistors, and capacitors are used to implement the proposed chaotic Rikitake systems. Finally, the experimental results validate the proposed Rikitake chaotic synchronization approach. Copyright © 2017. Published by Elsevier Ltd.

Stability enhancement of high Prandtl number chaotic convection in an anisotropic porous layer with feedback control

NASA Astrophysics Data System (ADS)

Mahmud, M. N.

2018-04-01

The chaotic dynamical behaviour of thermal convection in an anisotropic porous layer subject to gravity, heated from below and cooled from above, is studied based on theory of dynamical system in the presence of feedback control. The extended Darcy model, which includes the time derivative has been employed in the momentum equation to derive a low dimensional Lorenz-like equation by using Galerkin-truncated approximation. The classical fourth-order Runge-Kutta method is used to obtain the numerical solution in order to exemplify the dynamics of the nonlinear autonomous system. The results show that stability enhancement of chaotic convection is feasible via feedback control.

Menstruation, perimenopause, and chaos theory.

PubMed

Derry, Paula S; Derry, Gregory N

2012-01-01

This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.

Preliminary Chaotic Model of Snapover on High Voltage Solar Cells

NASA Technical Reports Server (NTRS)

Mackey, Willie R.

1995-01-01

High voltage power systems in space will interact with the space plasma in a variety of ways. One of these, Snapover, is characterized by a sudden enlargement of the electron current collection area across normally insulating surfaces. A power drain on solar array power systems will results from this enhanced current collection. Optical observations of the snapover phenomena in the laboratory indicates a functional relation between bia potential and surface glow area. This paper shall explore the potential benefits of modeling the relation between current and bia potential as an aspect of bifurcation analysis in chaos theory. Successful characterizations of snapover as a chaotic phenomena may provide a means of snapover prevention and control through chaotic synchronization.

Illusion optics in chaotic light

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

Zhang Suheng; Gan Shu; Xiong Jun

2010-08-15

The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoreticalmore » proposal of similar effects in complementary media.« less

Chaotic behaviour of the Rossler model and its analysis by using bifurcations of limit cycles and chaotic attractors

NASA Astrophysics Data System (ADS)

Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.

2018-05-01

The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.

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.

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.

Chaotic patterns of autonomic activity during hypnotic recall.

PubMed

Bob, Petr; Siroka, Ivana; Susta, Marek

2009-01-01

Chaotic neural dynamics likely emerge in cognitive processes and may present time periods that are extremely sensitive to influences affecting the neural system. Recent findings suggest that this sensitivity may increase during retrieval of stressful emotional experiences reflecting underlying mechanism related to consolidation of traumatic memories. In this context, hypnotic recall of anxiety memories in 10 patients, simultaneously with ECG measurement was performed. The same measurement was performed during control cognitive task in 8 anxiety patients and 22 healthy controls. Nonlinear data analysis of ECG records indicates significant increase in the degree of chaos during retrieval of stressful memory in all the patients. The results suggest a role of chaotic neural dynamics during processing of anxiety-related stressful memories.

A Simple Approach to Achieve Modified Projective Synchronization between Two Different Chaotic Systems

PubMed Central

2013-01-01

A new approach, the projective system approach, is proposed to realize modified projective synchronization between two different chaotic systems. By simple analysis of trajectories in the phase space, a projective system of the original chaotic systems is obtained to replace the errors system to judge the occurrence of modified projective synchronization. Theoretical analysis and numerical simulations show that, although the projective system may not be unique, modified projective synchronization can be achieved provided that the origin of any of projective systems is asymptotically stable. Furthermore, an example is presented to illustrate that even a necessary and sufficient condition for modified projective synchronization can be derived by using the projective system approach. PMID:24187522

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.

Comment on "Synchronization of chaotic systems with delay using intermittent linear state feedback" [Chaos 18, 033122 (2008)].

PubMed

Zhang, Yinping; Wang, Qing-Guo

2008-12-01

In the referenced paper, there is technical carelessness in the third lemma and in the main result. Hence, it is a possible failure when the result is used to design the intermittent linear state feedback controller for exponential synchronization of two chaotic delayed systems.

Chaotic LIDAR for Naval Applications

DTIC Science & Technology

2014-08-29

Perot Fiber Laser PD ^^ /- x —► -(YDF\\ {SMFV X — FBG 1 0 r utput FBG 70 Fabry-Perot Laser Output Pump Power (mW) Fig 2. Fabry-Perot...chaotic fiber laser. Left: Block diagram of the laser. Right: Output power versus pump power. (PD: Pump Diode; FBG : Fiber Braggs Grating; YDF: Ytterbium

Leadership Training in an Industry Context: Preparing Student Leaders for a Chaotic News Media

ERIC Educational Resources Information Center

Herndon, Keith; Krueger, Vicki

2016-01-01

This application brief explains the creation and execution of a leadership training program within the context of journalism education. The news media has experienced profound changes in an era of digital disruption. Massive job loss, financial distress, and ownership consolidation have resulted in a chaotic industry. Promising young journalists…

Chaotic He-Ne laser

NASA Astrophysics Data System (ADS)

Kuusela, Tom A.

2017-09-01

A He-Ne laser is an example of a class A laser, which can be described by a single nonlinear differential equation of the complex electric field. This laser system has only one degree of freedom and is thus inherently stable. A He-Ne laser can be driven to the chaotic condition when a large fraction of the output beam is injected back to the laser. In practice, this can be done simply by adding an external mirror. In this situation, the laser system has infinite degrees of freedom and therefore it can have a chaotic attractor. We show the fundamental laser equations and perform elementary stability analysis. In experiments, the laser intensity variations are measured by a simple photodiode circuit. The laser output intensity time series is studied using nonlinear analysis tools which can be found freely on the internet. The results show that the laser system with feedback has an attractor of a reasonably high dimension and that the maximal Lyapunov exponent is positive, which is clear evidence of chaotic behaviour. The experimental setup and analysis steps are so simple that the studies can even be implemented in the undergraduate physics laboratory.

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

Chaotic behavior of channeling particles.

PubMed

Chen, Ling; Kaloyeros, Alain E.; Wang, Guang-Hou

1994-03-01

Channeling describes the collimated motion of energetic charged particles along the lattice plane or axis in a crystal. The energetic particles are steered through the channels formed by strings of atomic constituents in the lattice. In the case of planar channeling, the motion of a charged particle between the atomic planes can be periodic or quasiperiodic, such as a simple oscillatory motion in the transverse direction. In practice, however, the periodic motion of the channeling particles can be accompanied by an irregular, chaotic behavior. In this paper, the Moliere potential, which is considered as a good analytical approximation for the interaction of channeling particles with the rows of atoms in the lattice, is used to simulate the channeling behavior of positively charged particles in a tungsten (100) crystal plane. By appropriate selection of channeling parameters, such as the projectile energy E(0) and incident angle psi(0), the transition of channeling particles from regular to chaotic motion is demonstrated. It is argued that the fine structures that appear in the angular scan channeling experiments are due to the particles' chaotic motion.

Generation of 2N + 1-scroll existence in new three-dimensional chaos systems

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

Liu, Yue; Guan, Jian; Ma, Chunyang

2016-08-15

We propose a systematic methodology for creating 2N + 1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a{sub 12}a{sub 21} = 0, while the Chua system satisfies a{sub 12}a{sub 21} > 0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2N + 1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2N + 1-scroll attractors. Finally, to explore the potential usemore » in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1-, 3-, 5-, and 7-scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.« less

Intermittent and sustained periodic windows in networked chaotic Rössler oscillators

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

He, Zhiwei; Sun, Yong; University of the Chinese Academy of Sciences, Beijing 100049

Route to chaos (or periodicity) in dynamical systems is one of fundamental problems. Here, dynamical behaviors of coupled chaotic Rössler oscillators on complex networks are investigated and two different types of periodic windows with the variation of coupling strength are found. Under a moderate coupling, the periodic window is intermittent, and the attractors within the window extremely sensitively depend on the initial conditions, coupling parameter, and topology of the network. Therefore, after adding or removing one edge of network, the periodic attractor can be destroyed and substituted by a chaotic one, or vice versa. In contrast, under an extremely weakmore » coupling, another type of periodic window appears, which insensitively depends on the initial conditions, coupling parameter, and network. It is sustained and unchanged for different types of network structure. It is also found that the phase differences of the oscillators are almost discrete and randomly distributed except that directly linked oscillators more likely have different phases. These dynamical behaviors have also been generally observed in other networked chaotic oscillators.« less

Chaotic Fluid Mixing in Crystalline Sphere Arrays

NASA Astrophysics Data System (ADS)

Turuban, R.; Lester, D. R.; Le Borgne, T.; Méheust, Y.

2017-12-01

We study the Lagrangian dynamics of steady 3D Stokes flow over simple cubic (SC) and body-centered cubic (BCC) lattices of close-packed spheres, and uncover the mechanisms governing chaotic mixing. Due to the cusp-shaped sphere contacts, the topology of the skin friction field is fundamentally different to that of continuous (non-granular) media (e.g. open pore networks), with significant implications for fluid mixing. Weak symmetry breaking of the flow orientation with respect to the lattice symmetries imparts a transition from regular to strong chaotic mixing in the BCC lattice, whereas the SC lattice only exhibits weak mixing. Whilst the SC and BCC lattices share the same symmetry point group, these differences are explained in terms of their space groups, and we find that a glide symmetry of the BCC lattice generates chaotic mixing. These insight are used to develop accurate predictions of the Lyapunov exponent distribution over the parameter space of mean flow orientation, and point to a general theory of mixing and dispersion based upon the inherent symmetries of arbitrary crystalline structures.

Fast, Parallel and Secure Cryptography Algorithm Using Lorenz's Attractor

NASA Astrophysics Data System (ADS)

Marco, Anderson Gonçalves; Martinez, Alexandre Souto; Bruno, Odemir Martinez

A novel cryptography method based on the Lorenz's attractor chaotic system is presented. The proposed algorithm is secure and fast, making it practical for general use. We introduce the chaotic operation mode, which provides an interaction among the password, message and a chaotic system. It ensures that the algorithm yields a secure codification, even if the nature of the chaotic system is known. The algorithm has been implemented in two versions: one sequential and slow and the other, parallel and fast. Our algorithm assures the integrity of the ciphertext (we know if it has been altered, which is not assured by traditional algorithms) and consequently its authenticity. Numerical experiments are presented, discussed and show the behavior of the method in terms of security and performance. The fast version of the algorithm has a performance comparable to AES, a popular cryptography program used commercially nowadays, but it is more secure, which makes it immediately suitable for general purpose cryptography applications. An internet page has been set up, which enables the readers to test the algorithm and also to try to break into the cipher.

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.

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.

Gyrotactic suppression and emergence of chaotic trajectories of swimming particles in three-dimensional flows

NASA Astrophysics Data System (ADS)

Richardson, S. I. Heath; Baggaley, A. W.; Hill, N. A.

2018-02-01

We study the effects of imposed three-dimensional flows on the trajectories and mixing of gyrotactic swimming microorganisms and identify phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor-Green and Arnold-Beltrami-Childress (ABC) flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical "plumelike" structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. Furthermore, studies of Lyapunov exponents reveal that, as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds.

Banknote authentication using chaotic elements technology

NASA Astrophysics Data System (ADS)

Ambadiyil, Sajan; P. S., Krishnendu; Mahadevan Pillai, V. P.; Prabhu, Radhakrishna

2017-10-01

The counterfeit banknote is a growing threat to the society since the advancements in the field of computers, scanners and photocopiers, as they have made the duplication process for banknote much simpler. The fake note detection systems developed so far have many drawbacks such as high cost, poor accuracy, unavailability, lack of user-friendliness and lower effectiveness. One possible solution to this problem could be the use of a system uniquely linked to the banknote itself. In this paper, we present a unique identification and authentication process for the banknote using chaotic elements embedded in it. A chaotic element means that the physical elements are formed from a random process independent from human intervention. The chaotic elements used in this paper are the random distribution patterns of such security fibres set into the paper pulp. A unique ID is generated from the fibre pattern obtained from UV image of the note, which can be verified by any person who receives the banknote to decide whether the banknote is authentic or not. Performance analysis of the system is also studied in this paper.

External Source of Infection and Nutritional Efficiency Control Chaos in a Predator-Prey Model with Disease in the Predator

NASA Astrophysics Data System (ADS)

Pada Das, Krishna; Roy, Prodip; Ghosh, Subhabrata; Maiti, Somnath

This paper deals with an eco-epidemiological approach with disease circulating through the predator species. Disease circulation in the predator species can be possible by contact as well as by external sources. Here, we try to discuss the role of external source of infection along with nutritional value on system dynamics. To establish our findings, we have worked out the local and global stability analysis of the equilibrium points with Hopf bifurcation analysis associated with interior equilibrium point. The ecological consequence by ecological basic reproduction number as well as the disease basic reproduction number or basic reproductive ratio are obtained and we have analyzed the community structure of the particular system with the help of ecological and disease basic reproduction numbers. Further we pay attention to the chaotic dynamics which is produced by disease circulating in predator species by contact. Our numerical simulations reveal that eco-epidemiological system without external source of infection induced chaotic dynamics for increasing force of infection due to contact, whereas in the presence of external source of infection, it exhibits stable solution. It is also observed that nutritional value can prevent chaotic dynamics. We conclude that chaotic dynamics can be controlled by the external source of infection as well as nutritional value. We apply basic tools of nonlinear dynamics such as Poincare section and maximum Lyapunov exponent to investigate chaotic behavior of the system.

An annealed chaotic maximum neural network for bipartite subgraph problem.

PubMed

Wang, Jiahai; Tang, Zheng; Wang, Ronglong

2004-04-01

In this paper, based on maximum neural network, we propose a new parallel algorithm that can help the maximum neural network escape from local minima by including a transient chaotic neurodynamics for bipartite subgraph problem. The goal of the bipartite subgraph problem, which is an NP- complete problem, is to remove the minimum number of edges in a given graph such that the remaining graph is a bipartite graph. Lee et al. presented a parallel algorithm using the maximum neural model (winner-take-all neuron model) for this NP- complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to a local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm. The simulation results show that our algorithm finds the optimum or near-optimum solution for the bipartite subgraph problem superior to that of the best existing parallel algorithms.