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Sample records for lyapunov weighted path

  1. Assessment of weighted-least-squares-based gas path analysis

    NASA Astrophysics Data System (ADS)

    Doel, D. L.

    1994-04-01

    Manufacturers of gas turbines have searched for three decades for a reliable way to use gas path measurements to determine the health of jet engine components. They have been hindered in this pursuit by the quality of the measurements used to carry out the analysis. Engine manufacturers have chosen weighted-least-squares techniques to reduce the inaccuracy caused by sensor error. While these algorithms are clearly an improvement over the previous generation of gas path analysis programs, they still fail in many situations. This paper describes some of the failures and explores their relationship to the underlying analysis technique. It also describes difficulties in implementing a gas path analysis program. The paper concludes with an appraisal of weighted-least-squares-based gas path analysis.

  2. Transport path optimization algorithm based on fuzzy integrated weights

    NASA Astrophysics Data System (ADS)

    Hou, Yuan-Da; Xu, Xiao-Hao

    2014-11-01

    Natural disasters cause significant damage to roads, making route selection a complicated logistical problem. To overcome this complexity, we present a method of using a trapezoidal fuzzy number to select the optimal transport path. Using the given trapezoidal fuzzy edge coefficients, we calculate a fuzzy integrated matrix, and incorporate the fuzzy multi-weights into fuzzy integrated weights. The optimal path is determined by taking two sets of vertices and transforming undiscovered vertices into discoverable ones. Our experimental results show that the model is highly accurate, and requires only a few measurement data to confirm the optimal path. The model provides an effective, feasible, and convenient method to obtain weights for different road sections, and can be applied to road planning in intelligent transportation systems.

  3. Paths in the minimally weighted path model are incompatible with Schramm-Loewner evolution

    NASA Astrophysics Data System (ADS)

    Norrenbrock, C.; Melchert, O.; Hartmann, A. K.

    2013-03-01

    We study numerically the geometrical properties of minimally weighted paths that appear in the minimally weighted path (MWP) model on two-dimensional lattices assuming a combination of periodic and free boundary conditions (BCs). Each realization of the disorder consists of a random fraction (1-ρ) of bonds with unit strength and a fraction ρ of bond strengths drawn from a Gaussian distribution with zero mean and unit width. For each such sample, a path is forced to span the lattice along the direction with the free BCs. The path and a set of negatively weighted loops form a ground state. A ground state on such a lattice can be determined performing a nontrivial transformation of the original graph and applying sophisticated matching algorithms. Here we examine whether the geometrical properties of the paths are in accordance with the predictions of the Schramm-Loewner evolution (SLE). Measuring the fractal dimension, considering the winding angle statistics, and reviewing Schramm's left passage formula indicate that the paths cannot be described in terms of SLE.

  4. Finding the optimal-path maps for path planning across weighted regions

    SciTech Connect

    Rowe, N.C.; Alexander, R.S.

    2000-02-01

    Optimal-path maps tell robots or people the best way to reach a goal point from anywhere in a known terrain area, eliminating most of the need to plan during travel. The authors address the construction of optimal-path maps for two-dimensional polygonal weighted-region terrain, terrain partitioned into polygonal areas such that the cost per unit of distance traveled is homogeneous and isotropic within each area. This is useful for overland route planning across varied ground surfaces and vegetation. The authors propose a new algorithm that recursively partitions terrain into regions of similar optimal-path behavior, and defines corresponding path subspaces for these regions. This process constructs a piecewise-smooth function of terrain position whose gradient direction is everywhere the optimal-path direction, permitting quick path finding. The algorithm used is more complicated than the current path-caching and wavefront-propagation algorithms, but it gives more accurate maps requiring less space to represent. Experiments with an implementation confirm the practicality of the authors' algorithm.

  5. Scaling of average weighted shortest path and average receiving time on weighted expanded Koch networks

    NASA Astrophysics Data System (ADS)

    Wu, Zikai; Hou, Baoyu; Zhang, Hongjuan; Jin, Feng

    2014-04-01

    Deterministic network models have been attractive media for discussing dynamical processes' dependence on network structural features. On the other hand, the heterogeneity of weights affect dynamical processes taking place on networks. In this paper, we present a family of weighted expanded Koch networks based on Koch networks. They originate from a r-polygon, and each node of current generation produces m r-polygons including the node and whose weighted edges are scaled by factor w in subsequent evolutionary step. We derive closed-form expressions for average weighted shortest path length (AWSP). In large network, AWSP stays bounded with network order growing (0 < w < 1). Then, we focus on a special random walks and trapping issue on the networks. In more detail, we calculate exactly the average receiving time (ART). ART exhibits a sub-linear dependence on network order (0 < w < 1), which implies that nontrivial weighted expanded Koch networks are more efficient than un-weighted expanded Koch networks in receiving information. Besides, efficiency of receiving information at hub nodes is also dependent on parameters m and r. These findings may pave the way for controlling information transportation on general weighted networks.

  6. Most probable paths in temporal weighted networks: An application to ocean transport

    NASA Astrophysics Data System (ADS)

    Ser-Giacomi, Enrico; Vasile, Ruggero; Hernández-García, Emilio; López, Cristóbal

    2015-07-01

    We consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of paths and to a subset of highly probable paths that incorporate most of the connection probability. These concepts are used to provide alternative definitions of betweenness centrality. We apply our formalism to a transport network describing surface flow in the Mediterranean sea. Despite the full transport dynamics is described by a very large number of paths we find that, for realistic time scales, only a very small subset of high probability paths (or even a single most probable one) is enough to characterize global connectivity properties of the network.

  7. Finding the complete path and weight enumerators of convolutional codes

    NASA Technical Reports Server (NTRS)

    Onyszchuk, I.

    1990-01-01

    A method for obtaining the complete path enumerator T(D, L, I) of a convolutional code is described. A system of algebraic equations is solved, using a new algorithm for computing determinants, to obtain T(D, L, I) for the (7,1/2) NASA standard code. Generating functions, derived from T(D, L, I) are used to upper bound Viterbi decoder error rates. This technique is currently feasible for constraint length K less than 10 codes. A practical, fast algorithm is presented for computing the leading nonzero coefficients of the generating functions used to bound the performance of constraint length K less than 20 codes. Code profiles with about 50 nonzero coefficients are obtained with this algorithm for the experimental K = 15, rate 1/4, code in the Galileo mission and for the proposed K = 15, rate 1/6, 2-dB code.

  8. Negative-weight Percolation: Review of Existing Literature and Scaling Behavior of the Path Weight in 2d

    NASA Astrophysics Data System (ADS)

    Melchert, O.; Norrenbrock, C.; Hartmann, A. K.

    We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary condi- tions in all relevant dimensions from d = 2 to the upper critical dimension d = 6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in the statistical properties of the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops that comprise the "loops only" variant of the NWP problem. The NWP phenomenon refers to the disorder driven proliferation of system span- ning loops of total negative weight. For the numerical simulations we employ a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allows for the numerically exact study of large systems with good statistics, important to ensure a reliable disorder average. Early simulations for the 2d setup led to suggest that the resulting negative-weight percolation (NWP) problem is fundamentally different from conventional percolation. Here, we review several studies that reported on results of numerical simulations aimed at clarifying the geometric properties of NWP on hypercubic lattice graphs and random graphs. Finally we present additional new results for the scaling behavior of the geometric properties and the configurational weight of minimum-weight paths (MWPs) in the "loops + MWP" variant of the model, characterizing an additional threshold ?, above which the disorder averaged MWP weight (ωp) is negative, thereby highlighting a characteristic limiting case of the NWP model at small densities of negative edges.

  9. Perfect quantum state transfer of hard-core bosons on weighted path graphs

    NASA Astrophysics Data System (ADS)

    Large, Steven J.; Underwood, Michael S.; Feder, David L.

    2015-03-01

    The ability to accurately transfer quantum information through networks is an important primitive in distributed quantum systems. While perfect quantum state transfer (PST) can be effected by a single particle undergoing continuous-time quantum walks on a variety of graphs, it is not known if PST persists for many particles in the presence of interactions. We show that if single-particle PST occurs on one-dimensional weighted path graphs, then systems of hard-core bosons undergoing quantum walks on these paths also undergo PST. The analysis extends the Tonks-Girardeau ansatz to weighted graphs using techniques in algebraic graph theory. The results suggest that hard-core bosons do not generically undergo PST, even on graphs which exhibit single-particle PST.

  10. Correlation between weighted spectral distribution and average path length in evolving networks

    NASA Astrophysics Data System (ADS)

    Jiao, Bo; Shi, Jianmai; Wu, Xiaoqun; Nie, Yuanping; Huang, Chengdong; Du, Jing; Zhou, Ying; Guo, Ronghua; Tao, Yerong

    2016-02-01

    The weighted spectral distribution (WSD) is a metric defined on the normalized Laplacian spectrum. In this study, synchronic random graphs are first used to rigorously analyze the metric's scaling feature, which indicates that the metric grows sublinearly as the network size increases, and the metric's scaling feature is demonstrated to be common in networks with Gaussian, exponential, and power-law degree distributions. Furthermore, a deterministic model of diachronic graphs is developed to illustrate the correlation between the slope coefficient of the metric's asymptotic line and the average path length, and the similarities and differences between synchronic and diachronic random graphs are investigated to better understand the correlation. Finally, numerical analysis is presented based on simulated and real-world data of evolving networks, which shows that the ratio of the WSD to the network size is a good indicator of the average path length.

  11. Correlation between weighted spectral distribution and average path length in evolving networks.

    PubMed

    Jiao, Bo; Shi, Jianmai; Wu, Xiaoqun; Nie, Yuanping; Huang, Chengdong; Du, Jing; Zhou, Ying; Guo, Ronghua; Tao, Yerong

    2016-02-01

    The weighted spectral distribution (WSD) is a metric defined on the normalized Laplacian spectrum. In this study, synchronic random graphs are first used to rigorously analyze the metric's scaling feature, which indicates that the metric grows sublinearly as the network size increases, and the metric's scaling feature is demonstrated to be common in networks with Gaussian, exponential, and power-law degree distributions. Furthermore, a deterministic model of diachronic graphs is developed to illustrate the correlation between the slope coefficient of the metric's asymptotic line and the average path length, and the similarities and differences between synchronic and diachronic random graphs are investigated to better understand the correlation. Finally, numerical analysis is presented based on simulated and real-world data of evolving networks, which shows that the ratio of the WSD to the network size is a good indicator of the average path length. PMID:26931591

  12. Lyapunov decay in quantum irreversibility.

    PubMed

    García-Mata, Ignacio; Roncaglia, Augusto J; Wisniacki, Diego A

    2016-06-13

    The Loschmidt echo--also known as fidelity--is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is carried out. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as has been shown for quantum maps. In this work, we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime. PMID:27140966

  13. Two Upper Bounds for the Weighted Path Length of Binary Trees. Report No. UIUCDCS-R-73-565.

    ERIC Educational Resources Information Center

    Pradels, Jean Louis

    Rooted binary trees with weighted nodes are structures encountered in many areas, such as coding theory, searching and sorting, information storage and retrieval. The path length is a meaningful quantity which gives indications about the expected time of a search or the length of a code, for example. In this paper, two sharp bounds for the total…

  14. Lyapunov Spectra in Diffusion Replicator Equation

    NASA Astrophysics Data System (ADS)

    Orihashi, Kenji; Aizawa, Yoji

    2008-11-01

    Statistical Properties of the turbulence in the diffusion replicator equation of three species are numerically studied. The maximal Lyapunov exponent and Lyapunov dimension are derived precisely. Further, these characteristics obey some characteristic scaling laws.

  15. Nurses’ self-efficacy and practices relating to weight management of adult patients: a path analysis

    PubMed Central

    2013-01-01

    Background Health professionals play a key role in the prevention and treatment of excess weight and obesity, but many have expressed a lack of confidence in their ability to manage obese patients with their delivery of weight-management care remaining limited. The specific mechanism underlying inadequate practices in professional weight management remains unclear. The primary purpose of this study was to examine a self-efficacy theory-based model in understanding Registered Nurses’ (RNs) professional performance relating to weight management. Methods A self-report questionnaire was developed based upon the hypothesized model and administered to a convenience sample of 588 RNs. Data were collected regarding socio-demographic variables, psychosocial variables (attitudes towards obese people, professional role identity, teamwork beliefs, perceived skills, perceived barriers and self-efficacy) and professional weight management practices. Structural equation modeling was conducted to identify correlations between the above variables and to test the goodness of fit of the proposed model. Results The survey response rate was 71.4% (n = 420). The respondents reported a moderate level of weight management practices. Self-efficacy directly and positively predicted the weight management practices of the RNs (β = 0.36, p < 0.01), and fully or partially mediated the relationships between perceived skills, perceived barriers, professional role identity and teamwork beliefs and weight management practices. The final model constructed in this study demonstrated a good fit to the data [χ2 (14) =13.90, p = 0.46; GFI = 0.99; AGFI = 0.98; NNFI = 1.00; CFI = 1.00; RMSEA = 0.00; AIC = 57.90], accounting for 38.4% and 43.2% of the variance in weight management practices and self-efficacy, respectively. Conclusions Self-efficacy theory appears to be useful in understanding the weight management practices of RNs. Interventions targeting the

  16. Study of Double-Weighted Graph Model and Optimal Path Planning for Tourist Scenic Area Oriented Intelligent Tour Guide

    NASA Astrophysics Data System (ADS)

    Shi, Y.; Long, Y.; Wi, X. L.

    2014-04-01

    When tourists visiting multiple tourist scenic spots, the travel line is usually the most effective road network according to the actual tour process, and maybe the travel line is different from planned travel line. For in the field of navigation, a proposed travel line is normally generated automatically by path planning algorithm, considering the scenic spots' positions and road networks. But when a scenic spot have a certain area and have multiple entrances or exits, the traditional described mechanism of single point coordinates is difficult to reflect these own structural features. In order to solve this problem, this paper focuses on the influence on the process of path planning caused by scenic spots' own structural features such as multiple entrances or exits, and then proposes a doubleweighted Graph Model, for the weight of both vertexes and edges of proposed Model can be selected dynamically. And then discusses the model building method, and the optimal path planning algorithm based on Dijkstra algorithm and Prim algorithm. Experimental results show that the optimal planned travel line derived from the proposed model and algorithm is more reasonable, and the travelling order and distance would be further optimized.

  17. Computing Lyapunov exponents of switching systems

    NASA Astrophysics Data System (ADS)

    Guglielmi, Nicola; Protasov, Vladimir

    2016-06-01

    We discuss a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems. The method we propose allows to decide the uniform stability of a switching system and to compute the Lyapunov exponent with an arbitrary precision. The method relies on the discretization of the system and provides - for any given discretization stepsize - a lower and an upper bound for the Lyapunov exponent. The efficiency of the new method is illustrated by numerical examples. For a more extensive discussion we remand the reader to [8].

  18. Logical composition of Lyapunov functions

    NASA Astrophysics Data System (ADS)

    Balestrino, A.; Caiti, A.; Crisostomi, E.

    2011-03-01

    This article introduces the use of R-functions to compose single Lyapunov functions (LFs) via classic Boolean operators, with the aim to obtain a rich family of non-conventional, generally non-convex functions. The main benefit of the proposed composition is the nice geometric interpretation, since it corresponds to intersection and union operations in the phase space region. The composition of LFs is parameterised through a variable γ and classic compositions of LFs through min and max operations are recovered as a special case for a particular value of γ. The proposed logical composition is applied to region of asymptotic stability (RAS) estimation problems, where the union of several LFs corresponds to the union of the RAS estimates obtained from the separate use of each LF. Likewise, the intersection of several LFs defined on independent subsets of the state space variables provides a single LF for the overall dynamical system. Sufficient conditions for the composition function to be an LF are provided and results are described through several examples of classic nonlinear dynamical systems.

  19. Lyapunov analysis: from dynamical systems theory to applications

    NASA Astrophysics Data System (ADS)

    Cencini, Massimo; Ginelli, Francesco

    2013-06-01

    mathematical development and only provide access to partial pieces of information. Moreover, the scattered state of the present literature, with key contributions published in journals read by different communities (mathematicians, nonlinear and statistical physicists, fluid dynamicists and geophysicists), makes it difficult to develop a general picture. This special issue aims to offer an up-to-date view of current research on Lyapunov analysis, discussing both its mathematical theory and its applications to a number of different problems. Moreover, in order to facilitate the comparison and exchange of ideas and tools among different fields of research, contributions (either original or topical reviews) from researchers working in different disciplines have been selected for this issue. After the compact review of the basic mathematical results on Lyapunov exponents by Lai-Sang Young, the special issue is organized into nine sections broadly focused on the following topics: Large deviations and rare trajectories. Lyapunov exponents are mean quantities which characterize the sensitivity to initial conditions of typical trajectories. A large deviation theory of their finite time fluctuations, however, is relevant for the construction of a thermodynamic formalism of deterministic chaos. Moreover, the weighted sampling of extreme fluctuations allows one to access rare trajectories and phase-space topological structures. Random matrices. Lyapunov exponents are suitable quantities to statistically characterize products of random matrices, with a number of applications to transfer matrix methods and, more generally, to the statistical mechanics of disordered systems. In particular, Lyapunov exponents have long played a central role in the theory of Anderson localization. These aspects are reviewed here, together with an original application to the transfer matrix. Covariant Lyapunov vectors: theory and applications. CLVs constitute an intrinsic tangent space decomposition into

  20. A Survey of Quantum Lyapunov Control Methods

    PubMed Central

    2013-01-01

    The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed. PMID:23766732

  1. A comparison of correlation and Lyapunov dimensions

    NASA Astrophysics Data System (ADS)

    Chlouverakis, Konstantinos E.; Sprott, J. C.

    2005-01-01

    This paper investigates the relation between the correlation ( D2) and the Kaplan-Yorke dimension ( DKY) of three-dimensional chaotic flows. Besides the Kaplan-Yorke dimension, a new Lyapunov dimension ( DΣ), derived using a polynomial interpolation instead of a linear one, is compared with DKY and D2. Various systems from the literature are used in this analysis together with some special cases that span a range of dimension 2 < DKY ≤ 3. A linear regression to the data produces a new fitted Lyapunov dimension of the form Dfit = α - βλ1/ λ3, where λ1 and λ3 are the largest and smallest Lyapunov exponents, respectively. This form correlates better with the correlation dimension D2 than do either DKY or DΣ. Additional forms of the fitted dimension are investigated to improve the fit to D2, and the results are discussed and interpreted with respect to the Kaplan-Yorke conjecture.

  2. Hall magnetohydrodynamics: Conservation laws and Lyapunov stability

    NASA Astrophysics Data System (ADS)

    Holm, Darryl D.

    1987-05-01

    Hall electric fields produce circulating mass flow in confined ideal-fluid plasmas. The conservation laws, Hamiltonian structure, equilibrium state relations, and Lyapunov stability conditions are presented here for ideal Hall magnetohydrodynamics (HMHD) in two and three dimensions. The approach here is to use the remarkable array of nonlinear conservation laws for HMHD that follow from its Hamiltonian structure in order to construct explicit Lyapunov functionals for the HMHD equilibrium states. In this way, the Lyapunov stability analysis provides classes of HMHD equilibria that are stable and whose linearized initial-value problems are well posed (in the sense of possessing continuous dependence on initial conditions). Several examples are discussed in both two and three dimensions.

  3. ON LYAPUNOV FAMILIES AROUND COLLINEAR LIBRATION POINTS

    SciTech Connect

    Hou, X. Y.; Liu, L.

    2009-06-15

    Evolution details of the planar and vertical Lyapunov families around the three collinear libration points in the restricted three-body problem were studied. Researches before were generally restricted to be within the colliding orbits with the primaries and for fixed mass parameters {mu}. In this paper, members after colliding orbits were computed. With increasing {mu}, how these families evolve was studied.

  4. The Lyapunov dimension and its estimation via the Leonov method

    NASA Astrophysics Data System (ADS)

    Kuznetsov, N. V.

    2016-06-01

    Along with widely used numerical methods for estimating and computing the Lyapunov dimension there is an effective analytical approach, proposed by G.A. Leonov in 1991. The Leonov method is based on the direct Lyapunov method with special Lyapunov-like functions. The advantage of the method is that it allows one to estimate the Lyapunov dimension of invariant sets without localization of the set in the phase space and, in many cases, to get effectively an exact Lyapunov dimension formula. In this work the invariance of the Lyapunov dimension with respect to diffeomorphisms and its connection with the Leonov method are discussed. For discrete-time dynamical systems an analog of Leonov method is suggested. In a simple but rigorous way, here it is presented the connection between the Leonov method and the key related works: Kaplan and Yorke (the concept of the Lyapunov dimension, 1979), Douady and Oesterlé (upper bounds of the Hausdorff dimension via the Lyapunov dimension of maps, 1980), Constantin, Eden, Foiaş, and Temam (upper bounds of the Hausdorff dimension via the Lyapunov exponents and Lyapunov dimension of dynamical systems, 1985-90), and the numerical calculation of the Lyapunov exponents and dimension.

  5. Low Density Expansion for Lyapunov Exponents

    NASA Astrophysics Data System (ADS)

    Schulz-Baldes, Hermann

    A perturbative formula for the Lyapunov exponent of a one-dimensional random medium for weakly coupled disorder was first given by Thouless [12] and then proven rigorously by Pastur and Figotin [9]. Anomalies in the perturbation theory at the band center were discovered by Kappus and Wegner [7] and further discussed by various other authors [2,3,11]. The Lyapunov exponent is then identified with the inverse localization length of the system. This short note concerns the behavior of the Lyapunov exponent for a low density of impurities, each of which may, however, be large. The presented method is as [6,10,11] a further application of diagonalizing the transfer matrices without perturbation (here the low density of impurities) and then rigorously controlling the error terms by means of oscillatory sums of rotating modi- fied Prüfer phases. Some of the oscillatory sums remain large if the rotation phases (here the quasi-momenta) are rational. This leads to supplementary contributions of the Kappus-Wegner type.

  6. Lyapunov exponents for infinite dimensional dynamical systems

    NASA Technical Reports Server (NTRS)

    Mhuiris, Nessan Mac Giolla

    1987-01-01

    Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

  7. Diverging Fluctuations of the Lyapunov Exponents

    NASA Astrophysics Data System (ADS)

    Pazó, Diego; López, Juan M.; Politi, Antonio

    2016-07-01

    We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of suitably correlated background noise.

  8. Probability-theoretical analog of the vector Lyapunov function method

    SciTech Connect

    Nakonechnyi, A.N.

    1995-01-01

    The main ideas of the vector Lyapunov function (VLF) method were advanced in 1962 by Bellman and Matrosov. In this method, a Lyapunov function and a comparison equation are constructed for each subsystem. Then the dependences between the subsystems and the effect of external noise are allowed for by constructing a vector Lyapunov function (as a collection of the scalar Lyapunov functions of the subsystems) and an aggregate comparison function for the entire complex system. A probability-theoretical analog of this method for convergence analysis of stochastic approximation processes has been developed. The abstract approach proposed elsewhere eliminates all restrictions on the system phase space, the system trajectories, the class of Lyapunov functions, etc. The analysis focuses only on the conditions that relate sequences of Lyapunov function values with the derivative and ensure a particular type (mode, character) of stability. In our article, we extend this approach to the VLF method for discrete stochastic dynamic systems.

  9. Transient Stability Enhancement of Power Systems by Lyapunov-Based Recurrent Neural Networks UPFC Controllers

    NASA Astrophysics Data System (ADS)

    Chu, Chia-Chi; Tsai, Hung-Chi; Chang, Wei-Neng

    A Lyapunov-based recurrent neural networks unified power flow controller (UPFC) is developed for improving transient stability of power systems. First, a simple UPFC dynamical model, composed of a controllable shunt susceptance on the shunt side and an ideal complex transformer on the series side, is utilized to analyze UPFC dynamical characteristics. Secondly, we study the control configuration of the UPFC with two major blocks: the primary control, and the supplementary control. The primary control is implemented by standard PI techniques when the power system is operated in a normal condition. The supplementary control will be effective only when the power system is subjected by large disturbances. We propose a new Lyapunov-based UPFC controller of the classical single-machine-infinite-bus system for damping enhancement. In order to consider more complicated detailed generator models, we also propose a Lyapunov-based adaptive recurrent neural network controller to deal with such model uncertainties. This controller can be treated as neural network approximations of Lyapunov control actions. In addition, this controller also provides online learning ability to adjust the corresponding weights with the back propagation algorithm built in the hidden layer. The proposed control scheme has been tested on two simple power systems. Simulation results demonstrate that the proposed control strategy is very effective for suppressing power swing even under severe system conditions.

  10. Preparation of topological modes by Lyapunov control

    PubMed Central

    Shi, Z. C.; Zhao, X. L.; Yi, X. X.

    2015-01-01

    By Lyapunov control, we present a proposal to drive quasi-particles into a topological mode in quantum systems described by a quadratic Hamiltonian. The merit of this control is the individual manipulations on the boundary sites. We take the Kitaev’s chain as an illustration for Fermi systems and show that an arbitrary excitation mode can be steered into the Majorana zero mode by manipulating the chemical potential of the boundary sites. For Bose systems, taking the noninteracting Su-Schrieffer-Heeger (SSH) model as an example, we illustrate how to drive the system into the edge mode. The sensitivity of the fidelity to perturbations and uncertainties in the control fields and initial modes is also examined. The experimental feasibility of the proposal and the possibility to replace the continuous control field with square wave pulses is finally discussed. PMID:26346317

  11. Preparation of topological modes by Lyapunov control

    NASA Astrophysics Data System (ADS)

    Shi, Z. C.; Zhao, X. L.; Yi, X. X.

    2015-09-01

    By Lyapunov control, we present a proposal to drive quasi-particles into a topological mode in quantum systems described by a quadratic Hamiltonian. The merit of this control is the individual manipulations on the boundary sites. We take the Kitaev’s chain as an illustration for Fermi systems and show that an arbitrary excitation mode can be steered into the Majorana zero mode by manipulating the chemical potential of the boundary sites. For Bose systems, taking the noninteracting Su-Schrieffer-Heeger (SSH) model as an example, we illustrate how to drive the system into the edge mode. The sensitivity of the fidelity to perturbations and uncertainties in the control fields and initial modes is also examined. The experimental feasibility of the proposal and the possibility to replace the continuous control field with square wave pulses is finally discussed.

  12. Preparation of topological modes by Lyapunov control.

    PubMed

    Shi, Z C; Zhao, X L; Yi, X X

    2015-01-01

    By Lyapunov control, we present a proposal to drive quasi-particles into a topological mode in quantum systems described by a quadratic Hamiltonian. The merit of this control is the individual manipulations on the boundary sites. We take the Kitaev's chain as an illustration for Fermi systems and show that an arbitrary excitation mode can be steered into the Majorana zero mode by manipulating the chemical potential of the boundary sites. For Bose systems, taking the noninteracting Su-Schrieffer-Heeger (SSH) model as an example, we illustrate how to drive the system into the edge mode. The sensitivity of the fidelity to perturbations and uncertainties in the control fields and initial modes is also examined. The experimental feasibility of the proposal and the possibility to replace the continuous control field with square wave pulses is finally discussed. PMID:26346317

  13. Covariant Lyapunov analysis of chaotic Kolmogorov flows.

    PubMed

    Inubushi, Masanobu; Kobayashi, Miki U; Takehiro, Shin-ichi; Yamada, Michio

    2012-01-01

    Hyperbolicity is an important concept in dynamical system theory; however, we know little about the hyperbolicity of concrete physical systems including fluid motions governed by the Navier-Stokes equations. Here, we study numerically the hyperbolicity of the Navier-Stokes equation on a two-dimensional torus (Kolmogorov flows) using the method of covariant Lyapunov vectors developed by Ginelli et al. [Phys. Rev. Lett. 99, 130601 (2007)]. We calculate the angle between the local stable and unstable manifolds along an orbit of chaotic solution to evaluate the hyperbolicity. We find that the attractor of chaotic Kolmogorov flows is hyperbolic at small Reynolds numbers, but that smaller angles between the local stable and unstable manifolds are observed at larger Reynolds numbers, and the attractor appears to be nonhyperbolic at a certain Reynolds numbers. Also, we observed some relations between these hyperbolic properties and physical properties such as time correlation of the vorticity and the energy dissipation rate. PMID:22400681

  14. Numerical solution of large Lyapunov equations

    NASA Technical Reports Server (NTRS)

    Saad, Youcef

    1989-01-01

    A few methods are proposed for solving large Lyapunov equations that arise in control problems. The common case where the right hand side is a small rank matrix is considered. For the single input case, i.e., when the equation considered is of the form AX + XA(sup T) + bb(sup T) = 0, where b is a column vector, the existence of approximate solutions of the form X = VGV(sup T) where V is N x m and G is m x m, with m small is established. The first class of methods proposed is based on the use of numerical quadrature formulas, such as Gauss-Laguerre formulas, applied to the controllability Grammian. The second is based on a projection process of Galerkin type. Numerical experiments are presented to test the effectiveness of these methods for large problems.

  15. Calculating Lyapunov Exponents: Applying Products and Evaluating Integrals

    ERIC Educational Resources Information Center

    McCartney, Mark

    2010-01-01

    Two common examples of one-dimensional maps (the tent map and the logistic map) are generalized to cases where they have more than one control parameter. In the case of the tent map, this still allows the global Lyapunov exponent to be found analytically, and permits various properties of the resulting global Lyapunov exponents to be investigated…

  16. Carbohydrate Reward and Psychosis: An Explanation For Neuroleptic Induced Weight Gain and Path to Improved Mental Health?

    PubMed Central

    Thornley, Simon; Russell, Bruce; Kydd, Rob

    2011-01-01

    Evidence links dopamine release in the mid-brain to the pathophysiology of psychosis, addiction and reward. Repeated ingestion of refined carbohydrate may stimulate the same mesolimbic dopaminergic pathway, rewarding such eating behaviour and resulting in excessive food intake along with obesity. In this paper, we explore the role of dopamine in reward and psychosis, and discuss how reward pathways may contribute to the weight gain that commonly follows antipsychotic drug use, in people with psychotic illness. Our theory also explains the frequent co-occurrence of substance abuse and psychosis. From our hypothesis, we discuss the use of carbohydrate modified diets as an adjunctive treatment for people with psychosis. PMID:22131945

  17. Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection

    NASA Astrophysics Data System (ADS)

    Xu, M.; Paul, M. R.

    2016-06-01

    We explore numerically the high-dimensional spatiotemporal chaos of Rayleigh-Bénard convection using covariant Lyapunov vectors. We integrate the three-dimensional and time-dependent Boussinesq equations for a convection layer in a shallow square box geometry with an aspect ratio of 16 for very long times and for a range of Rayleigh numbers. We simultaneously integrate many copies of the tangent space equations in order to compute the covariant Lyapunov vectors. The dynamics explored has fractal dimensions of 20 ≲Dλ≲50 , and we compute on the order of 150 covariant Lyapunov vectors. We use the covariant Lyapunov vectors to quantify the degree of hyperbolicity of the dynamics and the degree of Oseledets splitting and to explore the temporal and spatial dynamics of the Lyapunov vectors. Our results indicate that the chaotic dynamics of Rayleigh-Bénard convection is nonhyperbolic for all of the Rayleigh numbers we have explored. Our results yield that the entire spectrum of covariant Lyapunov vectors that we have computed are tangled as indicated by near tangencies with neighboring vectors. A closer look at the spatiotemporal features of the Lyapunov vectors suggests contributions from structures at two different length scales with differing amounts of localization.

  18. Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection.

    PubMed

    Xu, M; Paul, M R

    2016-06-01

    We explore numerically the high-dimensional spatiotemporal chaos of Rayleigh-Bénard convection using covariant Lyapunov vectors. We integrate the three-dimensional and time-dependent Boussinesq equations for a convection layer in a shallow square box geometry with an aspect ratio of 16 for very long times and for a range of Rayleigh numbers. We simultaneously integrate many copies of the tangent space equations in order to compute the covariant Lyapunov vectors. The dynamics explored has fractal dimensions of 20≲D_{λ}≲50, and we compute on the order of 150 covariant Lyapunov vectors. We use the covariant Lyapunov vectors to quantify the degree of hyperbolicity of the dynamics and the degree of Oseledets splitting and to explore the temporal and spatial dynamics of the Lyapunov vectors. Our results indicate that the chaotic dynamics of Rayleigh-Bénard convection is nonhyperbolic for all of the Rayleigh numbers we have explored. Our results yield that the entire spectrum of covariant Lyapunov vectors that we have computed are tangled as indicated by near tangencies with neighboring vectors. A closer look at the spatiotemporal features of the Lyapunov vectors suggests contributions from structures at two different length scales with differing amounts of localization. PMID:27415256

  19. Lyapunov exponent in two-leg ladder model

    NASA Astrophysics Data System (ADS)

    Datta, P. K.

    2010-09-01

    Lyapunov exponent is one of the properties to study localization-delocalization transition in disordered systems. Perfect as well as disordered two-leg ladder is studied in tight-binding description. In perfectly two-leg ladder two bands are obtained due to symmetric and antisymmetric wave functions. But, the analytical expression of Lyapunov exponent indicates the presence of extended states at the overlapping region of two bands. Beyond this region of energy states are localized. Two models of disordered ladder network are studied here numerically. These studies show that the Lyapunov exponent indicates the presence of extended states provided both the even and odd modes are extended in transmission analysis. If the transmission coefficient shows the localization behavior for one of the modes the Lyapunov exponent also indicates the localization of those states. The behavior of first Lyapunov exponent is consistent with that of the Lyapunov exponent. on the other hand, the study of second Lyapunov exponent is consistent with the transmission analysis.

  20. Nonlinear dynamics of the blood flow studied by Lyapunov exponents.

    PubMed

    Bracic, M; Stefanovska, A

    1998-05-01

    In order to gain an insight into the dynamics of the cardiovascular system throughout which the blood circulates, the signals measured from peripheral blood flow in humans were analyzed by calculating the Lyapunov exponents. Over a wide range of algorithm parameters, paired values of both the global and the local Lyapunov exponents were obtained, and at least one exponent equaled zero within the calculation error. This may be an indication of the deterministic nature and finite number of degrees of freedom of the cardiovascular system governing the blood-flow dynamics on a time scale of minutes. A difference was observed in the Lyapunov dimension of controls and athletes. PMID:9608852

  1. Lyapunov Exponents for Surface Group Representations

    NASA Astrophysics Data System (ADS)

    Deroin, Bertrand; Dujardin, Romain

    2015-12-01

    Let be a holomorphic family of representations of a surface group into , where S is a topological (possibly punctured) surface with negative Euler characteristic. Given a structure of Riemann surface of finite type on S we construct a bifurcation current on the parameter space Λ, that is a (1,1) positive closed current attached to the bifurcations of the family. It is defined as the dd c of the Lyapunov exponent of the representation with respect to the Brownian motion on the Riemann surface S, endowed with its Poincaré metric. We show that this bifurcation current describes the asymptotic distribution of various codimension 1 phenomena in Λ. For instance, the random hypersurfaces of Λ defined by the condition that a random closed geodesic on S is mapped under ρ λ to a parabolic element or the identity are asymptotically equidistributed with respect to the bifurcation current. The proofs are based on our previous work (Deroin and Dujardin, Invent Math 190:57-118, 2012), and on a careful control of a discretization procedure of the Brownian motion.

  2. Lyapunov exponents, noise-induced synchronization, and Parrondo's paradox.

    PubMed

    Kocarev, Ljupco; Tasev, Zarko

    2002-04-01

    We show that Lyapunov exponents of a stochastic system, when computed for a specific realization of the noise process, are related to conditional Lyapunov exponents in deterministic systems. We propose to use the term stochastically induced regularity instead of noise-induced synchronization and explain the reason why. The nature of stochastically induced regularity is discussed: in some instances, it is a dynamical analog of Parrondo's paradox. PMID:12005984

  3. Local Lyapunov Exponent for the Bak Sneppen Model

    NASA Astrophysics Data System (ADS)

    Ma, Ke; Yang, Chun-Bin; Cai, Xu

    2003-12-01

    The chaotic property of the Bak-Sneppen model is studied from the local Lyapunov exponent in the same way as for dynamical nonlinear systems. Similar behaviour is found for the one- and two-dimensional Bak-Sneppen models. The Lyapunov exponents for the two cases have the same order of magnitude and both decrease at early evolution but show a slow increasing saturation at late evolution.

  4. A Spectral Lyapunov Function for Exponentially Stable LTV Systems

    NASA Technical Reports Server (NTRS)

    Zhu, J. Jim; Liu, Yong; Hang, Rui

    2010-01-01

    This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

  5. On Lyapunov boundary control of unstable magnetohydrodynamic plasmas

    SciTech Connect

    Tasso, H.; Throumoulopoulos, G. N.

    2013-02-15

    Starting from a simple, marginally stable model considered for Lyapunov based boundary control of flexible mechanical systems, we add a term driving an instability and prove that for an appropriate control condition the system can become Lyapunov stable. A similar approximate extension is found for the general energy principle of linearized magnetohydrodynamics. The implementation of such external instantaneous actions may, however, impose challenging constraints for fusion plasmas.

  6. An efficient method for recovering Lyapunov vectors from singular vectors

    NASA Astrophysics Data System (ADS)

    Wolfe, Christopher L.; Samelson, Roger M.

    2007-05-01

    Lyapunov vectors are natural generalizations of normal modes for linear disturbances to aperiodic deterministic flows and offer insights into the physical mechanisms of aperiodic flow and the maintenance of chaos. Most standard techniques for computing Lyapunov vectors produce results which are norm-dependent and lack invariance under the linearized flow (except for the leading Lyapunov vector) and these features can make computation and physical interpretation problematic. An efficient, norm-independent method for constructing the n most rapidly growing Lyapunov vectors from n - 1 leading forward and n leading backward asymptotic singular vectors is proposed. The Lyapunov vectors so constructed are invariant under the linearized flow in the sense that, once computed at one time, they are defined, in principle, for all time through the tangent linear propagator. An analogous method allows the construction of the n most rapidly decaying Lyapunov vectors from n decaying forward and n - 1 decaying backward singular vectors. This method is demonstrated using two low-order geophysical models.

  7. Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

    NASA Astrophysics Data System (ADS)

    Kuznetsov, N. V.; Mokaev, T. N.; Vasilyev, P. A.

    2014-04-01

    Exact Lyapunov dimension of attractors of many classical chaotic systems (such as Lorenz, Henon, and Chirikov systems) is obtained. While exact Lyapunov dimension for Rössler system is not known, Leonov formulated the following conjecture: Lyapunov dimension of Rössler attractor is equal to local Lyapunov dimension in one of its stationary points. In the present work Leonov's conjecture on Lyapunov dimension of various Rössler systems with standard parameters is checked numerically.

  8. Lyapunov Exponent Criterion in the CR3BP

    NASA Astrophysics Data System (ADS)

    Quarles, Billy; Eberle, Jason; Cuntz, Manfred; Musielak, Zdzislaw

    2010-10-01

    Our specific focus is to describe the motion of an extra solar planet in a binary star system. We aim to accomplish this by using the methods of chaos theory as an alternate method to our previously established Hodograph method in the circular restricted 3-body problem (CR3BP). Previously Eberle et al. (2010) has shown that a parameter space exists depending only on the mass ratio μ and distance ratio ρo which allowed them to identify regions of stability. Our method will validate the previous results while also providing more information relating to the presence of resonances and their effects on orbital stability. We extend the previous studies by increasing the simulation time, applying the method of Lyapunov exponents, calculating the time series spectrum of the orbit, and determining the Lyapunov dimension. The obtained results demonstrate when a system becomes unstable by orbital energy criterion and the method of Lyapunov exponents provides a quantitative classification scale to characterize the instability. By applying the maximum Lyapunov exponent (MLE) to the parameter space, we determine a region of stability with MLE values larger than the surrounding region. The time series spectra and the Lyapunov Dimension methods are used to illustrate the reasons behind the stability plateau which eludes to the resonance phenomena.

  9. Anisotropies in magnetic field evolution and local Lyapunov exponents

    SciTech Connect

    Tang, X.Z.; Boozer, A.H.

    2000-01-13

    The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian flow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates.

  10. Lyapunov exponents of stochastic systems—from micro to macro

    NASA Astrophysics Data System (ADS)

    Laffargue, Tanguy; Tailleur, Julien; van Wijland, Frédéric

    2016-03-01

    Lyapunov exponents of dynamical systems are defined from the rates of divergence of nearby trajectories. For stochastic systems, one typically assumes that these trajectories are generated under the ‘same noise realization’. The purpose of this work is to critically examine what this expression means. For Brownian particles, we consider two natural interpretations of the noise: intrinsic to the particles or stemming from the fluctuations of the environment. We show how they lead to different distributions of the largest Lyapunov exponent as well as different fluctuating hydrodynamics for the collective density field. We discuss, both at microscopic and macroscopic levels, the limits in which these noise prescriptions become equivalent. We close this paper by providing an estimate of the largest Lyapunov exponent and of its fluctuations for interacting particles evolving with Dean-Kawasaki dynamics.

  11. Scaling law for the Lyapunov spectra in globally coupled tent maps

    NASA Astrophysics Data System (ADS)

    Morita, Satoru

    1998-10-01

    The collective motions in globally coupled tent maps are investigated in terms of Lyapunov spectra. The scattered states are separated into two distinct phases by the characteristics of the Lyapunov spectra. In the weak-coupling phase, the Lyapunov spectra obey a scaling law with varying system size. This scaling law holds even in the strong-coupling phase except for the singular property of the largest Lyapunov exponent. The Lyapunov exponents are estimated theoretically by using the random field approximation. These approximate results reveal the relation between the Lyapunov exponents and the distribution of the elements. Furthermore, the features of the band structure in the distribution are explored.

  12. Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence

    NASA Astrophysics Data System (ADS)

    Johnson, Perry L.; Meneveau, Charles

    2015-08-01

    One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ1 : λ2 : λ3 is shown to be about 4:1:-5, compared to about 8:3:-11 when using only the strain-rate tensor for calculating fluid volume deformations. The results

  13. Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence

    SciTech Connect

    Johnson, Perry L. Meneveau, Charles

    2015-08-15

    One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixing properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume

  14. Lyapunov exponent for aging process in induction motor

    NASA Astrophysics Data System (ADS)

    Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat

    2012-09-01

    Nonlinear systems like electrical circuits and systems, mechanics, optics and even incidents in nature may pass through various bifurcations and steady states like equilibrium point, periodic, quasi-periodic, chaotic states. Although chaotic phenomena are widely observed in physical systems, it can not be predicted because of the nature of the system. On the other hand, it is known that, chaos is strictly dependent on initial conditions of the system [1-3]. There are several methods in order to define the chaos. Phase portraits, Poincaré maps, Lyapunov Exponents are the most common techniques. Lyapunov Exponents are the theoretical indicator of the chaos, named after the Russian mathematician Aleksandr Lyapunov (1857-1918). Lyapunov Exponents stand for the average exponential divergence or convergence of nearby system states, meaning estimating the quantitive measure of the chaotic attractor. Negative numbers of the exponents stand for a stable system whereas zero stands for quasi-periodic systems. On the other hand, at least if one of the exponents is positive, this situation is an indicator of the chaos. For estimating the exponents, the system should be modeled by differential equation but even in that case mathematical calculation of Lyapunov Exponents are not very practical and evaluation of these values requires a long signal duration [4-7]. For experimental data sets, it is not always possible to acquire the differential equations. There are several different methods in literature for determining the Lyapunov Exponents of the system [4, 5]. Induction motors are the most important tools for many industrial processes because they are cheap, robust, efficient and reliable. In order to have healthy processes in industrial applications, the conditions of the machines should be monitored and the different working conditions should be addressed correctly. To the best of our knowledge, researches related to Lyapunov exponents and electrical motors are mostly

  15. Largest Lyapunov exponents for lattices of interacting classical spins.

    PubMed

    de Wijn, A S; Hess, B; Fine, B V

    2012-07-20

    We investigate how generic the onset of chaos in interacting many-body classical systems is in the context of lattices of classical spins with nearest-neighbor anisotropic couplings. Seven large lattices in different spatial dimensions were considered. For each lattice, more than 2000 largest Lyapunov exponents for randomly sampled Hamiltonians were numerically computed. Our results strongly suggest the absence of integrable nearest-neighbor Hamiltonians for the infinite lattices except for the trivial Ising case. In the vicinity of the Ising case, the largest Lyapunov exponents exhibit a power-law growth, while further away they become rather weakly sensitive to the Hamiltonian anisotropy. We also provide an analytical derivation of these results. PMID:22861854

  16. Quantum synchronization in an optomechanical system based on Lyapunov control

    NASA Astrophysics Data System (ADS)

    Li, Wenlin; Li, Chong; Song, Heshan

    2016-06-01

    We extend the concepts of quantum complete synchronization and phase synchronization, which were proposed in A. Mari et al., Phys. Rev. Lett. 111, 103605 (2013), 10.1103/PhysRevLett.111.103605, to more widespread quantum generalized synchronization. Generalized synchronization can be considered a necessary condition or a more flexible derivative of complete synchronization, and its criterion and synchronization measure are proposed and analyzed in this paper. As examples, we consider two typical generalized synchronizations in a designed optomechanical system. Unlike the effort to construct a special coupling synchronization system, we purposefully design extra control fields based on Lyapunov control theory. We find that the Lyapunov function can adapt to more flexible control objectives, which is more suitable for generalized synchronization control, and the control fields can be achieved simply with a time-variant voltage. Finally, the existence of quantum entanglement in different generalized synchronizations is also discussed.

  17. Removing zero Lyapunov exponents in volume-preserving flows

    NASA Astrophysics Data System (ADS)

    Bessa, Mário; Rocha, Jorge

    2007-04-01

    Baraviera and Bonatti (2003 Ergod. Theory Dyn. Syst. 23 1655-70) proved that it is possible to perturb, in the C1-topology, a stably ergodic, volume-preserving and partially hyperbolic diffeomorphism in order to obtain a non-zero sum of all the Lyapunov exponents in the central direction. In this paper we obtain the analogous result for volume-preserving flows.

  18. Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

    PubMed Central

    Forgoston, Eric; Bianco, Simone; Shaw, Leah B.; Schwartz, Ira B.

    2010-01-01

    Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path. PMID:20352495

  19. Lyapunov exponents for the Miles’ spherical pendulum equations

    NASA Astrophysics Data System (ADS)

    Tritton, D. J.; Groves, M.

    1999-02-01

    Lyapunov exponents and hence the Lyapunov dimension have been evaluated for the equations developed by Miles [Quart. Appl. Math. 20 (1962) 21; Physica D 11 (1984) 309] as an approximation to the equations of motion of a spherical pendulum forced at a frequency close to its natural frequency. Computations have been performed throughout the frequency range in which there are no stable fixed points and a little on either side of this range, for various values of the damping parameter. The results include: strong dependence on the damping of both the probability of finding chaotic motion and the typical Lyapunov dimension of such motion; the co-existence of alternative types of attractor in regions both inside and outside the range with no stable fixed points; and the occurrence of metastable chaos. The transitions to chaos at either end of a limit cycle window, chosen as one that has also been observed in the laboratory, have been explored in some detail. The results are compared with other computations and with observations with laboratory pendulums, and the implications of the results for future laboratory studies are discussed. Some results are presented for the mathematically related problem of liquid surface waves in a vibrating cylinder.

  20. Path Finder

    Energy Science and Technology Software Center (ESTSC)

    2014-01-07

    PathFinder is a graph search program, traversing a directed cyclic graph to find pathways between labeled nodes. Searches for paths through ordered sequences of labels are termed signatures. Determining the presence of signatures within one or more graphs is the primary function of Path Finder. Path Finder can work in either batch mode or interactively with an analyst. Results are limited to Path Finder whether or not a given signature is present in the graph(s).

  1. Lyapunov analysis: from dynamical systems theory to applications

    NASA Astrophysics Data System (ADS)

    Cencini, Massimo; Ginelli, Francesco

    2013-06-01

    The study of deterministic laws of evolution has characterized the development of science since Newton's times. Chaos, namely the manifestation of irregular and unpredictable dynamics (not random but look random [1]), entered the debate on determinism at the end of the 19th century with the discovery of sensitivity to initial conditions, meaning that small infinitesimal differences in the initial state might lead to dramatic differences at later times. Poincaré [2, 3] was the first to realize that solutions of the three-body problem are generically highly sensitive to initial conditions. At about the same time, this property was recognized in geodesic flows with negative curvature by Hadamard [4]. One of the first experimental observations of chaos, as understood much later, was when irregular noise was heard by Van der Pol in 1927 [5] while studying a periodically forced nonlinear oscillator. Nevertheless, it was only with the advent of digital computing that chaos started to attract the interest of the wider scientific community. After the pioneering investigation of ergodicity in a chain of nonlinear oscillators by Fermi, Pasta and Ulam in 1955 [6], it was in the early 1960s that the numerical studies of Lorenz [7] and Hénon and Heiles [8] revealed that irregular and unpredictable motions are a generic feature of low-dimensional nonlinear deterministic systems. The existence and onset of chaos was then rigorously analyzed in several systems. While an exhaustive list of such mathematical proofs is beyond the scope of this preface, one should mention the contributions of Kolmogorov [9, 10], Chirikov [11], Smale [12], Ruelle and Takens [13], Li and Yorke [14] and Feigenbaum [15]. The characteristic Lyapunov exponents introduced by Oseledets in 1968 [16] are the fundamental quantities for measuring the sensitivity to initial conditions. Oseledets' work generalized the concept of Lyapunov stability to irregular trajectories building upon earlier studies of Birkhoff

  2. Intelligent, Robust Control of Deteriorated Turbofan Engines via Linear Parameter Varying Quadratic Lyapunov Function Design

    NASA Technical Reports Server (NTRS)

    Turso, James A.; Litt, Jonathan S.

    2004-01-01

    A method for accommodating engine deterioration via a scheduled Linear Parameter Varying Quadratic Lyapunov Function (LPVQLF)-Based controller is presented. The LPVQLF design methodology provides a means for developing unconditionally stable, robust control of Linear Parameter Varying (LPV) systems. The controller is scheduled on the Engine Deterioration Index, a function of estimated parameters that relate to engine health, and is computed using a multilayer feedforward neural network. Acceptable thrust response and tight control of exhaust gas temperature (EGT) is accomplished by adjusting the performance weights on these parameters for different levels of engine degradation. Nonlinear simulations demonstrate that the controller achieves specified performance objectives while being robust to engine deterioration as well as engine-to-engine variations.

  3. A Lyapunov-Based Extension to Particle Swarm Dynamics for Continuous Function Optimization

    PubMed Central

    Bhattacharya, Sayantani; Konar, Amit; Das, Swagatam; Han, Sang Yong

    2009-01-01

    The paper proposes three alternative extensions to the classical global-best particle swarm optimization dynamics, and compares their relative performance with the standard particle swarm algorithm. The first extension, which readily follows from the well-known Lyapunov's stability theorem, provides a mathematical basis of the particle dynamics with a guaranteed convergence at an optimum. The inclusion of local and global attractors to this dynamics leads to faster convergence speed and better accuracy than the classical one. The second extension augments the velocity adaptation equation by a negative randomly weighted positional term of individual particle, while the third extension considers the negative positional term in place of the inertial term. Computer simulations further reveal that the last two extensions outperform both the classical and the first extension in terms of convergence speed and accuracy. PMID:22303158

  4. Shortest Paths.

    ERIC Educational Resources Information Center

    Shore, M. L.

    1980-01-01

    There are many uses for the shortest path algorithm presented which are limited only by our ability to recognize when a problem may be converted into the shortest path in a graph representation. (Author/TG)

  5. Lyapunov Schmidt reduction algorithm for three-dimensional discrete vortices

    NASA Astrophysics Data System (ADS)

    Lukas, Mike; Pelinovsky, Dmitry; Kevrekidis, P. G.

    2008-03-01

    We address the persistence and stability of three-dimensional vortex configurations in the discrete nonlinear Schrödinger equation and develop a symbolic package based on Wolfram’s MATHEMATICA for computations of the Lyapunov-Schmidt reduction method. The Lyapunov-Schmidt reduction method is a theoretical tool which enables us to study continuations and terminations of the discrete vortices for small coupling between lattice nodes as well as the spectral stability of the persistent configurations. The method was developed earlier in the context of the two-dimensional lattice and applied to the onsite and offsite configurations (called the vortex cross and the vortex cell) by using semianalytical computations [D.E. Pelinovsky, P.G. Kevrekidis, D. Frantzeskakis, Physica D 212 (2005) 20-53; P.G. Kevrekidis, D.E. Pelinovsky, Proc. R. Soc. A 462 (2006) 2671-2694]. The present treatment develops a full symbolic computational package which takes a desired waveform at the anticontinuum limit of uncoupled sites, performs a required number of Lyapunov-Schmidt reductions and outputs the predictions on whether the configuration persists, for finite coupling, in the three-dimensional lattice and whether it is stable or unstable. It also provides approximations for the eigenvalues of the linearized stability problem. We report a number of applications of the algorithm to important multisite three-dimensional configurations, such as the simple cube, the double cross and the diamond. For each configuration, we identify exactly one solution, which is stable for small coupling between lattice nodes.

  6. Behaviour of Lyapunov's function for different strategies of circuit optimisation

    NASA Astrophysics Data System (ADS)

    Zemliak, Alexander; Markina, Tatiana

    2015-04-01

    The process of analogue circuit optimisation is mathematically defined as a controllable dynamic system. In this context the minimisation of the processor time of designing can be formulated as a problem of time minimisation for transitional process of dynamic system. In order to analyse the properties of such a system, it is proposed to use the concept of Lyapunov function of dynamic system. Using this function and its time derivative, the special functions have been built that allow us to predict the total processor time for circuit optimisation by analysing the initial interval of the optimisation process. Numerical results indicate the possibility of predicting the processor time of different strategies for circuit optimisation.

  7. Lyapunov Orbits in the Jupiter System Using Electrodynamic Tethers

    NASA Technical Reports Server (NTRS)

    Bokelmann, Kevin; Russell, Ryan P.; Lantoine, Gregory

    2013-01-01

    Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.

  8. The experimental observation on Lyapunov exponent in type V intermittency

    NASA Astrophysics Data System (ADS)

    Wang, Yingmei; He, Da-Ren; Hou, Yuqing

    1998-03-01

    We have obtained the first experimental proof for the scaling law of Lyapunov exponent in type V intermittency[1] in an electronic relaxation oscillator[2]. The results are in good agreement with the theoretical prediction obtained by a simplified model[1], and with numerical computations conducted with the theoretical model of the oscillator. [1]: S.Wu,E.J.Ding,D.-R.He, Phys.Lett.A, 197(1995)287. [2]: F.Ji and D.-R.He, Phys.Lett.A, 177(1993)125.

  9. Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks

    NASA Astrophysics Data System (ADS)

    Chen, Diyi; Zhang, Runfan; Liu, Xinzhi; Ma, Xiaoyi

    2014-12-01

    In this paper, we bring attention to the existence of fractional order Lyapunov stability theorem which is strictly descripted by mathematic formulas. Firstly, we introduce fractional-order Lyapunov function based on the definition of fractional calculation and integer order Lyapunov theory. By using the classical stability theorem of linear fractional order systems, we demonstrate convincingly the existence of fractional-order Lyapunov function and present a mathematical description of fractional-order Lyapunov stability theorem. Furthermore, as an example, we apply the presented fractional order Lyapunov stability theorem to synchronization of both direct and undirected complex networks with fractional order equation nodes. Based on the proposed theorem, a novel T-S fuzzy model pining controller with minimum control nodes is designed. Finally, numerical simulations are agreement with theoretical analysis, which both confirm that the correctness of the presented theory.

  10. 14 CFR 23.57 - Takeoff path.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Takeoff path. 23.57 Section 23.57... path. For normal, utility, and acrobatic category multiengine jets of more than 6,000 pounds maximum weight and commuter category airplanes, the takeoff path is as follows: (a) The takeoff path extends...

  11. 14 CFR 23.57 - Takeoff path.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Takeoff path. 23.57 Section 23.57... path. For normal, utility, and acrobatic category multiengine jets of more than 6,000 pounds maximum weight and commuter category airplanes, the takeoff path is as follows: (a) The takeoff path extends...

  12. Probabilistic neural networks employing Lyapunov exponents for analysis of Doppler ultrasound signals.

    PubMed

    Ubeyli, Elif Derya

    2008-01-01

    The implementation of probabilistic neural networks (PNNs) with the Lyapunov exponents for Doppler ultrasound signals classification is presented. This study is directly based on the consideration that Doppler ultrasound signals are chaotic signals. This consideration was tested successfully using the nonlinear dynamics tools, like the computation of Lyapunov exponents. Decision making was performed in two stages: computation of Lyapunov exponents as representative features of the Doppler ultrasound signals and classification using the PNNs trained on the extracted features. The present research demonstrated that the Lyapunov exponents are the features which well represent the Doppler ultrasound signals and the PNNs trained on these features achieved high classification accuracies. PMID:17709103

  13. A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents

    NASA Astrophysics Data System (ADS)

    Hu, Guo-Si

    2009-12-01

    There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs (positive Lyapunov exponents). A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs.

  14. Computation of entropy and Lyapunov exponent by a shift transform

    NASA Astrophysics Data System (ADS)

    Matsuoka, Chihiro; Hiraide, Koichi

    2015-10-01

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

  15. Computation of entropy and Lyapunov exponent by a shift transform.

    PubMed

    Matsuoka, Chihiro; Hiraide, Koichi

    2015-10-01

    We present a novel computational method to estimate the topological entropy and Lyapunov exponent of nonlinear maps using a shift transform. Unlike the computation of periodic orbits or the symbolic dynamical approach by the Markov partition, the method presented here does not require any special techniques in computational and mathematical fields to calculate these quantities. In spite of its simplicity, our method can accurately capture not only the chaotic region but also the non-chaotic region (window region) such that it is important physically but the (Lebesgue) measure zero and usually hard to calculate or observe. Furthermore, it is shown that the Kolmogorov-Sinai entropy of the Sinai-Ruelle-Bowen measure (the physical measure) coincides with the topological entropy. PMID:26520076

  16. Characterizing heart rate variability by scale-dependent Lyapunov exponent

    NASA Astrophysics Data System (ADS)

    Hu, Jing; Gao, Jianbo; Tung, Wen-wen

    2009-06-01

    Previous studies on heart rate variability (HRV) using chaos theory, fractal scaling analysis, and many other methods, while fruitful in many aspects, have produced much confusion in the literature. Especially the issue of whether normal HRV is chaotic or stochastic remains highly controversial. Here, we employ a new multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize HRV. SDLE has been shown to readily characterize major models of complex time series including deterministic chaos, noisy chaos, stochastic oscillations, random 1/f processes, random Levy processes, and complex time series with multiple scaling behaviors. Here we use SDLE to characterize the relative importance of nonlinear, chaotic, and stochastic dynamics in HRV of healthy, congestive heart failure, and atrial fibrillation subjects. We show that while HRV data of all these three types are mostly stochastic, the stochasticity is different among the three groups.

  17. Computation of entropy and Lyapunov exponent by a shift transform

    SciTech Connect

    Matsuoka, Chihiro; Hiraide, Koichi

    2015-10-15

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

  18. GPU and APU computations of Finite Time Lyapunov Exponent fields

    NASA Astrophysics Data System (ADS)

    Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros

    2012-03-01

    We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.

  19. Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices

    NASA Astrophysics Data System (ADS)

    Romero-Bastida, M.; Pazó, Diego; López, Juan M.; Rodríguez, Miguel A.

    2010-09-01

    In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and Φ4 models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. We are able to compute characteristic LVs in large systems thanks to a “bit reversible” algorithm, which completely obviates computer memory limitations.

  20. Average Transient Lifetime and Lyapunov Dimension for Transient Chaos in a High-Dimensional System

    NASA Astrophysics Data System (ADS)

    Chen, Hong; Tang, Jian-Xin; Tang, Shao-Yan; Xiang, Hong; Chen, Xin

    2001-11-01

    The average transient lifetime of a chaotic transient versus the Lyapunov dimension of a chaotic saddle is studied for high-dimensional nonlinear dynamical systems. Typically the average lifetime depends upon not only the system parameter but also the Lyapunov dimension of the chaotic saddle. The numerical example uses the delayed feedback differential equation.

  1. Scaling and interleaving of subsystem Lyapunov exponents for spatio-temporal systems

    NASA Astrophysics Data System (ADS)

    Carretero-González, R.; Ørstavik, S.; Huke, J.; Broomhead, D. S.; Stark, J.

    1999-06-01

    The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the subsystem by truncating the original Jacobian without modifying the original dynamics and thus taking into account only a portion of the information of the entire system. In doing so we notice that the Lyapunov spectra for consecutive subsystem sizes are interleaved and we discuss the possible ways in which this may arise. We also present a new rescaling method, which gives a significantly better fit to the original Lyapunov spectrum. We evaluate the performance of our rescaling method by comparing it to the conventional rescaling (dividing by the relative subsystem volume) for one- and two-dimensional lattices in spatio-temporal chaotic regimes. Finally, we use the new rescaling to approximate quantities derived from the Lyapunov spectrum (largest Lyapunov exponent, Lyapunov dimension, and Kolmogorov-Sinai entropy), finding better convergence as the subsystem size is increased than with conventional rescaling.

  2. Scaling and interleaving of subsystem Lyapunov exponents for spatio-temporal systems.

    PubMed

    Carretero-Gonzalez, R.; Orstavik, S.; Huke, J.; Broomhead, D. S.; Stark, J.

    1999-06-01

    The computation of the entire Lyapunov spectrum for extended dynamical systems is a very time consuming task. If the system is in a chaotic spatio-temporal regime it is possible to approximately reconstruct the Lyapunov spectrum from the spectrum of a subsystem by a suitable rescaling in a very cost effective way. We compute the Lyapunov spectrum for the subsystem by truncating the original Jacobian without modifying the original dynamics and thus taking into account only a portion of the information of the entire system. In doing so we notice that the Lyapunov spectra for consecutive subsystem sizes are interleaved and we discuss the possible ways in which this may arise. We also present a new rescaling method, which gives a significantly better fit to the original Lyapunov spectrum. We evaluate the performance of our rescaling method by comparing it to the conventional rescaling (dividing by the relative subsystem volume) for one- and two-dimensional lattices in spatio-temporal chaotic regimes. Finally, we use the new rescaling to approximate quantities derived from the Lyapunov spectrum (largest Lyapunov exponent, Lyapunov dimension, and Kolmogorov-Sinai entropy), finding better convergence as the subsystem size is increased than with conventional rescaling. (c) 1999 American Institute of Physics. PMID:12779843

  3. Path ANalysis

    SciTech Connect

    Snell, Mark K.

    2007-07-14

    The PANL software determines path through an Adversary Sequence Diagram (ASD) with minimum Probability of Interruption, P(I), given the ASD information and data about site detection, delay, and response force times. To accomplish this, the software generates each path through the ASD, then applies the Estimate of Adversary Sequence Interruption (EASI) methodology for calculating P(I) to each path, and keeps track of the path with the lowest P(I). Primary use is for training purposes during courses on physical security design. During such courses PANL will be used to demonstrate to students how more complex software codes are used by the US Department of Energy to determine the most-vulnerable paths and, where security needs improvement, how such codes can help determine physical security upgrades.

  4. Path ANalysis

    Energy Science and Technology Software Center (ESTSC)

    2007-07-14

    The PANL software determines path through an Adversary Sequence Diagram (ASD) with minimum Probability of Interruption, P(I), given the ASD information and data about site detection, delay, and response force times. To accomplish this, the software generates each path through the ASD, then applies the Estimate of Adversary Sequence Interruption (EASI) methodology for calculating P(I) to each path, and keeps track of the path with the lowest P(I). Primary use is for training purposes duringmore » courses on physical security design. During such courses PANL will be used to demonstrate to students how more complex software codes are used by the US Department of Energy to determine the most-vulnerable paths and, where security needs improvement, how such codes can help determine physical security upgrades.« less

  5. Construction of Lyapunov Function for Power System based on Solving Linear Matrix Inequality

    NASA Astrophysics Data System (ADS)

    Ishigame, Atsushi; Sakaguchi, Hiromu; Takashima, Jun; Suzaki, Shirou

    This paper presents a constructing Lyapunov function for power system based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering with dynamics of load characteristic and AVR control system. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the curl equation and the sector condition. An induction machine and a synchronous machine are considered as load characteristics. One machine and one load infinite bus system is considered taking into account the flux decay effects and AVR with one time constant of the generator. To verify the proposed Lyapunov function, the transient stability assessment is shown. The critical clearing times given by the proposed Lyapunov function are compared with those obtained by the numerical integration method, and they are shown to be practical.

  6. The applicability of Lyapunov characteristic numbers in the study of the stability of satellite orbits

    NASA Technical Reports Server (NTRS)

    Broucke, R.

    1982-01-01

    It is pointed out that the Lyapunov Characteristic Numbers constitute a new tool for determining stability of trajectories of dynamical systems, or, even more generally, of solutions of systems of ordinary differential equations. In contrast with the characteristic exponents, which apply only to periodic solutions, the Lyapunov Characteristic Numbers apply to arbitrary nonperiodic solutions as well. A description is presented of the numerical experiments which have been made in order to investigate the practical value of the Lyapunov Characteristic Number and the Kolmogorov Entropy for the purpose of estimating the stability of trajectories and/or numerical integration methods in celestial mechanics. It is found that the Lyapunov Characteristic Numbers are extremely useful for the classification of the solutions of nonintegrable dynamical systems, especially in order to distinguish between quasi-periodic and chaotic solutions. However, the Lyapunov Characteristics Numbers do not appear to be useful for the purpose of evaluating numerical integration methods.

  7. Path Pascal

    NASA Technical Reports Server (NTRS)

    Campbell, R. H.; Kolstad, R. B.; Holle, D. F.; Miller, T. J.; Krause, P.; Horton, K.; Macke, T.

    1983-01-01

    Path Pascal is high-level experimental programming language based on PASCAL, which incorporates extensions for systems and real-time programming. Pascal is extended to treat real-time concurrent systems.

  8. Multi-Criteria Path Finding

    NASA Astrophysics Data System (ADS)

    Mohammadi, E.; Hunter, A.

    2012-07-01

    Path finding solutions are becoming a major part of many GIS applications including location based services and web-based GIS services. Most traditional path finding solutions are based on shortest path algorithms that tend to minimize the cost of travel from one point to another. These algorithms make use of some cost criteria that is usually an attribute of the edges in the graph network. Providing one shortest path limits user's flexibility when choosing a possible route, especially when more than one parameter is utilized to calculate cost (e.g., when length, number of traffic lights, and number of turns are used to calculate network cost.) K shortest path solutions tend to overcome this problem by providing second, third, and Kth shortest paths. These algorithms are efficient as long as the graphs edge weight does not change dynamically and no other parameters affect edge weights. In this paper we try to go beyond finding shortest paths based on some cost value, and provide all possible paths disregarding any parameter that may affect total cost. After finding all possible paths, we can rank the results by any parameter or combination of parameters, without a substantial increase in time complexity.

  9. Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles

    NASA Astrophysics Data System (ADS)

    Baetens, Jan M.; Gravner, Janko

    2016-05-01

    We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.

  10. An Eulerian approach for computing the finite time Lyapunov exponent

    NASA Astrophysics Data System (ADS)

    Leung, Shingyu

    2011-05-01

    We propose efficient Eulerian methods for approximating the finite-time Lyapunov exponent (FTLE). The idea is to compute the related flow map using the Level Set Method and the Liouville equation. There are several advantages of the proposed approach. Unlike the usual Lagrangian-type computations, the resulting method requires the velocity field defined only at discrete locations. No interpolation of the velocity field is needed. Also, the method automatically stops a particle trajectory in the case when the ray hits the boundary of the computational domain. The computational complexity of the algorithm is O(Δ x-( d+1) ) with d the dimension of the physical space. Since there are the same number of mesh points in the x- t space, the computational complexity of the proposed Eulerian approach is optimal in the sense that each grid point is visited for only O(1) time. We also extend the algorithm to compute the FTLE on a co-dimension one manifold. The resulting algorithm does not require computation on any local coordinate system and is simple to implement even for an evolving manifold.

  11. Decadal ENSO variability as reflected by Local Lyapunov Exponents

    NASA Astrophysics Data System (ADS)

    Karamperidou, C.; Cane, M. A.; Wittenberg, A. T.; Lall, U.; Di Nezio, P. N.

    2011-12-01

    Decadal variability of ENSO is present in historical and paleo records, and has been simulated by a hierarchy of dynamical and statistical models. The ENSO variability in the IPCC AR4 Coupled GCMs ranges from constant periodicity or amplitude to significant inter-decadal variability in both period and amplitude. While long runs of intermediate dynamical models that exhibit inter-decadal and inter-centennial variability, such as the ZC model, have been a subject of numerous studies, only recently have long runs of coupled GCMs, such as the GFDL CM2.1 2000-yr control run, become available. The presence of such rich variability in the absence of external forcing that could induce persistent regimes, along with the length of the simulation, provides new ground for investigation of the causes of long-term modulation of ENSO behavior and the implications for predictability at multiple time-scales from the short-range to the decadal. In this work, we investigate ENSO predictability in long unforced runs of a fully coupled GCM (GFDL's CM2.1) and the intermediate ZC model in a dynamical systems theory context. We compute the Local Lyapunov Exponents (LLEs) of the NINO3 time series, and use them as a means of classifying epochs of distinct ENSO behavior. The 'loss' or 'gain' of predictability across these epochs and their relation to the physical evolution of the ENSO events is examined. The correspondence of the LLE statistics with prediction error in 'perfect-model' reforecasts is also discussed.

  12. Bifurcation analysis of a Lyapunov-based controlled boost converter

    NASA Astrophysics Data System (ADS)

    Spinetti-Rivera, Mario; Olm, Josep M.; Biel, Domingo; Fossas, Enric

    2013-11-01

    Lyapunov-based controlled boost converters have a unique equilibrium point, which is globally asymptotically stable, for known resistive loads. This article investigates the dynamic behaviors that appear in the system when the nominal load differs from the actual one and no action is taken by the controller to compensate for the mismatch. Exploiting the fact that the closed-loop system is, in fact, planar and quadratic, one may provide not only local but also global stability results: specifically, it is proved that the number of equilibria of the converter may grow up to three and that, in any case, the system trajectories are always bounded, i.e. it is a bounded quadratic system. The possible phase portraits of the closed-loop system are also characterized in terms of the selected bifurcation parameters, namely, the actual load value and the gain of the control law. Accordingly, the analysis allows the numerical illustration of many bifurcation phenomena that appear in bounded quadratic systems through a physical example borrowed from power electronics.

  13. [A Standing Balance Evaluation Method Based on Largest Lyapunov Exponent].

    PubMed

    Liu, Kun; Wang, Hongrui; Xiao, Jinzhuang; Zhao, Qing

    2015-12-01

    In order to evaluate the ability of human standing balance scientifically, we in this study proposed a new evaluation method based on the chaos nonlinear analysis theory. In this method, a sinusoidal acceleration stimulus in forward/backward direction was forced under the subjects' feet, which was supplied by a motion platform. In addition, three acceleration sensors, which were fixed to the shoulder, hip and knee of each subject, were applied to capture the balance adjustment dynamic data. Through reconstructing the system phase space, we calculated the largest Lyapunov exponent (LLE) of the dynamic data of subjects' different segments, then used the sum of the squares of the difference between each LLE (SSDLLE) as the balance capabilities evaluation index. Finally, 20 subjects' indexes were calculated, and compared with evaluation results of existing methods. The results showed that the SSDLLE were more in line with the subjects' performance during the experiment, and it could measure the body's balance ability to some extent. Moreover, the results also illustrated that balance level was determined by the coordinate ability of various joints, and there might be more balance control strategy in the process of maintaining balance. PMID:27079089

  14. Are Bred Vectors The Same As Lyapunov Vectors?

    NASA Astrophysics Data System (ADS)

    Kalnay, E.; Corazza, M.; Cai, M.

    Regional loss of predictability is an indication of the instability of the underlying flow, where small errors in the initial conditions (or imperfections in the model) grow to large amplitudes in finite times. The stability properties of evolving flows have been studied using Lyapunov vectors (e.g., Alligood et al, 1996, Ott, 1993, Kalnay, 2002), singular vectors (e.g., Lorenz, 1965, Farrell, 1988, Molteni and Palmer, 1993), and, more recently, with bred vectors (e.g., Szunyogh et al, 1997, Cai et al, 2001). Bred vectors (BVs) are, by construction, closely related to Lyapunov vectors (LVs). In fact, after an infinitely long breeding time, and with the use of infinitesimal ampli- tudes, bred vectors are identical to leading Lyapunov vectors. In practical applications, however, bred vectors are different from Lyapunov vectors in two important ways: a) bred vectors are never globally orthogonalized and are intrinsically local in space and time, and b) they are finite-amplitude, finite-time vectors. These two differences are very significant in a dynamical system whose size is very large. For example, the at- mosphere is large enough to have "room" for several synoptic scale instabilities (e.g., storms) to develop independently in different regions (say, North America and Aus- tralia), and it is complex enough to have several different possible types of instabilities (such as barotropic, baroclinic, convective, and even Brownian motion). Bred vectors share some of their properties with leading LVs (Corazza et al, 2001a, 2001b, Toth and Kalnay, 1993, 1997, Cai et al, 2001). For example, 1) Bred vectors are independent of the norm used to define the size of the perturba- tion. Corazza et al. (2001) showed that bred vectors obtained using a potential enstro- phy norm were indistinguishable from bred vectors obtained using a streamfunction squared norm, in contrast with singular vectors. 2) Bred vectors are independent of the length of the rescaling period as long as the

  15. Learning in a noisy environment: a Lyapunov equation approach

    NASA Astrophysics Data System (ADS)

    Solla, Sara A.; Cohen, Yarden; Cvitanovic, Predrag

    Consider a behavioral task described as a finite time trajectory through a d-dimensional space, segmented in K time steps, and thus fully specified by a vector X in the n = dK dimensional state space of possible trajectories. Consider the dynamics of learning a desired target trajectory X*. In the vicinity of X*, the learning dynamics at the t-th discrete learning time step can be linearized to Yt + 1 = MYt +ξt , where, Yt =Xt -X* and ξ is independent Gaussian noise of zero mean and covariance Δ. The balance between Contracting dynamics and noise leads to an asymptotic covariance Q that obeys the Lyapunov equation Q = MQMT + Δ . Given Q, how can the unknown deterministic component M be estimated the presence of noise? We propose the use of systematic target perturbations X* -->X* + ɛVj , with unit vectors Vj, 1 <= j <= n that span the space X. We argue, convincingly if not rigorously, that the linear response to these perturbations fully characterizes the asymptotic dynamics of the learning process. We illustrate the method by analyzing networks of neurons with either intrinsic or extrinsic noise, at time resolutions that span from spike timing to spiking rates.

  16. Estimating the Lyapunov spectrum of time delay feedback systems from scalar time series

    NASA Astrophysics Data System (ADS)

    Hegger, Rainer

    1999-08-01

    On the basis of a recently developed method for modeling time delay systems, we propose a procedure to estimate the spectrum of Lyapunov exponents from a scalar time series. It turns out that the spectrum is approximated very well and allows for good estimates of the Lyapunov dimension even if the sampling rate of the time series is so low that the infinite dimensional tangent space is spanned quite sparsely.

  17. Estimating the Lyapunov spectrum of time delay feedback systems from scalar time series.

    PubMed

    Hegger, R

    1999-08-01

    On the basis of a recently developed method for modeling time delay systems, we propose a procedure to estimate the spectrum of Lyapunov exponents from a scalar time series. It turns out that the spectrum is approximated very well and allows for good estimates of the Lyapunov dimension even if the sampling rate of the time series is so low that the infinite dimensional tangent space is spanned quite sparsely. PMID:11969918

  18. Exact Lyapunov dimension of the universal attractor for the complex Ginzburg-Landau equation

    SciTech Connect

    Doering, C.R.; Gibbon, J.D.; Holm, D.D.; Nicolaenko, B.

    1987-12-28

    We present an exact analytic computation of the Lyapunov dimension of the universal attractor of the complex Ginzburg-Landau partial differential equation for a finite range of its parameter values. We obtain upper bounds on the attractor's dimension when the parameters do not permit an exact evaluation by our methods. The exact Lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode-counting argument.

  19. Zeta function for the Lyapunov exponent of a product of random matrices

    SciTech Connect

    Mainieri, R. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 )

    1992-03-30

    A cycle expansion for the Lyapunov exponent of a product of random matrices is derived. The formula is nonperturbative and numerically effective, which allows the Lyapunov exponent to be computed to high accuracy. In particular, the free energy and heat capacity are computed for the one-dimensional Ising model with quenched disorder. The formula is derived by using a Bernoulli dynamical system to mimic the randomness.

  20. Exploring the Spatiotemporal Dynamics of Covariant Lyapunov Vectors for Chaotic Convection

    NASA Astrophysics Data System (ADS)

    Xu, Mu; Paul, Mark

    Covariant Lyapunov vectors provide access to fundamental features of chaos in high-dimensional systems that are driven far-from-equilibrium. We explore the spatiotemporal dynamics of covariant Lyapunov vectors for chaotic Rayleigh-Bénard convection to provide new physical insights. We use the covariant Lyapunov vectors to quantify the transition from hyperbolic to non-hyperbolic dynamics, to determine the degree of Oseledec splitting exhibited by the dynamics, and to shed light upon upon the tangled nature of the Lyapunov vectors. In this talk, we will explore the spatiotemporal dynamics of the Lyapunov vectors and their relation with the chaotic pattern dynamics of the flow field. Our results suggest that the Lyapunov vectors contain two distinct spatiotemporal features consisting of highly localized regions near defect structures and a spatially distributed checkerboard pattern. We will explore the connection between these features and the ideas of physical and spurious modes that may compose the dynamics. This research was funded by NSF Grant No. DMS-1125234.

  1. Lyapunov Exponent Criterion for Stability of Planetary Orbits in Binary Systems

    NASA Astrophysics Data System (ADS)

    Musielak, Zdzislaw E.; Quarles, B.; Eberle, J.; Cuntz, M.

    2011-01-01

    The existence of planets in stellar binary systems is now well-confirmed by many observations. Stability of planetary orbits in these systems has extensively been studied and some attempts have been made to establish stringent stability criteria for the orbits. In this paper, we contribute to the ongoing work on the stability criteria in binary systems by introducing a Lyapunov exponent criterion. We have computed the Lyapunov exponents, the Lyapunov dimension and the time series spectra for planets in binary system. The obtained results demonstrate when a system becomes unstable by orbital energy criterion and the method of Lyapunov exponents provides a quantitative classification scale to characterize the instability. By applying the maximum Lyapunov exponent to the parameter space, which covers mass and distance ratios for the considered binary systems, we determined regions of stability and used the time series spectra and the Lyapunov dimension to illustrate the reasons behind the stability. Specific applications of the criterion to binary systems with known planets will also be discussed.

  2. A statistical approach to estimate the LYAPUNOV spectrum in disc brake squeal

    NASA Astrophysics Data System (ADS)

    Oberst, S.; Lai, J. C. S.

    2015-01-01

    The estimation of squeal propensity of a brake system from the prediction of unstable vibration modes using the linear complex eigenvalue analysis (CEA) in the frequency domain has its fair share of successes and failures. While the CEA is almost standard practice for the automotive industry, time domain methods and the estimation of LYAPUNOV spectra have not received much attention in brake squeal analyses. One reason is the challenge in estimating the true LYAPUNOV exponents and their discrimination against spurious ones in experimental data. A novel method based on the application of the ECKMANN-RUELLE matrices is proposed here to estimate LYAPUNOV exponents by using noise in a statistical procedure. It is validated with respect to parameter variations and dimension estimates. By counting the number of non-overlapping confidence intervals for LYAPUNOV exponent distributions obtained by moving a window of increasing size over bootstrapped same-length estimates of an observation function, a dispersion measure's width is calculated and fed into a BAYESIAN beta-binomial model. Results obtained using this method for benchmark models of white and pink noise as well as the classical HENON map indicate that true LYAPUNOV exponents can be isolated from spurious ones with high confidence. The method is then applied to accelerometer and microphone data obtained from brake squeal tests. Estimated LYAPUNOV exponents indicate that the pad's out-of-plane vibration behaves quasi-periodically on the brink to chaos while the microphone's squeal signal remains periodic.

  3. Global path following control for underactuated stratospheric airship

    NASA Astrophysics Data System (ADS)

    Zheng, Zewei; Wu, Zhe

    2013-10-01

    This paper develops a nonlinear path following control method that drives an underactuated stratospheric airship onto a predefined planar path with a given speed profile. The dynamic model of the airship used for controller design is first introduced with kinematics and dynamics equations. In order to render good pilot behavior for the control action, a guidance controller by referring to the guidance-based path following principle is derived. Then the controller is extended to cope with the airship attitude and velocity by resorting to the backstepping and Lyapunov-based techniques. The designed control system finally possesses a cascaded structure which consists of guidance loop, attitude control loop and velocity control loop. Stability analysis shows that the controlled closed-loop system is globally asymptotically stable, and the sway velocity which cannot be directly controlled is bounded. Simulation results for the airship following typical paths are illustrated to verify effectiveness of the proposed approach.

  4. The instability transition for the restricted 3-body problem. III. The Lyapunov exponent criterion

    NASA Astrophysics Data System (ADS)

    Quarles, B.; Eberle, J.; Musielak, Z. E.; Cuntz, M.

    2011-09-01

    Aims: We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The criterion augments our earlier results given in the two previous papers of this series where stability criteria have been developed based on the Jacobi constant and the hodograph method. Methods: The centerpiece of our method is the concept of Lyapunov exponents, which are incorporated into the analysis of orbital stability by integrating the Jacobian of the CR3BP and orthogonalizing the tangent vectors via a well-established algorithm originally developed by Wolf et al. The criterion for orbital stability based on the Lyapunov exponents is independently verified by using power spectra. The obtained results are compared to results presented in the two previous papers of this series. Results: It is shown that the maximum Lyapunov exponent can be used as an indicator for chaotic behaviour of planetary orbits, which is consistent with previous applications of this method, particularly studies for the Solar System. The chaotic behaviour corresponds to either orbital stability or instability, and it depends solely on the mass ratio μ of the binary components and the initial distance ratio ρ0 of the planet relative to the stellar separation distance. Detailed case studies are presented for μ = 0.3 and 0.5. The stability limits are characterized based on the value of the maximum Lyapunov exponent. However, chaos theory as well as the concept of Lyapunov time prevents us from predicting exactly when the planet is ejected. Our method is also able to indicate evidence of quasi-periodicity. Conclusions: For different mass ratios of the stellar components, we are able to characterize stability limits for the CR3BP based on the value of the maximum Lyapunov exponent. This theoretical result allows us to link the study of planetary orbital stability to chaos

  5. The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance

    PubMed Central

    Liu, Kun; Wang, Hongrui; Xiao, Jinzhuang

    2015-01-01

    The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body's standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age. PMID:26064182

  6. Predicting the evolutionary dynamic behavior of a laser with injected signal using Lyapunov exponents

    NASA Astrophysics Data System (ADS)

    Bandy, D. K.; Hall, J. R.; Denker, M. E.

    2015-07-01

    We show that the role of the Lyapunov exponents can be extended beyond the customary local instability, such as limit cycle behavior, to include its use as an evolutionary predictor of the dynamics of a laser with injected signal (LIS). Numerical studies of LIS reveal that as a function of the input-signal strength the evolution of two nonzero Lyapunov exponents (generally equal) distinctively predicts the evolutionary trend of the fundamental frequency of the laser output signal (an important dynamic characteristic of the LIS) even with the presence of some noise. This globally predictive behavior of the Lyapunov exponents includes also the dynamic behavior of the individual coexisting attractors. Different coexisting attractors of LIS and configurations of Lyapunov exponents for both individual attractors and the global system are reported. Two LIS case studies are considered: (I) a high-gain system with a rich history of nonlinear behavior but not experimentally accessible, and (II) a low-gain system that has complex dynamics and is experimentally accessible for Class B lasers. Universality arguments support the thesis that these different configurations and the extended role of the Lyapunov exponents as an evolutionary predictor of the dynamics will be observed in other nonlinear, dynamic dissipative systems as well.

  7. On the Calculation of Lyapunov Indicators with Post-stabilization in a Weyl Field

    NASA Astrophysics Data System (ADS)

    Wu, Xin; Zhang, Hong; Wan, Xiao-Sheng

    2006-04-01

    We present details of a work aiming at the overestimation of Lyapunov exponents defined by the geodesic deviation equations in the previous work. The geodesic deviation vector with post-stabilization is used to compute the fast Lyapunov indicator, considered to be a very sensitive tool for discrimination between ordered or weakly chaotic motions. We make a detailed study of the dynamics in the superposed Weyl field between a black hole and shell of octopoles by using the fast Lyapunov indicator with the Poincaré surface of section. In particular, we examine the effects on the dynamics around the fixed points, of varying one of the three parameters (specific energy E, specific angular momentum L and octopolar moment Script O), while keeping the other two fixed, and identify the intervals of the varying parameter where the motion is regular or chaotic.

  8. Non-monotonicity of Lyapunov functions for functional differential equations with enlightenments for related research methods

    NASA Astrophysics Data System (ADS)

    Zhao, Xueyan; Deng, Feiqi

    2016-07-01

    In this paper, a particular property of Lyapunov functions for functional differential equations (FDEs) is developed, that is the direct dependence of the signs of the derivatives of the Lyapunov functions on the initial data. This property implies that the derivatives of the Lyapunov functions for FDEs cannot be guaranteed to be negative definite generally, and then makes the FDEs differ from the ordinary differential equations constitutionally. With this property, we give some enlightenments for the research methods for establishing stability theorems or criteria for FDEs, which may help us to form a common view about the choice of the investigation methods on the stability of FDEs. The conclusion is stated in both the deterministic and stochastic versions. Two illustrative examples are given to show and verify our conclusion through the paper.

  9. Collective Patterns of Swarm Dynamics and the Lyapunov Analysis of Individual Behaviors

    NASA Astrophysics Data System (ADS)

    Shiraishi, Masashi; Aizawa, Yoji

    2015-05-01

    In this report, the collective patterns of swarms dynamics are theoretically studied using a self-propelled particle model, and the dynamics of the individual particles in the swarms is precisely studied using Lyapunov analysis. Furthermore, the collective behaviors of the swarms are classified into several patterns characterized by the following statistical quantities: Lyapunov spectrum, Lyapunov dimension, and stability and instability indices. Consequently, we propose individual instability exponents (IIEs) that describes the sensitivity of the individual particles in the swarm, and show that the IIEs is a significant order parameter that demonstrates changes in the pattern and expresses the activity of the swarm dynamics. Furthermore, we show that the mean and variance obtained after calculating the speed distribution of individual particles reveal marked variations corresponding to the change in the pattern in a manner similar to those of the IIEs.

  10. Regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence

    NASA Astrophysics Data System (ADS)

    Inubushi, Masanobu; Takehiro, Shin-ichi; Yamada, Michio

    2015-08-01

    Considering a wall turbulence as a chaotic dynamical system, we study regeneration cycles in a minimal wall turbulence from the viewpoint of orbital instability by employing the covariant Lyapunov analysis developed by [F. Ginelli et al. Phys. Rev. Lett. 99, 130601 (2007), 10.1103/PhysRevLett.99.130601]. We divide the regeneration cycle into two phases and characterize them with the local Lyapunov exponents and the covariant Lyapunov vectors of the Navier-Stokes turbulence. In particular, we show numerically that phase (i) is dominated by instabilities related to the sinuous mode and the streamwise vorticity, and there is no instability in phase (ii). Furthermore, we discuss a mechanism of the regeneration cycle, making use of an energy budget analysis.

  11. State feedback integral control for a rotary direct drive servo valve using a Lyapunov function approach.

    PubMed

    Yu, Jue; Zhuang, Jian; Yu, Dehong

    2015-01-01

    This paper concerns a state feedback integral control using a Lyapunov function approach for a rotary direct drive servo valve (RDDV) while considering parameter uncertainties. Modeling of this RDDV servovalve reveals that its mechanical performance is deeply influenced by friction torques and flow torques; however, these torques are uncertain and mutable due to the nature of fluid flow. To eliminate load resistance and to achieve satisfactory position responses, this paper develops a state feedback control that integrates an integral action and a Lyapunov function. The integral action is introduced to address the nonzero steady-state error; in particular, the Lyapunov function is employed to improve control robustness by adjusting the varying parameters within their value ranges. This new controller also has the advantages of simple structure and ease of implementation. Simulation and experimental results demonstrate that the proposed controller can achieve higher control accuracy and stronger robustness. PMID:25234140

  12. Stabilisation of a class of 2-DOF underactuated mechanical systems via direct Lyapunov approach

    NASA Astrophysics Data System (ADS)

    Turker, Turker; Gorgun, Haluk; Cansever, Galip

    2013-06-01

    This paper represents an alternative stabilisation procedure for a class of two degree-of-freedom underactuated mechanical systems based on a set of transformations and a Lyapunov function. After simplifying dynamic equations of the system via partial feedback linearisation and coordinate changes, the stability of the system is provided with Lyapunov's direct method. Proposed control scheme is used on two different examples and asymptotic convergence for each system is proven by means of La Salle's invariance principle. The designed controller is successfully illustrated through numerical simulations for each example.

  13. Structured scale dependence in the Lyapunov exponent of a Boolean chaotic map.

    PubMed

    Cohen, Seth D

    2015-04-01

    We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network, which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we show that the structured scale-dependence in the system's Lyapunov exponent is the result of the discrete logic elements in the map operator's stretching function. PMID:25974572

  14. Structured scale dependence in the Lyapunov exponent of a Boolean chaotic map

    NASA Astrophysics Data System (ADS)

    Cohen, Seth D.

    2015-04-01

    We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network, which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we show that the structured scale-dependence in the system's Lyapunov exponent is the result of the discrete logic elements in the map operator's stretching function.

  15. Toward a new task assignment and path evolution (TAPE) for missile defense system (MDS) using intelligent adaptive SOM with recurrent neural networks (RNNs).

    PubMed

    Wang, Chi-Hsu; Chen, Chun-Yao; Hung, Kun-Neng

    2015-06-01

    In this paper, a new adaptive self-organizing map (SOM) with recurrent neural network (RNN) controller is proposed for task assignment and path evolution of missile defense system (MDS). We address the problem of N agents (defending missiles) and D targets (incoming missiles) in MDS. A new RNN controller is designed to force an agent (or defending missile) toward a target (or incoming missile), and a monitoring controller is also designed to reduce the error between RNN controller and ideal controller. A new SOM with RNN controller is then designed to dispatch agents to their corresponding targets by minimizing total damaging cost. This is actually an important application of the multiagent system. The SOM with RNN controller is the main controller. After task assignment, the weighting factors of our new SOM with RNN controller are activated to dispatch the agents toward their corresponding targets. Using the Lyapunov constraints, the weighting factors for the proposed SOM with RNN controller are updated to guarantee the stability of the path evolution (or planning) system. Excellent simulations are obtained using this new approach for MDS, which show that our RNN has the lowest average miss distance among the several techniques. PMID:25148679

  16. Computing the optimal path in stochastic dynamical systems.

    PubMed

    Bauver, Martha; Forgoston, Eric; Billings, Lora

    2016-08-01

    In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces. PMID:27586597

  17. Computing the optimal path in stochastic dynamical systems

    NASA Astrophysics Data System (ADS)

    Bauver, Martha; Forgoston, Eric; Billings, Lora

    2016-08-01

    In stochastic systems, one is often interested in finding the optimal path that maximizes the probability of escape from a metastable state or of switching between metastable states. Even for simple systems, it may be impossible to find an analytic form of the optimal path, and in high-dimensional systems, this is almost always the case. In this article, we formulate a constructive methodology that is used to compute the optimal path numerically. The method utilizes finite-time Lyapunov exponents, statistical selection criteria, and a Newton-based iterative minimizing scheme. The method is applied to four examples. The first example is a two-dimensional system that describes a single population with internal noise. This model has an analytical solution for the optimal path. The numerical solution found using our computational method agrees well with the analytical result. The second example is a more complicated four-dimensional system where our numerical method must be used to find the optimal path. The third example, although a seemingly simple two-dimensional system, demonstrates the success of our method in finding the optimal path where other numerical methods are known to fail. In the fourth example, the optimal path lies in six-dimensional space and demonstrates the power of our method in computing paths in higher-dimensional spaces.

  18. Characterizing two-timescale nonlinear dynamics using finite-time Lyapunov exponents and subspaces

    NASA Astrophysics Data System (ADS)

    Mease, K. D.; Topcu, U.; Aykutluğ, E.; Maggia, M.

    2016-07-01

    Finite-time Lyapunov exponents and subspaces are used to define and diagnose boundary-layer type, two-timescale behavior in the tangent linear dynamics and to determine the associated manifold structure in the flow of a finite-dimensional nonlinear autonomous dynamical system. Two-timescale behavior is characterized by a slow-fast splitting of the tangent bundle for a state space region. The slow-fast splitting is defined using finite-time Lyapunov exponents and vectors, guided by the asymptotic theory of partially hyperbolic sets, with important modifications for the finite-time case; for example, finite-time Lyapunov analysis relies more heavily on the Lyapunov vectors due to their relatively fast convergence compared to that of the corresponding exponents. The splitting is used to characterize and locate points approximately on normally hyperbolic center manifolds via tangency conditions for the vector field. Determining manifolds from tangent bundle structure is more generally applicable than approaches, such as the singular perturbation method, that require special normal forms or other a priori knowledge. The use, features, and accuracy of the approach are illustrated via several detailed examples.

  19. Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

    NASA Astrophysics Data System (ADS)

    Lombardo, S.; Mulone, G.; Trovato, M.

    2008-06-01

    We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.

  20. Real-time measurements of the largest Lyapunov exponent in optical fields

    NASA Astrophysics Data System (ADS)

    Gavrylyak, M. S.; Maksimyak, P. P.

    2012-01-01

    An analog interference method for measuring the largest Lyapunov exponent in optical fields generated by scattering objects and mediums is proposed. The method is used to make a device for high-speed real time transverse correlation function optical fields measurement.

  1. Real-time measurements of the largest Lyapunov exponent in optical fields

    NASA Astrophysics Data System (ADS)

    Gavrylyak, M. S.; Maksimyak, P. P.

    2011-09-01

    An analog interference method for measuring the largest Lyapunov exponent in optical fields generated by scattering objects and mediums is proposed. The method is used to make a device for high-speed real time transverse correlation function optical fields measurement.

  2. Determination of Limit Cycles Using Both the Slope of Correlation Integral and Dominant Lyapunov Methods

    SciTech Connect

    Castillo, Rogelio; Alonso, Gustavo; Palacios, Javier C.

    2004-02-15

    A method for nonlinear analysis of instabilities in boiling water reactors (BWRs) is presented. Both the Dominant Lyapunov Exponent method and the Slope of the Correlation Integral (SOCI) method are used to analyze the average power reactor monitor (APRM) signals from a BWR. The main advantage of using the two methods in a complementary manner is that doing so results in an enhancement of the capability to analyze noisy systems, such as the APRM signals in a BWR. Previously, such nonlinear analysis had been performed using independently either the Dominant Lyapunov Exponent Method or the SOCI method. These two methods are sensitive to noise in a signal and normally require large amounts of data for a reliable analysis.This proposed system for nonlinear analysis is composed first of a home-developed computer program called 'SLOPE', which is based on the SOCI method. Then, the signal analysis is also performed by the 'LENNS' code, which is used to obtain the dominant Lyapunov exponent. Since only the dominant Lyapunov exponent is computed, there is no need to acquire large amounts of data; thus, computational processing time is greatly reduced, even in the case of noisy data.The system was used to analyze BWR signals containing stationary and nonstationary limit cycles. It was found that this method satisfactorily calculates the limit cycles, extracting useful information from noisy signals.

  3. No ISCOs in Charged Myers Perry Spacetimes by Measuring Lyapunov Exponent

    NASA Astrophysics Data System (ADS)

    Pradhan, Parthapratim

    2015-01-01

    By computing coordinate time Lyapunov exponent, we prove that for more than four spacetime dimensions (N ≥ 3), there are no Innermost Stable Circular Orbit (ISCO) in charged Myers Perry blackhole spacetime.Using it, we show that the instability of equatorial circular geodesics, both massive and massless particles for such types of blackhole space-times.

  4. On relations among the entropic chaos degree, the Kolmogorov-Sinai entropy and the Lyapunov exponent

    SciTech Connect

    Kamizawa, T. Hara, T.; Ohya, M.

    2014-03-15

    There exist several criteria to describe the chaotic behaviour of a dynamical system. In this paper, we discuss the relations among three criteria: Entropic Chaos Degree, Kolmogorov-Shinai entropy, and Lyapunov exponent. Moreover, the problems of their computation are discussed.

  5. Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data

    SciTech Connect

    Josiński, Henryk; Świtoński, Adam; Michalczuk, Agnieszka; Wojciechowski, Konrad

    2015-03-10

    The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.

  6. Numerical Estimation of the Lyapunov Exponents of Chaotic Time Series Corrupted by Noises of Large Amplitude

    NASA Astrophysics Data System (ADS)

    Mera, M. Eugenia; Morán, Manuel

    2009-09-01

    We show that the Lyapunov spectrum of chaotic vector time series corrupted by noises with a noise-to-signal ratio of up to 100% in one of the coordinates can be estimated using the output of a noise reduction algorithm designed to deal with noises of large amplitude.

  7. Using Covariant Lyapunov Vectors to Build a Physical Understanding of Spatiotemporal Chaos in Rayleigh-Bénard Convection

    NASA Astrophysics Data System (ADS)

    Xu, Mu; Paul, Mark

    2015-11-01

    We explore the high-dimensional spatiotemporal chaos of Rayleigh-Bénard convection using covariant Lyapunov vectors. We integrate the three-dimensional and time dependent Boussinesq equations for a convection layer for very long-times and for a range of Rayleigh numbers. We simultaneously integrate many copies of the tangent space equations in order to compute the covariant Lyapunov vectors. We explore chaotic dynamics with a fractal dimension of nearly 50 and we compute over 150 covariant Lyapunov vectors. Using the Lyapunov vectors we quantify the hyperbolicity of the dynamics, the degree of Oseledec splitting, and explore the temporal, spatial, and spectral dynamics of the Lyapunov vectors. Our results indicate that the dynamics undergoes a hyperbolic to non-hyperbolic transition as the Rayleigh number is increased. Our results yield that all of the Lyapunov vectors computed have near tangencies with neighboring vectors. A closer look at the vectors suggests that the dynamics are composed of physical modes that are connected with tangled spurious modes that extend to all of the covariant Lyapunov vectors we have computed. This research was funded by NSF grant no. DMS-1125234. The computations were done using resources from the Virginia Tech ADVANCED Research Computing center.

  8. Second-law irreversibility and phase-space dimensionality loss from time-reversible nonequilibrium steady-state Lyapunov spectra

    NASA Astrophysics Data System (ADS)

    Hoover, W. G.; Posch, H. A.

    1994-03-01

    We consider steady-state nonequilibrium many-body flows of mass and momentum. For several such diffusive and viscous flows we estimate the phase-space strange-attractor Lyapunov dimensions from the complete spectrum of Lyapunov exponents. We vary the number of particles and the number of thermostated degrees of freedom, as well as the deviation from equilibrium. The resulting Lyapunov spectra provide numerical evidence that the fractal dimensionality loss in such systems remains extensive in a properly defined nonequilibrium analog of the equilibrium large-system thermodynamic limit. The data also suggest a variational principle in the vicinity of nonequilibrium steady states.

  9. 14 CFR 23.61 - Takeoff flight path.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Takeoff flight path. 23.61 Section 23.61... flight path. For normal, utility, and acrobatic category multiengine jets of more than 6,000 pounds maximum weight and commuter category airplanes, the takeoff flight path must be determined as follows:...

  10. 14 CFR 23.61 - Takeoff flight path.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Takeoff flight path. 23.61 Section 23.61... flight path. For normal, utility, and acrobatic category multiengine jets of more than 6,000 pounds maximum weight and commuter category airplanes, the takeoff flight path must be determined as follows:...

  11. Adaptive external torque estimation by means of tracking a Lyapunov function

    SciTech Connect

    Schaub, H.; Junkins, J.L.; Robinett, R.D.

    1996-03-01

    A real-time method is presented to adoptively estimate three-dimensional unmodeled external torques acting on a spacecraft. This is accomplished by forcing the tracking error dynamics to follow the Lyapunov function underlying the feedback control law. For the case where the external torque is constant, the tracking error dynamics are shown to converge asypmtotically. The methodology applies not only to the control law used in this paper, but can also be applied to most Lyapunov derived feedback control laws. The adaptive external torque estimation is very robust in the presence of measurement noise, since a numerical integration is used instead of a numerical differentiation. Spacecraft modeling errors, such as in the inertia matrix, are also compensated for by this method. Several examples illustrate the practical significance of these ideas.

  12. Construction of the Lyapunov Spectrum in a Chaotic System Displaying Phase Synchronization

    NASA Astrophysics Data System (ADS)

    De Carlo, Leonardo; Gentile, Guido; Giuliani, Alessandro

    2016-06-01

    We consider a three-dimensional chaotic system consisting of the suspension of Arnold's cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense that the relative phase between the suspension flow and the clock locks to a special value, thus making the motion fall onto a lower dimensional attractor. More specifically, we construct the attractive invariant manifold, of dimension smaller than three, using a convergent perturbative expansion. Moreover, we compute via convergent series the Lyapunov exponents, including notably the central one. The result generalizes a previous construction of the attractive invariant manifold in a similar but simpler model. The main novelty of the current construction relies in the computation of the Lyapunov spectrum, which consists of non-trivial analytic exponents. Some conjectures about a possible smoothening transition of the attractor as the coupling is increased are also discussed.

  13. Dissipative dynamics in a finite chaotic environment: Relationship between damping rate and Lyapunov exponent

    NASA Astrophysics Data System (ADS)

    Xavier, J. C.; Strunz, W. T.; Beims, M. W.

    2015-08-01

    We consider the energy flow between a classical one-dimensional harmonic oscillator and a set of N two-dimensional chaotic oscillators, which represents the finite environment. Using linear response theory we obtain an analytical effective equation for the system harmonic oscillator, which includes a frequency dependent dissipation, a shift, and memory effects. The damping rate is expressed in terms of the environment mean Lyapunov exponent. A good agreement is shown by comparing theoretical and numerical results, even for environments with mixed (regular and chaotic) motion. Resonance between system and environment frequencies is shown to be more efficient to generate dissipation than larger mean Lyapunov exponents or a larger number of bath chaotic oscillators.

  14. Asymptotics of finite system Lyapunov exponents for some random matrix ensembles

    NASA Astrophysics Data System (ADS)

    Forrester, Peter J.

    2015-05-01

    For products PN of N random matrices of size d× d, there is a natural notion of finite N Lyapunov exponents \\{{{μ }i}\\}i=1d. In the case of standard Gaussian random matrices with real, complex or real quaternion elements, and extended to the general variance case for {{μ }1}, methods known for the computation of \\mathop{lim }\\limitsN\\to ∞ < {{μ }i}> are used to compute the large N form of the variances of the exponents. Analogous calculations are performed in the case that the matrices making up PN are products of sub-blocks of random unitary matrices with Haar measure. Furthermore, we make some remarks relating to the coincidence of the Lyapunov exponents and the stability exponents relating to the eigenvalues of PN.

  15. Lyapunov Exponents for Branching Processes in a Random Environment: The Effect of Information

    NASA Astrophysics Data System (ADS)

    Hautphenne, Sophie; Latouche, Guy

    2016-04-01

    We consider multitype branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence of random matrices, which is a notoriously difficult problem. We define Markov chains associated to the branching process, and we construct bounds for the Lyapunov exponent. The bounds are obtained by adding or by removing information: to add information results in a lower bound, to remove information results in an upper bound, and we show that adding less information improves the lower bound. We give a few illustrative examples and we observe that the upper bound is generally more accurate than the lower bounds.

  16. Lyapunov stability and its application to systems of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Kennedy, E. W.

    1979-01-01

    An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

  17. GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS: Nonlinear Local Lyapunov Exponent and Quantification of Local Predictability

    NASA Astrophysics Data System (ADS)

    Ding, Rui-Qiang; Li, Jian-Ping; Ha, Kyung-Ja

    2008-05-01

    Nonlinear local Lyapunov exponent (NLLE) is applied to quantitatively determine the local predictability limit of chaotic systems. As an example, we find that the local predictability limit of Henon attractor varies considerably with time, and some underlying phase-spatial structure does not appear. The local predictability limit of initially adjacent points in phase space may be completely different. This will cause difficulties in making the long-time analogue forecast.

  18. Deterministic Bak Sneppen model: Lyapunov spectrum and avalanches as return times

    NASA Astrophysics Data System (ADS)

    Mendes, R. Vilela

    2006-02-01

    A deterministic version of the Bak-Sneppen model is studied. The role of the Lyapunov spectrum in the onset of scale-free behavior is established, as well as the measure-theoretic nature of the Bak-Sneppen self-organized state. Avalanches are interpreted as return times to a small measure set and the problem of accurate determination of the scaling exponents near the critical barrier is addressed.

  19. A Lower Bound on the Lyapunov Exponent for the Generalized Harper's Model

    NASA Astrophysics Data System (ADS)

    Jitomirskaya, Svetlana; Liu, Wencai

    2016-05-01

    We obtain a lower bound for the Lyapunov exponent of a family of discrete Schrödinger operators (Hu)_n=u_{n+1}+u_{n-1}+2a_1 cos 2π (θ +nα )u_n+2a_2 cos 4π (θ +nα )u_n , that incorporates both a_1 and a_2, thus going beyond the Herman's bound.

  20. Homogeneous piecewise polynomial Lyapunov function for robust stability of uncertain piecewise linear system

    SciTech Connect

    BenAbdallah, Abdallah; Hammami, Mohamed Ali; Kallel, Jalel

    2009-03-05

    In this paper we present some sufficient conditions for the robust stability and stabilization of time invariant uncertain piecewise linear system using homogenous piecewise polynomial Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities which can be numerically solved. An application of the obtained result is given. It consists in resolving the stabilization of piecewise uncertain linear control systems by using a state piecewise linear feedback.

  1. Path Separability of Graphs

    NASA Astrophysics Data System (ADS)

    Diot, Emilie; Gavoille, Cyril

    In this paper we investigate the structural properties of k-path separable graphs, that are the graphs that can be separated by a set of k shortest paths. We identify several graph families having such path separability, and we show that this property is closed under minor taking. In particular we establish a list of forbidden minors for 1-path separable graphs.

  2. Lyapunov Modes of Two-Dimensional Many-Body Systems; Soft Disks, Hard Disks, and Rotors

    NASA Astrophysics Data System (ADS)

    Hoover, Wm. G.; Posch, Harald A.; Forster, Christina; Dellago, Christoph; Zhou, Mary

    2002-11-01

    The dynamical instability of many-body systems can best be characterized through the local Lyapunov spectrum { λ}, its associated eigenvectors { δ}, and the time-averaged spectrum {< λ>}. Each local Lyapunov exponent λ describes the degree of instability associated with a well-defined direction—given by the associated unit vector δ—in the full many-body phase space. For a variety of hard-particle systems it is by now well-established that several of the δ vectors, all with relatively-small values of the time-averaged exponent < λ>, correspond to quite well-defined long-wavelength "modes." We investigate soft particles from the same viewpoint here, and find no convincing evidence for corresponding modes. The situation is similar—no firm evidence for modes—in a simple two-dimensional lattice-rotor model. We believe that these differences are related to the form of the time-averaged Lyapunov spectrum near < λ>=0.

  3. Estimation of Instantaneous Complex Dynamics through Lyapunov Exponents: A Study on Heartbeat Dynamics

    PubMed Central

    Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo

    2014-01-01

    Measures of nonlinearity and complexity, and in particular the study of Lyapunov exponents, have been increasingly used to characterize dynamical properties of a wide range of biological nonlinear systems, including cardiovascular control. In this work, we present a novel methodology able to effectively estimate the Lyapunov spectrum of a series of stochastic events in an instantaneous fashion. The paradigm relies on a novel point-process high-order nonlinear model of the event series dynamics. The long-term information is taken into account by expanding the linear, quadratic, and cubic Wiener-Volterra kernels with the orthonormal Laguerre basis functions. Applications to synthetic data such as the Hénon map and Rössler attractor, as well as two experimental heartbeat interval datasets (i.e., healthy subjects undergoing postural changes and patients with severe cardiac heart failure), focus on estimation and tracking of the Instantaneous Dominant Lyapunov Exponent (IDLE). The novel cardiovascular assessment demonstrates that our method is able to effectively and instantaneously track the nonlinear autonomic control dynamics, allowing for complexity variability estimations. PMID:25170911

  4. Experimental Realization of a Multiscroll Chaotic Oscillator with Optimal Maximum Lyapunov Exponent

    PubMed Central

    Pano-Azucena, Ana Dalia; Carbajal-Gomez, Victor Hugo; Sanchez-Sanchez, Mauro

    2014-01-01

    Nowadays, different kinds of experimental realizations of chaotic oscillators have been already presented in the literature. However, those realizations do not consider the value of the maximum Lyapunov exponent, which gives a quantitative measure of the grade of unpredictability of chaotic systems. That way, this paper shows the experimental realization of an optimized multiscroll chaotic oscillator based on saturated function series. First, from the mathematical description having four coefficients (a, b, c, d1), an optimization evolutionary algorithm varies them to maximize the value of the positive Lyapunov exponent. Second, a realization of those optimized coefficients using operational amplifiers is given. Herein a, b, c, d1 are implemented with precision potentiometers to tune up to four decimals of the coefficients having the range between 0.0001 and 1.0000. Finally, experimental results of the phase-space portraits for generating from 2 to 10 scrolls are listed to show that their associated value for the optimal maximum Lyapunov exponent increases by increasing the number of scrolls, thus guaranteeing a more complex chaotic behavior. PMID:24883379

  5. Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

    SciTech Connect

    Costa, Anthony B.; Green, Jason R.

    2013-08-01

    Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N{sup 2} (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.

  6. An Analysis on Lyapunov Spectrum of Hemodynamic Response in Functional Near Infrared Spectroscopic Measurement during Different Imaginary Motor Tasks

    NASA Astrophysics Data System (ADS)

    Soe, Ni Ni; Nakagawa, Masahiro

    2008-03-01

    This paper presents the novel approach to evaluate the effects of different motor activation tasks of functional near infrared spectroscopy signal (fNIRS). Functional near infrared spectroscopy is a practical non-invasive optical technique to detect characteristic of hemodynamic response during functional activation of the cerebral cortex. In this paper, fNIRS measurements were made in the area of motor cortex. Three subjects, aged 23-30 years, participated in the experiment. The application of the Lyapunov analysis which is a method of nonlinear analysis to analyze and to quantify the chaotic property in the time series of the hemoglobin dynamics of the various motor imagery tasks of fNIRS signal was presented. The strength of chaos was estimated by the Kolmogorov entropy which is related to Lyapunov spectrum. Experimental results show that these nonlinear measures are good discriminators of NIRS signals. The Lyapunov spectra, Lyapunov dimension (DL), and Kolmogorov entropy (K) all indicated chaotic behavior.

  7. The absolute path command

    SciTech Connect

    Moody, A.

    2012-05-11

    The ap command traveres all symlinks in a given file, directory, or executable name to identify the final absolute path. It can print just the final path, each intermediate link along with the symlink chan, and the permissions and ownership of each directory component in the final path. It has functionality similar to "which", except that it shows the final path instead of the first path. It is also similar to "pwd", but it can provide the absolute path to a relative directory from the current working directory.

  8. The absolute path command

    Energy Science and Technology Software Center (ESTSC)

    2012-05-11

    The ap command traveres all symlinks in a given file, directory, or executable name to identify the final absolute path. It can print just the final path, each intermediate link along with the symlink chan, and the permissions and ownership of each directory component in the final path. It has functionality similar to "which", except that it shows the final path instead of the first path. It is also similar to "pwd", but it canmore » provide the absolute path to a relative directory from the current working directory.« less

  9. Taxonomía de asteroides y cometas basada en los espectros de Lyapunov

    NASA Astrophysics Data System (ADS)

    Tancredi, G.; Motta, V.; Froeschlé, C.

    Estudiaremos dos familias de objetos que sufren encuentros cercanos con planetas, a saber: la familia de cometas de Júpiter (JF) y los asteroides cercanos a la Tierra (NEAs). El movimiento de estos objetos es caótico en una escala de tiempo corta. Más aún, debido a los cambios erráticos en los elementos orbitales, la comparación de los valores actuales da poca información acerca de la posible vinculación dinámica entre los objetos de una misma familia. Calculamos una estimación finita de los Exponentes Característicos de Lyapunov (LCE), los llamamos Indicadores Característicos de Lyapunov (LCI) para ambas familias y analizamos las características del espacio de fase donde tiene lugar el movimiento de estos objetos. Integrando en un período suficientemente largo (e.g. 20000 años), encontramos que el LCI alcanza un valor cuasi-constante. La mayoría de los miembros de ambas familias muestran una concentración de los tiempos de Lyapunov (inverso del LCI) de alrededor de 50-100 años (Tancredi, 1995, Astron & Astrop., 299, 288). La concentración de los tiempos de Lyapunov es mayor para la familia de Júpiter que para los NEAs. Entre estos últimos, la menor dispersión se da para aquellos que cruzan la órbita de la Tierra. Se demostró que el espectro de los `indicadores locales' (Froeschlé et. al., 1990, Cel. Mec. 56, 307) o ``números de estiramiento'' (Voglis and Contopoulos, 1994, J. Phys. A 26, 4899) (relacionados con el LCI) son invariantes y nos dan una información más completa sobre el comportamiento caótico. Mediante la comparación de espectros discutimos la similitud entre los objetos de una misma familia y analizamos las diferentes posibles rutas al caos. Los espectros se clasifican mediante la comparación de los momentos de las distribuciones de los `números de estiramiento'. Aplicamos un método de agrupamiento jerárquico (Zappala et. al., 1990, Astron. J. 100, 2030) para identificar ``familias'' de espectros (grupos de espectros

  10. Classification of Bifurcations of Quasi-Periodic Solutions Using Lyapunov Bundles

    NASA Astrophysics Data System (ADS)

    Kamiyama, Kyohei; Komuro, Motomasa; Endo, Tetsuro; Aihara, Kazuyuki

    In continuous-time dynamical systems, a periodic orbit becomes a fixed point on a certain Poincaré section. The eigenvalues of the Jacobian matrix at this fixed point determine the local stability of the periodic orbit. Analogously, a quasi-periodic orbit (2-torus) becomes an invariant closed curve (ICC) on a Poincaré section. From the Lyapunov exponents of an ICC, we can determine the time average of the exponential divergence rate of the orbit, which corresponds to the eigenvalues of a fixed point. We denote the Lyapunov exponent with the smallest nonzero absolute value as the Dominant Lyapunov Exponent (DLE). A local bifurcation manifests as a crossing or touch of the DLE locus with zero. However, the type of bifurcation cannot be determined from the DLE. To overcome this problem, we define the Dominant Lyapunov Bundle (DLB), which corresponds to the dominant eigenvectors of a fixed point. We prove that the DLB of a 1-torus in a map can be classified into four types: A+ (annulus and orientation preserving), A- (annulus and orientation reversing), M (Möbius band), and F (focus). The DLB of a 2-torus in a flow can be classified into three types: A+ × A+, A- × M (equivalently M × A- and M × M), and F × F. From the results, we conjecture the possible local bifurcations in both cases. For the 1-torus in a map, we conjecture that type A+ and A- DLBs correspond to a saddle-node and period-doubling bifurcations, respectively, whereas a type M DLB denotes a double-covering bifurcation, and type F relates to a Neimark-Sacker bifurcation. Similarly, for the 2-torus in a flow, we conjecture that type A+ × A+ DLBs correspond to saddle-node bifurcations, type A- × M DLBs to double-covering bifurcations, and type F × F DLBs to the Neimark-Sacker bifurcations. After introducing the mathematical concepts, we provide a DLB-calculating algorithm and illustrate all of the above bifurcations by examples.

  11. Uniform persistence and upper Lyapunov exponents for monotone skew-product semiflows

    NASA Astrophysics Data System (ADS)

    Novo, Sylvia; Obaya, Rafael; Sanz, Ana M.

    2013-09-01

    Several results of uniform persistence above and below a minimal set of an abstract monotone skew-product semiflow are obtained. When the minimal set has a continuous separation the results are given in terms of the principal spectrum. In the case that the semiflow is generated by the solutions of a family of non-autonomous differential equations of ordinary, delay or parabolic type, the former results are strongly improved. A method of calculus of the upper Lyapunov exponent of the minimal set is also determined.

  12. Fast Lyapunov Indicators OFLI and OMEGNO: Their Relationship and Special Features

    NASA Astrophysics Data System (ADS)

    Shefer, V. A.; Koksin, A. M.

    2016-05-01

    The orthogonal fast Lyapunov indicator (OFLI) and the modification of the mean exponential growth factor of nearby orbits (MEGNO) proposed recently and called the orthogonal MEGNO indicator (OMEGNO) are compared theoretically and numerically. It is shown that these indicators are expressed in terms of the same base function. Moreover, the OMEGNO, as well as the OFLI, is expressed analytically through the base function. A numerical comparison is performed on examples of studying the dynamics in the planar circular restricted three-body problem. These examples help one to understand the special features in the performance of both indicators.

  13. Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices

    NASA Astrophysics Data System (ADS)

    Szendro, Ivan G.; Pazó, Diego; Rodríguez, Miguel A.; López, Juan M.

    2007-08-01

    The spatiotemporal dynamics of Lyapunov vectors (LVs) in spatially extended chaotic systems is studied by means of coupled-map lattices. We determine intrinsic length scales and spatiotemporal correlations of LVs corresponding to the leading unstable directions by translating the problem to the language of scale-invariant growing surfaces. We find that the so-called characteristic LVs exhibit spatial localization, strong clustering around given spatiotemporal loci, and remarkable dynamic scaling properties of the corresponding surfaces. In contrast, the commonly used backward LVs (obtained through Gram-Schmidt orthogonalization) spread all over the system and do not exhibit dynamic scaling due to artifacts in the dynamical correlations by construction.

  14. Weighted aggregation

    NASA Technical Reports Server (NTRS)

    Feiveson, A. H. (Principal Investigator)

    1979-01-01

    The use of a weighted aggregation technique to improve the precision of the overall LACIE estimate is considered. The manner in which a weighted aggregation technique is implemented given a set of weights is described. The problem of variance estimation is discussed and the question of how to obtain the weights in an operational environment is addressed.

  15. Distributional properties of stochastic shortest paths for smuggled nuclear material

    SciTech Connect

    Cuellar, Leticia; Pan, Feng; Roach, Fred; Saeger, Kevin J

    2011-01-05

    The shortest path problem on a network with fixed weights is a well studied problem with applications to many diverse areas such as transportation and telecommunications. We are particularly interested in the scenario where a nuclear material smuggler tries to succesfully reach herlhis target by identifying the most likely path to the target. The identification of the path relies on reliabilities (weights) associated with each link and node in a multi-modal transportation network. In order to account for the adversary's uncertainty and to perform sensitivity analysis we introduce random reliabilities. We perform some controlled experiments on the grid and present the distributional properties of the resulting stochastic shortest paths.

  16. Graphs and matroids weighted in a bounded incline algebra.

    PubMed

    Lu, Ling-Xia; Zhang, Bei

    2014-01-01

    Firstly, for a graph weighted in a bounded incline algebra (or called a dioid), a longest path problem (LPP, for short) is presented, which can be considered the uniform approach to the famous shortest path problem, the widest path problem, and the most reliable path problem. The solutions for LPP and related algorithms are given. Secondly, for a matroid weighted in a linear matroid, the maximum independent set problem is studied. PMID:25126607

  17. Evaluation of nonlinear properties of epileptic activity using largest Lyapunov exponent

    NASA Astrophysics Data System (ADS)

    Medvedeva, Tatiana M.; Lüttjohann, Annika; van Luijtelaar, Gilles; Sysoev, Ilya V.

    2016-04-01

    Absence seizures are known to be highly non-linear large amplitude oscillations with a well pronounced main time scale. Whilst the appearance of the main frequency is usually considered as a transition from noisy complex dynamics of baseline EEG to more regular absence activity, the dynamical properties of this type of epileptiformic activity in genetic absence models was not studied precisely. Here, the estimation of the largest Lyapunov exponent from intracranial EEGs of 10 WAG/Rij rats (genetic model of absence epilepsy) was performed. Fragments of 10 seizures and 10 episodes of on-going EEG each of 4 s length were used for each animal, 3 cortical and 2 thalamic channels were analysed. The method adapted for short noisy data was implemented. The positive values of the largest Lyapunov exponent were found as for baseline as for spike wave discharges (SWDs), with values for SWDs being significantly less than for on-going activity. Current findings may indicate that SWD is a chaotic process with a well pronounced main timescale rather than a periodic regime. Also, the absence activity was shown to be less chaotic than the baseline one.

  18. A review of the hydrodynamic Lyapunov modes of hard disk systems

    NASA Astrophysics Data System (ADS)

    Morriss, Gary P.; Truant, Daniel P.

    2013-06-01

    A review of the results obtained for hard disk fluids confined to a quasi-one-dimensional (QOD) system is presented. One of the main achievements in recent years has been determining the hydrodynamic Lyapunov modes (HLMs) as covariant stable and unstable manifolds defined by k-vector analogues of the zero-exponent subspace of conserved quantities. The tangent space dynamics allows an interpretation of the HLMs as reduced hydrodynamic fields over the perturbations and is expanded upon in this paper. The time evolution of these modes is governed by the dynamics of conjugate pairs of stable and unstable directions. Each pair is seen to interact in a subspace almost completely separated from other vectors; the modes undergo a rotation until they are collinear with the stable or unstable manifold. The angle distributions between these covariant stable and unstable HLMs are also determined, and tangencies are not observed for a generic chaotic trajectory. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’.

  19. Lyapunov Redesign of Model Reference Adaptive Control System for long term ventilation of lung.

    PubMed

    Woo, J; Rootenberg, J

    1975-01-01

    A lyapunov redesign of Model reference adaptive control system for a long term, automatically regulated, ventilatory system is presented. A fixed resistance-capacitance RC analog lung model is used to generate a desirable (reference response) alveolar pressure. The instantaneous difference in alveolar pressures between the patient and its model is fed to an adaptive controller. The controller is designed to adjust the patient's inflating pressure in such a way as to reduce the instantaneous difference in the alveolar pressures to zero. The adaptive control system described can be implemented provided the patient's alveolar pressure is continuously measurable. Unfortunately, this measurement is impossible to realize; therefore, a method to estimate the continuous alveolar pressure of the patient is to be developed. This estimation is achieved indirectly from the identification process of the patient's respiratory parameter. The same Lyapunov redesign is used in this identification process. Digital simulation of the control of the patient's inflating pressure and the identification process, as well as the simulation of the combined system, were performed. The result has demonstrated the ability of this adaptive system to perform in a fast and stable manner. PMID:1184357

  20. Gain-scheduled H∞ control via parameter-dependent Lyapunov functions

    NASA Astrophysics Data System (ADS)

    Chumalee, Sunan; Whidborne, James F.

    2015-01-01

    Synthesising a gain-scheduled output feedback H∞ controller via parameter-dependent Lyapunov functions for linear parameter-varying (LPV) plant models involves solving an infinite number of linear matrix inequalities (LMIs). In practice, for affine LPV models, a finite number of LMIs can be achieved using convexifying techniques. This paper proposes an alternative approach to achieve a finite number of LMIs. By simple manipulations on the bounded real lemma inequality, a symmetric matrix polytope inequality can be formed. Hence, the LMIs need only to be evaluated at all vertices of such a symmetric matrix polytope. In addition, a construction technique of the intermediate controller variables is also proposed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameters. Computational results on a numerical example using the approach were compared with those from a multi-convexity approach in order to demonstrate the impacts of the approach on parameter-dependent Lyapunov-based stability and performance analysis. Furthermore, numerical simulation results show the effectiveness of these proposed techniques.

  1. 20 years of reprocessed Lyapunov Exponents from altimetry available on AVISO+

    NASA Astrophysics Data System (ADS)

    Pujol, Marie-Isabelle; Faugere, Yannice; D'Ovidio, Francesco; Morrow, Rosemary; Bronner, Emilie; Picot, Nicolas

    2015-04-01

    Altimetry-derived maps of Lyapunov exponents (LEs) provide proxies of (sub-)mesoscale transport fronts. They are being increasingly used in physical, biogeochemical, and ecological applications, ranging from real-time support to field studies to co-localisation of animal tracking with Lagrangian Coherent Structures. Their calculation however is more complex than standard Eulerian diagnostics, because it requires a Lagrangian algorithms which integrates the velocity field. During the past 20 years, in parallel with the altimeter measurement Level2 (a.k.a [O/I]GDR) to Level3 and Level4 (along-track cross-calibrated SLA, and multiple sensor merged maps) processing, different applications and derivated Level4+ products were developed by AVISO+. In order to better serve the users need, and in collaboration with different laboratories (LOCEAN and CTOH), the LEs and vectors are computed over the 21-year altimeter period and over the global ocean within the SSALTO/DUACS project. This product provides the position, and intensity, and orientation of fronts induced by the mesoscale eddies and underlining part of sub-mesoscale activity. We present here the Lyapunov products that will be available on AVISO+ early 2015, and some examples of applications.

  2. Passivity/Lyapunov based controller design for trajectory tracking of flexible joint manipulators

    NASA Technical Reports Server (NTRS)

    Sicard, Pierre; Wen, John T.; Lanari, Leonardo

    1992-01-01

    A passivity and Lyapunov based approach for the control design for the trajectory tracking problem of flexible joint robots is presented. The basic structure of the proposed controller is the sum of a model-based feedforward and a model-independent feedback. Feedforward selection and solution is analyzed for a general model for flexible joints, and for more specific and practical model structures. Passivity theory is used to design a motor state-based controller in order to input-output stabilize the error system formed by the feedforward. Observability conditions for asymptotic stability are stated and verified. In order to accommodate for modeling uncertainties and to allow for the implementation of a simplified feedforward compensation, the stability of the system is analyzed in presence of approximations in the feedforward by using a Lyapunov based robustness analysis. It is shown that under certain conditions, e.g., the desired trajectory is varying slowly enough, stability is maintained for various approximations of a canonical feedforward.

  3. Lyapunov-Based Sensor Failure Detection And Recovery For The Reverse Water Gas Shift Process

    NASA Technical Reports Server (NTRS)

    Haralambous, Michael G.

    2001-01-01

    Livingstone, a model-based AI software system, is planned for use in the autonomous fault diagnosis, reconfiguration, and control of the oxygen-producing reverse water gas shift (RWGS) process test-bed located in the Applied Chemistry Laboratory at KSC. In this report the RWGS process is first briefly described and an overview of Livingstone is given. Next, a Lyapunov-based approach for detecting and recovering from sensor failures, differing significantly from that used by Livingstone, is presented. In this new method, models used are in terms of the defining differential equations of system components, thus differing from the qualitative, static models used by Livingstone. An easily computed scalar inequality constraint, expressed in terms of sensed system variables, is used to determine the existence of sensor failures. In the event of sensor failure, an observer/estimator is used for determining which sensors have failed. The theory underlying the new approach is developed. Finally, a recommendation is made to use the Lyapunov-based approach to complement the capability of Livingstone and to use this combination in the RWGS process.

  4. LYAPUNOV-Based Sensor Failure Detection and Recovery for the Reverse Water Gas Shift Process

    NASA Technical Reports Server (NTRS)

    Haralambous, Michael G.

    2002-01-01

    Livingstone, a model-based AI software system, is planned for use in the autonomous fault diagnosis, reconfiguration, and control of the oxygen-producing reverse water gas shift (RWGS) process test-bed located in the Applied Chemistry Laboratory at KSC. In this report the RWGS process is first briefly described and an overview of Livingstone is given. Next, a Lyapunov-based approach for detecting and recovering from sensor failures, differing significantly from that used by Livingstone, is presented. In this new method, models used are in t e m of the defining differential equations of system components, thus differing from the qualitative, static models used by Livingstone. An easily computed scalar inequality constraint, expressed in terms of sensed system variables, is used to determine the existence of sensor failures. In the event of sensor failure, an observer/estimator is used for determining which sensors have failed. The theory underlying the new approach is developed. Finally, a recommendation is made to use the Lyapunov-based approach to complement the capability of Livingstone and to use this combination in the RWGS process.

  5. 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.

  6. Covariant Lyapunov Vectors in a Coupled Atmosphere-Ocean Model - Multiscale Effects and Geometric Degeneracy

    NASA Astrophysics Data System (ADS)

    Lucarini, Valerio; Vannitsem, Stephane

    2016-04-01

    We study a simplified coupled atmosphere-ocean model using the formalism of covariant Lyapunov vectors (CLVs), which link physically-based directions of perturbations to growth/decay rates. The model is obtained via a severe truncation of quasi-geostrophic equations for the two fluids, and includes a simple yet physically meaningful representation of their dynamical/thermodynamical coupling. The model has 36 degrees of freedom, and the parameters are chosen so that a chaotic behaviour is observed. One finds two positive Lyapunov exponents (LEs), sixteen negative LEs, and eighteen near-zero LEs. The presence of many near-zero LEs results from the vast time-scale separation between the characteristic time scales of the two fluids, and leads to nontrivial error growth properties in the tangent space spanned by the corresponding CLVs, which are geometrically very degenerate. Such CLVs correspond to two different classes of ocean/atmosphere coupled modes. The tangent space spanned by the CLVs corresponding to the positive and negative LEs has, instead, a non-pathological behaviour, and one can construct robust large deviations laws for the finite time LEs, thus providing a universal model for assessing predictability on long to ultra-long scales along such directions. Finally, it is somewhat surprising to find that the tangent space of the unstable manifold has strong projection on both atmospheric and oceanic components, thus giving evidence that coupled modes are responsible for the instability of the flow.

  7. Backward and covariant Lyapunov vectors and exponents for hard-disk systems with a steady heat current.

    PubMed

    Truant, Daniel P; Morriss, Gary P

    2014-11-01

    The covariant Lyapunov analysis is generalized to systems attached to deterministic thermal reservoirs that create a heat current across the system and perturb it away from equilibrium. The change in the Lyapunov exponents as a function of heat current is described and explained. Both the nonequilibrium backward and covariant hydrodynamic Lyapunov modes are analyzed and compared. The movement of the converged angle between the hydrodynamic stable and unstable conjugate manifolds with the free flight time of the dynamics is accurately predicted for any nonequilibrium system simply as a function of their exponent. The nonequilibrium positive and negative LP mode frequencies are found to be asymmetrical, causing the negative mode to oscillate between the two functional forms of each mode in the positive conjugate mode pair. This in turn leads to the angular distributions between the conjugate modes to oscillate symmetrically about π/2 at a rate given by the difference between the positive and negative mode frequencies. PMID:25493858

  8. Weight Control

    MedlinePlus

    ... obese. Achieving a healthy weight can help you control your cholesterol, blood pressure and blood sugar. It ... use more calories than you eat. A weight-control strategy might include Choosing low-fat, low-calorie ...

  9. Body Weight

    MedlinePlus

    ... heart failure, and kidney disease. Good nutrition and exercise can help in losing weight. Eating extra calories within a well-balanced diet and treating any underlying medical problems can help to add weight.

  10. Body Weight

    MedlinePlus

    ... to medicines, thyroid problems, heart failure, and kidney disease. Good nutrition and exercise can help in losing weight. Eating extra calories within a well-balanced diet and treating any underlying medical problems can help to add weight.

  11. The universal path integral

    NASA Astrophysics Data System (ADS)

    Lloyd, Seth; Dreyer, Olaf

    2016-02-01

    Path integrals calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration. This paper defines a universal path integral, which sums over all computable structures. This path integral contains as sub-integrals all possible computable path integrals, including those of field theory, the standard model of elementary particles, discrete models of quantum gravity, string theory, etc. The universal path integral possesses a well-defined measure that guarantees its finiteness. The probabilities for events corresponding to sub-integrals can be calculated using the method of decoherent histories. The universal path integral supports a quantum theory of the universe in which the world that we see around us arises out of the interference between all computable structures.

  12. Predictable nonwandering localization of covariant Lyapunov vectors and cluster synchronization in scale-free networks of chaotic maps.

    PubMed

    Kuptsov, Pavel V; Kuptsova, Anna V

    2014-09-01

    Covariant Lyapunov vectors for scale-free networks of Hénon maps are highly localized. We revealed two mechanisms of the localization related to full and phase cluster synchronization of network nodes. In both cases the localization nodes remain unaltered in the course of the dynamics, i.e., the localization is nonwandering. Moreover, this is predictable: The localization nodes are found to have specific dynamical and topological properties and they can be found without computing of the covariant vectors. This is an example of explicit relations between the system topology, its phase-space dynamics, and the associated tangent-space dynamics of covariant Lyapunov vectors. PMID:25314498

  13. A Model for Diagnosing Breast Cancerous Tissue from Thermal Images Using Active Contour and Lyapunov Exponent

    PubMed Central

    GHAYOUMI ZADEH, Hossein; HADDADNIA, Javad; MONTAZERI, Alimohammad

    2016-01-01

    Background: The segmentation of cancerous areas in breast images is important for the early detection of disease. Thermal imaging has advantages, such as being non-invasive, non-radiation, passive, quick, painless, inexpensive, and non-contact. Imaging technique is the focus of this research. Methods: The proposed model in this paper is a combination of surf and corners that are very resistant. Obtained features are resistant to changes in rotation and revolution then with the help of active contours, this feature has been used for segmenting cancerous areas. Results: Comparing the obtained results from the proposed method and mammogram show that proposed method is Accurate and appropriate. Benign and malignance of segmented areas are detected by Lyapunov exponent. Values obtained include TP=91.31%, FN=8.69%, FP=7.26%. Conclusion: The proposed method can classify those abnormally segmented areas of the breast, to the Benign and malignant cancer. PMID:27398339

  14. Volterra-type Lyapunov functions for fractional-order epidemic systems

    NASA Astrophysics Data System (ADS)

    Vargas-De-León, Cruz

    2015-07-01

    In this paper we prove an elementary lemma which estimates fractional derivatives of Volterra-type Lyapunov functions in the sense Caputo when α ∈ (0, 1) . Moreover, by using this result, we study the uniform asymptotic stability of some Caputo-type epidemic systems with a pair of fractional-order differential equations. These epidemic systems are the Susceptible-Infected-Susceptible (SIS), Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) models and Ross-Macdonald model for vector-borne diseases. We show that the unique endemic equilibrium is uniformly asymptotically stable if the basic reproductive number is greater than one. We illustrate our theoretical results with numerical simulations using the Adams-Bashforth-Moulton scheme implemented in the fde12 Matlab function.

  15. Optimal strategy for low-thrust spiral trajectories using Lyapunov-based guidance

    NASA Astrophysics Data System (ADS)

    Dalin, Yang; Bo, Xu; Youtao, Gao

    2015-09-01

    It is difficult and time-consuming to search the optimal low-thrust spiral trajectories. This is because the analytical solutions for long powered arcs are not available, and hundreds or even thousands of orbital revolutions are involved in transfer trajectories. This paper examines a smart guidance scheme based on Lyapunov feedback control which overcomes the difficulties found in control gains steering. In this guidance scheme, the artificial neural network is adopted to implement gains steering and the evolutionary algorithm is used as the learning algorithm for artificial neural network. In this paper, Earth J2 perturbation and Earth-shadow eclipse effects are considered. Finally, a comparison with solutions given by the literature demonstrates the effectiveness of the proposed method. Numerical simulation results show that the time-varying gains guidance scheme can decrease the transfer time with respect to constant gains cases.

  16. Estimating the largest Lyapunov exponent and noise level from chaotic time series.

    PubMed

    Yao, Tian-Liang; Liu, Hai-Feng; Xu, Jian-Liang; Li, Wei-Feng

    2012-09-01

    A novel method for estimating simultaneously the largest Lyapunov exponent (LLE) and noise level (NL) from a noisy chaotic time series is presented in this paper. We research the influence of noise on the average distance of different pairs of points in an embedding phase space and provide a rescaled formula for calculating the LLE when the time series is contaminated with noise. Our algorithm is proposed based on this formula and the invariant of the LLE in different dimensional embedding phase spaces. With numerical simulation, we find that the proposed method provides a reasonable estimate of the LLE and NL when the NL is less than 10% of the signal content. The comparison with Kantz algorithm shows that our method gives more accurate results of the LLE for the noisy time series. Furthermore, our method is not sensitive to the distribution of the noise. PMID:23020441

  17. Refining finite-time Lyapunov exponent ridges and the challenges of classifying them

    NASA Astrophysics Data System (ADS)

    Allshouse, Michael R.; Peacock, Thomas

    2015-08-01

    While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.

  18. A method to calculate finite-time Lyapunov exponents for inertial particles in incompressible flows

    NASA Astrophysics Data System (ADS)

    Garaboa-Paz, D.; Pérez-Muñuzuri, V.

    2015-10-01

    The present study aims to improve the calculus of finite-time Lyapunov exponents (FTLEs) applied to describe the transport of inertial particles in a fluid flow. To this aim, the deformation tensor is modified to take into account that the stretching rate between particles separated by a certain distance is influenced by the initial velocity of the particles. Thus, the inertial FTLEs (iFTLEs) are defined in terms of the maximum stretching between infinitesimally close trajectories that have different initial velocities. The advantages of this improvement, if compared to the standard method (Shadden et al., 2005), are discussed for the double-gyre flow and the meandering jet flow. The new method allows one to identify the initial velocity that inertial particles must have in order to maximize their dispersion.

  19. Refining finite-time Lyapunov exponent ridges and the challenges of classifying them.

    PubMed

    Allshouse, Michael R; Peacock, Thomas

    2015-08-01

    While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of a FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by a FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model. PMID:26328581

  20. Dynamic stability of running: The effects of speed and leg amputations on the maximal Lyapunov exponent

    NASA Astrophysics Data System (ADS)

    Look, Nicole; Arellano, Christopher J.; Grabowski, Alena M.; McDermott, William J.; Kram, Rodger; Bradley, Elizabeth

    2013-12-01

    In this paper, we study dynamic stability during running, focusing on the effects of speed, and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without unilateral transtibial amputations running at a wide range of speeds. We find that the dynamics of the affected leg with the running-specific prosthesis are less stable than the dynamics of the unaffected leg and also less stable than the biological legs of the non-amputee runners. Surprisingly, we find that the center-of-mass dynamics of runners with two intact biological legs are slightly less stable than those of runners with amputations. Our results suggest that while leg asymmetries may be associated with instability, runners may compensate for this effect by increased control of their center-of-mass dynamics.

  1. Dynamic stability of running: The effects of speed and leg amputations on the maximal Lyapunov exponent

    SciTech Connect

    Look, Nicole; Arellano, Christopher J.; Grabowski, Alena M.; Kram, Rodger; McDermott, William J.; Bradley, Elizabeth

    2013-12-15

    In this paper, we study dynamic stability during running, focusing on the effects of speed, and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without unilateral transtibial amputations running at a wide range of speeds. We find that the dynamics of the affected leg with the running-specific prosthesis are less stable than the dynamics of the unaffected leg and also less stable than the biological legs of the non-amputee runners. Surprisingly, we find that the center-of-mass dynamics of runners with two intact biological legs are slightly less stable than those of runners with amputations. Our results suggest that while leg asymmetries may be associated with instability, runners may compensate for this effect by increased control of their center-of-mass dynamics.

  2. Predictability of epileptic seizures: a comparative study using Lyapunov exponent and entropy based measures.

    PubMed

    Sabesan, Shivkumar; Narayanan, K; Prasad, Awadhesh; Spanias, A; Sackellares, J C; Iasemidis, L D

    2003-01-01

    In this paper, a comparative study involving measures from the theory of chaos, namely the short-term largest Lyapunov exponent, Shannon and Kullback-Leibler entropies from information theory, has been carried out in terms of their predictability of temporal lobe epileptic seizures. These three measures are estimated from electroencephalographic (EEG) recordings with sub-dural and in-depth electrodes from various brain locations in patients with temporal lobe epilepsy. Techniques from optimization theory are applied to select optimal sets of electrodes whose dynamics is then followed over time. Results from analysis of multiple seizures in two epileptic patients with these measures are presented and compared in terms of their ability to identify pre-ictal dynamical entrainment well ahead of seizure onset time. PMID:12724881

  3. Pinning Synchronization of Directed Networks With Switching Topologies: A Multiple Lyapunov Functions Approach.

    PubMed

    Wen, Guanghui; Yu, Wenwu; Hu, Guoqiang; Cao, Jinde; Yu, Xinghuo

    2015-12-01

    This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from M -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results. PMID:26595418

  4. On the validity of the conjugate pairing rule for Lyapunov exponents

    SciTech Connect

    Bonetto, F.; Cohen, E.G.D.; Pugh, C.

    1998-08-01

    For Hamiltonian systems subject to an external potential which in the presence of a thermostat will reach a nonequilibrium stationary state Dettmann and Morriss proved a strong conjugate pairing rule (SCPR) for pairs of Lyapunov exponents in the case of isokinetic (IK) stationary states which have a given kinetic energy. This SCPR holds for all initial phases of the system, all times t, and all numbers of particles N. This proof was generalized by Wojtkowski and Liverani to include hard interparticle potentials. A geometrical reformulation of those results is presented. The present paper proves numerically, using periodic orbits for the Lorentz gas, that SCPR cannot hold for isoenergetic (IE) stationary states which have a given total internal energy. In that case strong evidence is obtained for CPR to hold for large N and t, where it can be conjectured that the larger N, the smaller t will be. This suffices for statistical mechanics.

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

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

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

  6. Effective power-law dependence of Lyapunov exponents on the central mass in galaxies

    NASA Astrophysics Data System (ADS)

    Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

    2015-04-01

    Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L ∝ mp between the mean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p ≈ 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local `stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q ≈ 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x1 family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution ofx galaxies are discussed.

  7. Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

    NASA Technical Reports Server (NTRS)

    Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

    2015-01-01

    Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

  8. Dynamical Analysis of Blocking Events: Spatial and Temporal Fluctuations of Covariant Lyapunov Vectors

    NASA Astrophysics Data System (ADS)

    Schubert, Sebastian; Lucarini, Valerio

    2016-04-01

    One of the most relevant weather regimes in the mid latitudes atmosphere is the persistent deviation from the approximately zonally symmetric jet stream to the emergence of so-called blocking patterns. Such configurations are usually connected to exceptional local stability properties of the flow which come along with an improved local forecast skills during the phenomenon. It is instead extremely hard to predict onset and decay of blockings. Covariant Lyapunov Vectors (CLVs) offer a suitable characterization of the linear stability of a chaotic flow, since they represent the full tangent linear dynamics by a covariant basis which explores linear perturbations at all time scales. Therefore, we will test whether CLVs feature a signature of the blockings. We examine the CLVs for a quasi-geostrophic beta-plane two-layer model in a periodic channel baroclinically driven by a meridional temperature gradient ΔT. An orographic forcing enhances the emergence of localized blocked regimes. We detect the blocking events of the channel flow with a Tibaldi-Molteni scheme adapted to the periodic channel. When blocking occurs, the global growth rates of the fastest growing CLVs are significantly higher. Hence against intuition, globally the circulation is more unstable in blocked phases. Such an increase in the finite time Lyapunov exponents with respect to the long term average is attributed to stronger barotropic and baroclinic conversion in the case of high temperature gradients, while for low values of ΔT, the effect is only due to stronger barotropic instability. For the localization of the CLVs, we compare the meridionally averaged variance of the CLVs during blocked and unblocked phases. We find that on average the variance of the CLVs is clustered around the center of blocking. These results show that the blocked flow affects all time scales and processes described by the CLVs.

  9. Automated path planning of the Payload Inspection and Processing System

    NASA Technical Reports Server (NTRS)

    Byers, Robert M.

    1994-01-01

    The Payload Changeout Room Inspection and Processing System (PIPS) is a highly redundant manipulator intended for performing tasks in the crowded and sensitive environment of the Space Shuttle Orbiter payload bay. Its dexterity will be exploited to maneuver the end effector in a workspace populated with obstacles. A method is described by which the end effector of a highly redundant manipulator is directed toward a target via a Lyapunov stability function. A cost function is constructed which represents the distance from the manipulator links to obstacles. Obstacles are avoided by causing the vector of joint parameters to move orthogonally to the gradient of the workspace cost function. A C language program implements the algorithm to generate a joint history. The resulting motion is graphically displayed using the Interactive Graphical Robot Instruction Program (IGRIP) produced by Deneb Robotics. The graphical simulation has the potential to be a useful tool in path planning for the PIPS in the Shuttle Payload Bay environment.

  10. Indirect adaptive control for synchronous generator: comparison of MLP/RBF neural networks approach with Lyapunov stability analysis.

    PubMed

    Park, Jung-Wook; Harley, Ronald G; Venayagamoorthy, Ganesh K

    2004-03-01

    This paper compares two indirect adaptive neurocontrollers, namely a multilayer perceptron neurocontroller (MLPNC) and a radial basis function neurocontroller (RBFNC) to control a synchronous generator. The different damping and transient performances of two neurocontrollers are compared with those of conventional linear controllers, and analyzed based on the Lyapunov direct method. PMID:15384538

  11. Phase-space growth rates, local Lyapunov spectra, and symmetry breaking for time-reversible dissipative oscillators

    NASA Astrophysics Data System (ADS)

    Hoover, Wm. G.; Hoover, Carol G.; Grond, Florian

    2008-08-01

    We investigate and discuss the time-reversible nature of phase-space instabilities for several flows, x˙=f(x). The flows describe thermostated oscillator systems in from two through eight phase-space dimensions. We determine the local extremal phase-space growth rates, which bound the instantaneous comoving Lyapunov exponents. The extremal rates are point functions which vary continuously in phase space. The extremal rates can best be determined with a "singular-value decomposition" algorithm. In contrast to these precisely time-reversible local "point function" values, a time-reversibility analysis of the comoving Lyapunov spectra is more complex. The latter analysis is nonlocal and requires the additional storing and playback of relatively long (billion-step) trajectories. All the oscillator models studied here show the same time reversibility symmetry linking their time-reversed and time-averaged "global" Lyapunov spectra. Averaged over a long-time-reversed trajectory, each of the long-time-averaged Lyapunov exponents simply changes signs. The negative/positive sign of the summed-up and long-time-averaged spectra in the forward/backward time directions is the microscopic analog of the Second Law of Thermodynamics. This sign changing of the individual global exponents contrasts with typical more-complex instantaneous "local" behavior, where there is no simple relation between the forward and backward exponents other than the local (instantaneous) dissipative constraint on their sum. As the extremal rates are point functions, they too always satisfy the sum rule.

  12. Redundancy of space manipulator on free-flying vehicle and its nonholonomic path planning

    NASA Technical Reports Server (NTRS)

    Nakamura, Yoshihiko; Mukherjee, Ranjan

    1989-01-01

    The nonholonomic mechanical structure of space robots and path planning is discussed. The angular momentum conservation works as a nonholonomic constraint while the linear momentum conservation is a holonomic one. Thus, a vehicle with a 6 d.o.f. manipulator is described as a 9 variable system with 6 inputs. This implies the possibility of controlling the vehicle orientation and the joint variables of the manipulator by actuating the joint variables, but only if the trajectory is carefully planned; however, both of them cannot be controlled independently. It means that by assuming feasible-path planning, a system that consists of a vehicle and a 6 d.o.f. manipulator can be utilized as 9 d.o.f. system. Initially, the nonholonomic mechanical structure of space vehicle/manipulator system is shown. Then a path planning scheme for nonholonomic systems is proposed using Lyapunov functions.

  13. Path-tracking control of underactuated ships under tracking error constraints

    NASA Astrophysics Data System (ADS)

    Do, Khac Duc

    2015-12-01

    This paper presents a constructive design of new controllers that force underactuated ships under constant or slow time-varying sea loads to asymptotically track a parameterized reference path, that guarantees the distance from the ship to the reference path always be within a specified value. The control design is based on a global exponential disturbance observer, a transformation of the ship dynamics to an almost spherical form, an interpretation of the tracking errors in an earth-fixed frame, an introduction of dynamic variables to compensate for relaxation of the reference path generation, p-times differentiable step functions, and backstepping and Lyapunov's direct methods. The effectiveness of the proposed results is illustrated through simulations.

  14. Weight Management

    MedlinePlus

    ... Quit Smoking Benefits of Quitting Health Effects of Smoking Secondhand Smoke Withdrawal Ways to Quit QuitGuide Pregnancy & Motherhood Pregnancy & Motherhood Before Your Baby is Born From Birth to 2 Years Quitting for Two SmokefreeMom Healthy Kids Parenting & ... Weight Management Weight Management ...

  15. Tortuous path chemical preconcentrator

    DOEpatents

    Manginell, Ronald P.; Lewis, Patrick R.; Adkins, Douglas R.; Wheeler, David R.; Simonson, Robert J.

    2010-09-21

    A non-planar, tortuous path chemical preconcentrator has a high internal surface area having a heatable sorptive coating that can be used to selectively collect and concentrate one or more chemical species of interest from a fluid stream that can be rapidly released as a concentrated plug into an analytical or microanalytical chain for separation and detection. The non-planar chemical preconcentrator comprises a sorptive support structure having a tortuous flow path. The tortuosity provides repeated twists, turns, and bends to the flow, thereby increasing the interfacial contact between sample fluid stream and the sorptive material. The tortuous path also provides more opportunities for desorption and readsorption of volatile species. Further, the thermal efficiency of the tortuous path chemical preconcentrator is comparable or superior to the prior non-planar chemical preconcentrator. Finally, the tortuosity can be varied in different directions to optimize flow rates during the adsorption and desorption phases of operation of the preconcentrator.

  16. A Path to Discovery

    ERIC Educational Resources Information Center

    Stegemoller, William; Stegemoller, Rebecca

    2004-01-01

    The path taken and the turns made as a turtle traces a polygon are examined to discover an important theorem in geometry. A unique tool, the Angle Adder, is implemented in the investigation. (Contains 9 figures.)

  17. Lyapunov-based control of limit cycle oscillations in uncertain aircraft systems

    NASA Astrophysics Data System (ADS)

    Bialy, Brendan

    Store-induced limit cycle oscillations (LCO) affect several fighter aircraft and is expected to remain an issue for next generation fighters. LCO arises from the interaction of aerodynamic and structural forces, however the primary contributor to the phenomenon is still unclear. The practical concerns regarding this phenomenon include whether or not ordnance can be safely released and the ability of the aircrew to perform mission-related tasks while in an LCO condition. The focus of this dissertation is the development of control strategies to suppress LCO in aircraft systems. The first contribution of this work (Chapter 2) is the development of a controller consisting of a continuous Robust Integral of the Sign of the Error (RISE) feedback term with a neural network (NN) feedforward term to suppress LCO behavior in an uncertain airfoil system. The second contribution of this work (Chapter 3) is the extension of the development in Chapter 2 to include actuator saturation. Suppression of LCO behavior is achieved through the implementation of an auxiliary error system that features hyperbolic functions and a saturated RISE feedback control structure. Due to the lack of clarity regarding the driving mechanism behind LCO, common practice in literature and in Chapters 2 and 3 is to replicate the symptoms of LCO by including nonlinearities in the wing structure, typically a nonlinear torsional stiffness. To improve the accuracy of the system model a partial differential equation (PDE) model of a flexible wing is derived (see Appendix F) using Hamilton's principle. Chapters 4 and 5 are focused on developing boundary control strategies for regulating the bending and twisting deformations of the derived model. The contribution of Chapter 4 is the construction of a backstepping-based boundary control strategy for a linear PDE model of an aircraft wing. The backstepping-based strategy transforms the original system to a exponentially stable system. A Lyapunov-based stability

  18. Weight simulator

    NASA Technical Reports Server (NTRS)

    Howard, W. H.; Young, D. R.

    1972-01-01

    Device applies compressive force to bone to minimize loss of bone calcium during weightlessness or bedrest. Force is applied through weights, or hydraulic, pneumatic or electrically actuated devices. Device is lightweight and easy to maintain and operate.

  19. A Lyapunov-Razumikhin approach for stability analysis of logistics networks with time-delays

    NASA Astrophysics Data System (ADS)

    Dashkovskiy, Sergey; Karimi, Hamid Reza; Kosmykov, Michael

    2012-05-01

    Logistics network represents a complex system where different elements that are logistic locations interact with each other. This interaction contains delays caused by time needed for delivery of the material. Complexity of the system, time-delays and perturbations in a customer demand may cause unstable behaviour of the network. This leads to the loss of the customers and high inventory costs. Thus the investigation of the network on stability is desired during its design. In this article we consider local input-to-state stability of such logistics networks. Their behaviour is described by a functional differential equation with a constant time-delay. We are looking for verifiable conditions that guarantee stability of the network under consideration. Lyapunov-Razumikhin functions and the local small gain condition are utilised to obtain such conditions. Our stability conditions for the logistics network are based on the information about the interconnection properties between logistic locations and their production rates. Finally, numerical results are provided to demonstrate the proposed approach.

  20. Phenomenological study of irregular cellular automata based on Lyapunov exponents and Jacobians.

    PubMed

    Baetens, Jan M; De Baets, Bernard

    2010-09-01

    Originally, cellular automata (CA) have been defined upon regular tessellations of the n-dimensional Euclidean space, while CA on irregular tessellations have received only little attention from the scientific community, notwithstanding serious shortcomings are associated with the former manner of subdividing Rn. In this paper we present a profound phenomenological study of two-state, two-dimensional irregular CA from a dynamical systems viewpoint. We opted to exploit properly defined quantitative measures instead of resorting to qualitative methods for discriminating between behavioral classes. As such, we employ Lyapunov exponents, measuring the divergence rate of close trajectories in phase space, and Jacobians, formulated using Boolean derivatives and expressing the sensitivity of a cellular automaton to its inputs. Both are stated for two-state CA on irregular tessellations, enabling us to characterize these discrete dynamical systems, and advancing us to propose a classification scheme for this CA family. In addition, a relationship between these quantitative measures is established in extension of the insights already developed for the classical CA paradigm. Finally, we discuss the repercussions on the CA dynamics that arise when the geometric variability of the spatial entities is taken into account during the CA simulation. PMID:20887052

  1. Optimal low-thrust spiral trajectories using Lyapunov-based guidance

    NASA Astrophysics Data System (ADS)

    Yang, Da-lin; Xu, Bo; Zhang, Lei

    2016-09-01

    For an increasing number of electric propulsion systems used for real missions, it is very important to design optimal low-thrust spiral trajectories for these missions. However, it is particularly challenging to search for optimal low-thrust transfers. This paper describes an efficient optimal guidance scheme for the design of time-optimal and time-fixed fuel-optimal low-thrust spiral trajectories. The time-optimal solution is obtained with Lyapunov-based guidance, in which the artificial neural network (ANN) is adopted to implement control gains steering and the evolutionary algorithm is used as the learning algorithm for ANN. Moreover, the relative efficiency introduced in Q-law is analyzed and a periapis-and-apoapsis-centered burn structure is proposed for solving time-fixed fuel-optimal low-thrust orbit transfer problem. In this guidance scheme, the ANN is adopted to determine the burn structure within each orbital revolution and the optimal low-thrust orbit transfer problem is converted to the parameter optimization problem. This guidance scheme runs without an initial guess and provides closed form solutions. In addition, Earth J2 perturbation and Earth-shadow eclipse effects are considered in this paper. Finally, a comparison with solutions given by the literature demonstrates the effectiveness of the proposed method.

  2. Multiscale Analysis of Biological Data by Scale-Dependent Lyapunov Exponent

    PubMed Central

    Gao, Jianbo; Hu, Jing; Tung, Wen-wen; Blasch, Erik

    2012-01-01

    Physiological signals often are highly non-stationary (i.e., mean and variance change with time) and multiscaled (i.e., dependent on the spatial or temporal interval lengths). They may exhibit different behaviors, such as non-linearity, sensitive dependence on small disturbances, long memory, and extreme variations. Such data have been accumulating in all areas of health sciences and rapid analysis can serve quality testing, physician assessment, and patient diagnosis. To support patient care, it is very desirable to characterize the different signal behaviors on a wide range of scales simultaneously. The Scale-Dependent Lyapunov Exponent (SDLE) is capable of such a fundamental task. In particular, SDLE can readily characterize all known types of signal data, including deterministic chaos, noisy chaos, random 1/fα processes, stochastic limit cycles, among others. SDLE also has some unique capabilities that are not shared by other methods, such as detecting fractal structures from non-stationary data and detecting intermittent chaos. In this article, we describe SDLE in such a way that it can be readily understood and implemented by non-mathematically oriented researchers, develop a SDLE-based consistent, unifying theory for the multiscale analysis, and demonstrate the power of SDLE on analysis of heart-rate variability (HRV) data to detect congestive heart failure and analysis of electroencephalography (EEG) data to detect seizures. PMID:22291653

  3. Electroencephalograms in epilepsy: analysis and seizure prediction within the framework of Lyapunov theory

    NASA Astrophysics Data System (ADS)

    Moser, H. R.; Weber, B.; Wieser, H. G.; Meier, P. F.

    1999-06-01

    Epileptic seizures are defined as the clinical manifestation of excessive and hypersynchronous activity of neurons in the cerebral cortex and represent one of the most frequent malfunctions of the human central nervous system. Therefore, the search for precursors and predictors of a seizure is of utmost clinical relevance and may even guide us to a deeper understanding of the seizure generating mechanisms. We extract chaos-indicators such as Lyapunov exponents and Kolmogorov entropies from different types of electroencephalograms (EEGs): this covers mainly intracranial EEGs (semi-invasive and invasive recording techniques), but also scalp-EEGs from the surface of the skin. Among the analytical methods we tested up to now, we find that the spectral density of the local expansion exponents is best suited to predict the onset of a forthcoming seizure. We also evaluate the time-evolution of the dissipation in these signals: it exhibits strongly significant variations that clearly relate to the time relative to a seizure onset. This article is mainly devoted to an assessment of these methods with respect to their sensitivity to EEG changes, e.g., prior to a seizure. Further, we investigate interictal EEGs (i.e., far away from a seizure) in order to characterize their more general properties, such as the convergence of the reconstructed quantities with respect to the number of phase space dimensions. Generally we use multichannel reconstruction, but we also present a comparison with the delay-embedding technique.

  4. Adaptive neuro-fuzzy inference system for classification of ECG signals using Lyapunov exponents.

    PubMed

    Ubeyli, Elif Derya

    2009-03-01

    This paper describes the application of adaptive neuro-fuzzy inference system (ANFIS) model for classification of electrocardiogram (ECG) signals. Decision making was performed in two stages: feature extraction by computation of Lyapunov exponents and classification by the ANFIS trained with the backpropagation gradient descent method in combination with the least squares method. Four types of ECG beats (normal beat, congestive heart failure beat, ventricular tachyarrhythmia beat, and atrial fibrillation beat) obtained from the PhysioBank database were classified by four ANFIS classifiers. To improve diagnostic accuracy, the fifth ANFIS classifier (combining ANFIS) was trained using the outputs of the four ANFIS classifiers as input data. The proposed ANFIS model combined the neural network adaptive capabilities and the fuzzy logic qualitative approach. Some conclusions concerning the saliency of features on classification of the ECG signals were obtained through analysis of the ANFIS. The performance of the ANFIS model was evaluated in terms of training performance and classification accuracies and the results confirmed that the proposed ANFIS model has potential in classifying the ECG signals. PMID:19084286

  5. Lyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin scheme

    NASA Astrophysics Data System (ADS)

    Moura, R. C.; Silva, A. F. C.; Bigarella, E. D. V.; Fazenda, A. L.; Ortega, M. A.

    2016-08-01

    This paper proposes two important improvements to shock-capturing strategies using a discontinuous Galerkin scheme, namely, accurate shock identification via finite-time Lyapunov exponent (FTLE) operators and efficient shock treatment through a point-implicit discretization of a PDE-based artificial viscosity technique. The advocated approach is based on the FTLE operator, originally developed in the context of dynamical systems theory to identify certain types of coherent structures in a flow. We propose the application of FTLEs in the detection of shock waves and demonstrate the operator's ability to identify strong and weak shocks equally well. The detection algorithm is coupled with a mesh refinement procedure and applied to transonic and supersonic flows. While the proposed strategy can be used potentially with any numerical method, a high-order discontinuous Galerkin solver is used in this study. In this context, two artificial viscosity approaches are employed to regularize the solution near shocks: an element-wise constant viscosity technique and a PDE-based smooth viscosity model. As the latter approach is more sophisticated and preferable for complex problems, a point-implicit discretization in time is proposed to reduce the extra stiffness introduced by the PDE-based technique, making it more competitive in terms of computational cost.

  6. A perturbation method to the tent map based on Lyapunov exponent and its application

    NASA Astrophysics Data System (ADS)

    Cao, Lv-Chen; Luo, Yu-Ling; Qiu, Sen-Hui; Liu, Jun-Xiu

    2015-10-01

    Perturbation imposed on a chaos system is an effective way to maintain its chaotic features. A novel parameter perturbation method for the tent map based on the Lyapunov exponent is proposed in this paper. The pseudo-random sequence generated by the tent map is sent to another chaos function — the Chebyshev map for the post processing. If the output value of the Chebyshev map falls into a certain range, it will be sent back to replace the parameter of the tent map. As a result, the parameter of the tent map keeps changing dynamically. The statistical analysis and experimental results prove that the disturbed tent map has a highly random distribution and achieves good cryptographic properties of a pseudo-random sequence. As a result, it weakens the phenomenon of strong correlation caused by the finite precision and effectively compensates for the digital chaos system dynamics degradation. Project supported by the Guangxi Provincial Natural Science Foundation, China (Grant No. 2014GXNSFBA118271), the Research Project of Guangxi University, China (Grant No. ZD2014022), the Fund from Guangxi Provincial Key Laboratory of Multi-source Information Mining & Security, China (Grant No. MIMS14-04), the Fund from the Guangxi Provincial Key Laboratory of Wireless Wideband Communication & Signal Processing, China (Grant No. GXKL0614205), the Education Development Foundation and the Doctoral Research Foundation of Guangxi Normal University, the State Scholarship Fund of China Scholarship Council (Grant No. [2014]3012), and the Innovation Project of Guangxi Graduate Education, China (Grant No. YCSZ2015102).

  7. Local finite-time Lyapunov exponent, local sampling and probabilistic source and destination regions

    NASA Astrophysics Data System (ADS)

    BozorgMagham, A. E.; Ross, S. D.; Schmale, D. G., III

    2015-11-01

    The finite-time Lyapunov exponent (FTLE) is a powerful Lagrangian concept widely used for describing large-scale flow patterns and transport phenomena. However, field experiments usually have modest scales. Therefore, it is necessary to bridge the gap between the concept of FTLE and field experiments. In this paper, two independent observations are discussed: (i) approximation of the local FTLE time series at a fixed location as a function of known distances between the destination (or source) points of released (or collected) particles and local velocity, and (ii) estimation of the distances between the destination (or source) points of the released (or collected) particles when consecutive release (or sampling) events are performed at a fixed location. These two observations lay the groundwork for an ansatz methodology that can practically assist in field experiments where consecutive samples are collected at a fixed location, and it is desirable to attribute source locations to the collected particles, and also in planning of optimal local sampling of passive particles for maximal diversity monitoring of atmospheric assemblages of microorganisms. In addition to deterministic flows, the more realistic case of unresolved turbulence and low-resolution flow data that yield probabilistic source (or destination) regions are studied. It is shown that, similar to deterministic flows, Lagrangian coherent structures (LCS) and local FTLE can describe the separation of probabilistic source (or destination) regions corresponding to consecutively collected (or released) particles.

  8. Dominant Lyapunov exponent and approximate entropy in heart rate variability during emotional visual elicitation

    PubMed Central

    Valenza, Gaetano; Allegrini, Paolo; Lanatà, Antonio; Scilingo, Enzo Pasquale

    2012-01-01

    In this work we characterized the non-linear complexity of Heart Rate Variability (HRV) in short time series. The complexity of HRV signal was evaluated during emotional visual elicitation by using Dominant Lyapunov Exponents (DLEs) and Approximate Entropy (ApEn). We adopted a simplified model of emotion derived from the Circumplex Model of Affects (CMAs), in which emotional mechanisms are conceptualized in two dimensions by the terms of valence and arousal. Following CMA model, a set of standardized visual stimuli in terms of arousal and valence gathered from the International Affective Picture System (IAPS) was administered to a group of 35 healthy volunteers. Experimental session consisted of eight sessions alternating neutral images with high arousal content images. Several works can be found in the literature showing a chaotic dynamics of HRV during rest or relax conditions. The outcomes of this work showed a clear switching mechanism between regular and chaotic dynamics when switching from neutral to arousal elicitation. Accordingly, the mean ApEn decreased with statistical significance during arousal elicitation and the DLE became negative. Results showed a clear distinction between the neutral and the arousal elicitation and could be profitably exploited to improve the accuracy of emotion recognition systems based on HRV time series analysis. PMID:22393320

  9. Characteristic distribution of finite-time Lyapunov exponents for chimera states.

    PubMed

    Botha, André E

    2016-01-01

    Our fascination with chimera states stems partially from the somewhat paradoxical, yet fundamental trait of identical, and identically coupled, oscillators to split into spatially separated, coherently and incoherently oscillating groups. While the list of systems for which various types of chimeras have already been detected continues to grow, there is a corresponding increase in the number of mathematical analyses aimed at elucidating the fundamental reasons for this surprising behaviour. Based on the model systems, there are strong indications that chimera states may generally be ubiquitous in naturally occurring systems containing large numbers of coupled oscillators - certain biological systems and high-Tc superconducting materials, for example. In this work we suggest a new way of detecting and characterising chimera states. Specifically, it is shown that the probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a definite characteristic shape. Such distributions could be used as signatures of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. For such cases, we suggest that chimera states could perhaps be detected by reconstructing the characteristic distribution via standard embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist unnoticed. PMID:27374473

  10. The Application of Nonlinear Local Lyapunov Vectors to Ensemble Prediction in a barotropic quasi-geostrophicmodel

    NASA Astrophysics Data System (ADS)

    Ding, Ruiqiang; Feng, Jie; Liu, Deqiang; Li, Jianping

    2014-05-01

    The breeding method is used extensively as an ensemble generation technique for its simple concept and cheap computing. Bred vectors (BVs) are dynamically obtained from the nonlinear model and represent a set of fastest-growing modes that are globally quasi-orthogonal at each time. However, the BVs have similar local structures that may degrade the global orthogonality to some extent and the natural breeding may not be able to stably capture the fast-growing directions. In this paper, we introduced a new ensemble generation scheme, nonlinear Local Lyapunov Vectors (NLLVs), which is obtained by using the comparison and the Gram-Schmidt reorthonormalization (GSR) methods. The NLLVs are a set of strictly orthogonal vectors that represent the directions from the fastest growing direction to the fastest shrinking direction, and thus the first few of them could be used to provide the subspace of the fastest-growing errors. The performances of the NLLV and the BV schemes are systematically compared in a barotropic quasi-geostrophic model. The results show that the NLLVs perform more stable in capturing the fastest-growing modes and have greater diversity in both local and global regions than the BVs. The NLLVs also have improved performance according to various verification measures, such as the Brier scores and the rank histograms.

  11. Characteristic distribution of finite-time Lyapunov exponents for chimera states

    PubMed Central

    Botha, André E.

    2016-01-01

    Our fascination with chimera states stems partially from the somewhat paradoxical, yet fundamental trait of identical, and identically coupled, oscillators to split into spatially separated, coherently and incoherently oscillating groups. While the list of systems for which various types of chimeras have already been detected continues to grow, there is a corresponding increase in the number of mathematical analyses aimed at elucidating the fundamental reasons for this surprising behaviour. Based on the model systems, there are strong indications that chimera states may generally be ubiquitous in naturally occurring systems containing large numbers of coupled oscillators – certain biological systems and high-Tc superconducting materials, for example. In this work we suggest a new way of detecting and characterising chimera states. Specifically, it is shown that the probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a definite characteristic shape. Such distributions could be used as signatures of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. For such cases, we suggest that chimera states could perhaps be detected by reconstructing the characteristic distribution via standard embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist unnoticed. PMID:27374473

  12. Lyapunov based control of a six degee of freedom satellite testbed

    NASA Astrophysics Data System (ADS)

    Saulnier, Kelsey

    The development of novel techniques for the guidance, navigation, and control of spacecraft is a necessary step in the effort to create new autonomous spacecraft. The costs of on-orbit testing can be mitigated by the use of on-the-ground simulators which allow for hardware-in-the-loop debugging. Air-bearing spacecraft simulators have been used widely for this purpose. This work presents the first full six degree of freedom simulator which relies solely on air bearing reduced friction motion to achieve all six degrees of freedom, thus making simulations better represent the final system than can be expected from systems with limited degrees of freedom or powered stages. The system utilizes ON-OFF thrusters and is designed for testing guidance, navigation, and control algorithms for small scale satellites which have been becoming increasingly popular in recent years. This system is used to validate a nonlinear six degrees of freedom control strategy for specifically for ON-OFF thrusters which is based in Lyapunov theory and designed for systems, such as small scale satellites, with limited computational power.

  13. Power law scaling of the top Lyapunov exponent of a product of random matrices

    SciTech Connect

    Ravishankar, K.

    1989-01-01

    A sequence of i.i.d. matrix-valued random variables /X/sub n// x X/sub n/ = (/sub 0//sup 1/ /sub 1//sup d/) with probability p and X/sub n/ = (/sub c(var epsilon)//sup 1 + a(var epsilon)/ /sub 1 + a(var epsilon)//sup b(var epsilon)/) with probability 1 - p is considered. Let a(var epsilon) = a/sub 0/ var epsilon + o(var epsilon) = c/sub 0/ var epsilon + o(var epsilon) lim/sub var epsilon ..-->.. 0/ b(var epsilon) = 0, a/sub 0/, c/sub 0/, var epsilon > 0, and b(var epsilon) > 0 for all var epsilon > 0. It is shown that the top Lyapunov exponent of the matrix product X/sub n/X/sub n-1/... X/sub 1/, lambda = lim/sub n ..-->.. infinity/ (1/n)/n perpendicular to X/sub n/X/sub n-1/... X/sub i/ satisfies a power law with an exponent 1/2. That is, lim/sub var epsilon ..-->.. 0/(1n lambda/1n var epsilon) = 1/2.

  14. 20 years of reprocessed Lyapunov Exponents from altimetry available on AVISO+

    NASA Astrophysics Data System (ADS)

    Pujol, Marie-Isabelle; Faugere, Yannice; D'Ovidio, Francesco; Morrow, Rosemary; Bronner, Emilie; Picot, Nicolas

    2015-04-01

    SARAL/AltiKa is able to sample the small mesoscale signal with a noise measurement error never reached in nadir conventional altimetry. The SARAL/AltiKa 1-Hz measurement is used in the SSALTO/DUACS system since July 2013 and largely contributes to the quality of the Level4 merged products. These products, are now widely used to define the surface geostrophic currents and beyond that they are used to provide proxies of (sub-)mesoscale transport fronts via the Lyapunov Exponents (LEs). The LEs are being increasingly used in physical, biogeochemical, and ecological applications, ranging from real-time support to field studies to co-localisation of animal tracking with Lagrangian Coherent Structures. In order to better serve the users need, and in collaboration with different laboratories (LOCEAN and CTOH), the LEs and vectors are computed over the 21 year altimeter period and over the global ocean within the SSALTO/DUACS project. This product provides the position, and intensity, and orientation of fronts induced by the mesoscale eddies and underlining part of sub-mesoscale activity. We present here the LEs that will be available on AVISO+ early 2015.

  15. The Finite Time Lyapunov Exponent Field of N Interacting Vortices in the Zero Viscosity Limit

    NASA Astrophysics Data System (ADS)

    Galvez, Richard; Green, Melissa

    2015-11-01

    We present an analysis of the Finite Time Lyapunov Exponent (FTLE) field of interacting vortices in the potential flow limit. This work is based on an inviscid approximation, but develops a useful tool that will aid in the effort of understanding the interactions of vortices and turbulence in viscous fluids. The FTLE field of N interacting vortices is computed numerically in two dimensions in different physical scenarios: i) orbiting one another with no initial velocities, ii) approaching each other given an initial velocity and iii) as periodically produced behind a circular cylinder. For situation ii) we expand on the cases where the approach velocities of the vortices are less than or greater than a critical capture velocity, that is, the velocity necessary to escape a captured orbit between co-rotating vortices. We focus on the evolution and interaction of the Lagrangian coherent structures (LCS) in these scenarios to determine if there is a way to anticipate the character of vortex interaction by the initial structure of the LCS. Additional remarks will be made on the extrapolation of observations to a large number of interacting vortices (large N). This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.

  16. Characteristic distribution of finite-time Lyapunov exponents for chimera states

    NASA Astrophysics Data System (ADS)

    Botha, André E.

    2016-07-01

    Our fascination with chimera states stems partially from the somewhat paradoxical, yet fundamental trait of identical, and identically coupled, oscillators to split into spatially separated, coherently and incoherently oscillating groups. While the list of systems for which various types of chimeras have already been detected continues to grow, there is a corresponding increase in the number of mathematical analyses aimed at elucidating the fundamental reasons for this surprising behaviour. Based on the model systems, there are strong indications that chimera states may generally be ubiquitous in naturally occurring systems containing large numbers of coupled oscillators – certain biological systems and high-Tc superconducting materials, for example. In this work we suggest a new way of detecting and characterising chimera states. Specifically, it is shown that the probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a definite characteristic shape. Such distributions could be used as signatures of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. For such cases, we suggest that chimera states could perhaps be detected by reconstructing the characteristic distribution via standard embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist unnoticed.

  17. Competitive autocatalytic reactions in chaotic flows with diffusion: Prediction using finite-time Lyapunov exponents

    SciTech Connect

    Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.; Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208; The Northwestern Institute on Complex Systems , Northwestern University, Evanston, Illinois 60208 ; Lueptow, Richard M.

    2014-03-15

    We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics.

  18. Sampling diffusive transition paths

    SciTech Connect

    F. Miller III, Thomas; Predescu, Cristian

    2006-10-12

    We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with sampling infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with sampling the coarse features of long paths. The fine-features sampling stiffness is eliminated with the use of the fast sampling algorithm (FSA), and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. We use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.

  19. Sampling diffusive transition paths.

    PubMed

    Miller, Thomas F; Predescu, Cristian

    2007-04-14

    The authors address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with the sampling of infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with the sampling of the coarse features of long paths. The fine-feature sampling stiffness is eliminated with the use of the fast sampling algorithm, and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. The authors use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature. PMID:17444696

  20. Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

    NASA Astrophysics Data System (ADS)

    Faria, Flávio A.; Silva, Geraldo N.; Oliveira, Vilma A.

    2013-10-01

    In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented.

  1. Paths correlation matrix.

    PubMed

    Qian, Weixian; Zhou, Xiaojun; Lu, Yingcheng; Xu, Jiang

    2015-09-15

    Both the Jones and Mueller matrices encounter difficulties when physically modeling mixed materials or rough surfaces due to the complexity of light-matter interactions. To address these issues, we derived a matrix called the paths correlation matrix (PCM), which is a probabilistic mixture of Jones matrices of every light propagation path. Because PCM is related to actual light propagation paths, it is well suited for physical modeling. Experiments were performed, and the reflection PCM of a mixture of polypropylene and graphite was measured. The PCM of the mixed sample was accurately decomposed into pure polypropylene's single reflection, pure graphite's single reflection, and depolarization caused by multiple reflections, which is consistent with the theoretical derivation. Reflection parameters of rough surface can be calculated from PCM decomposition, and the results fit well with the theoretical calculations provided by the Fresnel equations. These theoretical and experimental analyses verify that PCM is an efficient way to physically model light-matter interactions. PMID:26371930

  2. Mobile transporter path planning

    NASA Technical Reports Server (NTRS)

    Baffes, Paul; Wang, Lui

    1990-01-01

    The use of a genetic algorithm (GA) for solving the mobile transporter path planning problem is investigated. The mobile transporter is a traveling robotic vehicle proposed for the space station which must be able to reach any point of the structure autonomously. Elements of the genetic algorithm are explored in both a theoretical and experimental sense. Specifically, double crossover, greedy crossover, and tournament selection techniques are examined. Additionally, the use of local optimization techniques working in concert with the GA are also explored. Recent developments in genetic algorithm theory are shown to be particularly effective in a path planning problem domain, though problem areas can be cited which require more research.

  3. Coherence-path duality relations for N paths

    NASA Astrophysics Data System (ADS)

    Hillery, Mark; Bagan, Emilio; Bergou, Janos; Cottrell, Seth

    2016-05-01

    For an interferometer with two paths, there is a relation between the information about which path the particle took and the visibility of the interference pattern at the output. The more path information we have, the smaller the visibility, and vice versa. We generalize this relation to a multi-path interferometer, and we substitute two recently defined measures of quantum coherence for the visibility, which results in two duality relations. The path information is provided by attaching a detector to each path. In the first relation, which uses an l1 measure of coherence, the path information is obtained by applying the minimum-error state discrimination procedure to the detector states. In the second, which employs an entropic measure of coherence, the path information is the mutual information between the detector states and the result of measuring them. Both approaches are quantitative versions of complementarity for N-path interferometers. Support provided by the John Templeton Foundation.

  4. A semi-free weighting matrices approach for neutral-type delayed neural networks

    NASA Astrophysics Data System (ADS)

    Mai, Huanhuan; Liao, Xiaofeng; Li, Chuandong

    2009-03-01

    In this paper, a new approach is proposed for stability issues of neutral-type neural networks (DNNs) with constant delay. First, the semi-free weighting matrices are proposed and used instead of the known free weighting matrices to express the relationship between the terms in the Leibniz-Newton formula to simplify the system synthesis and to obtain less computation demand. Second, global exponential stability conditions which are less conservative and restrictive than the known results are derived. At the same time, based on the above approach, fewer variable matrices are introduced in the construction of the Lyapunov functional and augmented Lyapunov functional. Two examples are given to show their effectiveness and advantages over others.

  5. Synchronization analysis of complex networks with multi-weights and its application in public traffic network

    NASA Astrophysics Data System (ADS)

    An, Xin-lei; Zhang, Li; Li, Yin-zhen; Zhang, Jian-gang

    2014-10-01

    On the basis of traditional weighted network, we study a new complex network model with multi-weights, which has one or several different types of weights between any two nodes. According to the method of network split, we split the complex network with multi-weights into several different complex networks with single weight, and study its global synchronization. Taking bus lines as the network nodes, a new public traffic roads network model with multi-weights is established by the proposed network model and space R modeling approach. Then based on the Lyapunov stability theory, the criteria is designed for the global synchronization of the public traffic roads networks with multi-weights. By changing the different weights and taking the Lorenz chaotic system for example, some numerical examples are given to discuss the balance of the whole public traffic roads network.

  6. Using finite-time Lyapunov exponents to investigate the effect of stratospheric sudden warmings on the polar vortices

    NASA Astrophysics Data System (ADS)

    Smith, M.; McDonald, A. J.

    2012-04-01

    Finite-time Lyapunov exponents are often used to measure mixing in the stratosphere and have been used to investigate the horizontal transport of trace gases near the polar vortices. A better understanding of the dynamics of the polar vortices should provide insight into the circumstances under which odd nitrogen and hydrogen produced by energetic particle precipitation (EPP) in the mesosphere and lower thermosphere (MLT) can be transported to lower levels of the atmosphere. A climatology of finite-time Lyapunov exponents for isentropic surfaces in the stratosphere ranging from 550-2300K for both the northern and southern hemispheres has been created for the observational period of the EOS-MLS instrument.The Lyapunov exponents are derived by using output from a Lagrangian trajectory model forced by data from the MERRA reanalysis. They are calculated at each point on a 2° x 4° global grid by running trajectories for two neighbouring parcels which are initially 1km apart and measuring their separation after a period of time. In order to ensure that the parcel trajectories remain close enough to each other for the exponents to be a good measure of local mixing, the distance between the parcels is periodically reset to 1km. In order to provide a consistency check Lyapunov exponents and trajectories have also been calculated at 550K using NCEP/NCAR reanalysis data. Initial comparisons suggest that the qualitative agreement is quite good between the results using the two different reanalyses. Comparison of the variations in the Lyapunov exponents and trace gas distributions using EOS-MLS data during periods where the stratospheric polar vortices are undisturbed and periods which are disturbed by stratospheric sudden warmings are also discussed. Studying how stratospheric sudden warmings (SSWs) affect the atmospheric dynamics in polar regions is particularly worthwhile since recent studies have shown that they have a significant modulating influence upon the EPP

  7. Following the Path

    ERIC Educational Resources Information Center

    Rodia, Becky

    2004-01-01

    This article profiles Diane Stanley, an author and illustrator of children's books. Although she was studying to be a medical illustrator in graduate school, Stanley's path changed when she got married and had children. As she was raising her children, she became increasingly enamored of the colorful children's books she would check out of the…

  8. An Unplanned Path

    ERIC Educational Resources Information Center

    McGarvey, Lynn M.; Sterenberg, Gladys Y.; Long, Julie S.

    2013-01-01

    The authors elucidate what they saw as three important challenges to overcome along the path to becoming elementary school mathematics teacher leaders: marginal interest in math, low self-confidence, and teaching in isolation. To illustrate how these challenges were mitigated, they focus on the stories of two elementary school teachers--Laura and…

  9. A set oriented definition of finite-time Lyapunov exponents and coherent sets

    NASA Astrophysics Data System (ADS)

    Tallapragada, Phanindra; Ross, Shane D.

    2013-05-01

    The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron-Frobenius operator. The FTLE measures the averaged local stretching around reference trajectories. Regions with high stretching are used to identify phase space transport barriers. One probabilistic method is to consider the spectrum of the Perron-Frobenius operator of the flow to identify almost-invariant densities. These almost-invariant densities are used to identify almost invariant sets. In this paper, a set-oriented definition of the FTLE is proposed which is applicable to phase space sets of finite size and reduces to the usual definition of FTLE in the limit of infinitesimal phase space elements. This definition offers a straightforward connection between the evolution of probability densities and finite-time stretching experienced by phase space curves. This definition also addresses some concerns with the standard computation of the FTLE. For the case of autonomous and periodic vector fields we provide a simplified method to calculate the set-oriented FTLE using the Perron-Frobenius operator. Based on the new definition of the FTLE we propose a simple definition of finite-time coherent sets applicable to vector fields of general time-dependence, which are the analogues of almost-invariant sets in autonomous and time-periodic vector fields. The coherent sets we identify will necessarily be separated from one another by ridges of high FTLE, providing a link between the framework of coherent sets and that of codimension one Lagrangian coherent structures. Our identification of coherent sets is applied to three examples.

  10. Intrinsic modulation of ENSO predictability viewed through a local Lyapunov lens

    NASA Astrophysics Data System (ADS)

    Karamperidou, Christina; Cane, Mark A.; Lall, Upmanu; Wittenberg, Andrew T.

    2013-04-01

    The presence of rich ENSO variability in the long unforced simulation of GFDL's CM2.1 motivates the use of tools from dynamical systems theory to study variability in ENSO predictability, and its connections to ENSO magnitude, frequency, and physical evolution. Local Lyapunov exponents (LLEs) estimated from the monthly NINO3 SSTa model output are used to characterize periods of increased or decreased predictability. The LLEs describe the growth of infinitesimal perturbations due to internal variability, and are a measure of the immediate predictive uncertainty at any given point in the system phase-space. The LLE-derived predictability estimates are compared with those obtained from the error growth in a set of re-forecast experiments with CM2.1. It is shown that the LLEs underestimate the error growth for short forecast lead times (less than 8 months), while they overestimate it for longer lead times. The departure of LLE-derived error growth rates from the re-forecast rates is a linear function of forecast lead time, and is also sensitive to the length of the time series used for the LLE calculation. The LLE-derived error growth rate is closer to that estimated from the re-forecasts for a lead time of 4 months. In the 2,000-year long simulation, the LLE-derived predictability at the 4-month lead time varies (multi)decadally only by 9-18 %. Active ENSO periods are more predictable than inactive ones, while epochs with regular periodicity and moderate magnitude are classified as the most predictable by the LLEs. Events with a deeper thermocline in the west Pacific up to five years prior to their peak, along with an earlier deepening of the thermocline in the east Pacific in the months preceding the peak, are classified as more predictable. Also, the GCM is found to be less predictable than nature under this measure of predictability.

  11. Intrinsic modulation of ENSO predictability viewed through a local Lyapunov lens

    NASA Astrophysics Data System (ADS)

    Karamperidou, Christina; Cane, Mark A.; Lall, Upmanu; Wittenberg, Andrew T.

    2014-01-01

    The presence of rich ENSO variability in the long unforced simulation of GFDL's CM2.1 motivates the use of tools from dynamical systems theory to study variability in ENSO predictability, and its connections to ENSO magnitude, frequency, and physical evolution. Local Lyapunov exponents (LLEs) estimated from the monthly NINO3 SSTa model output are used to characterize periods of increased or decreased predictability. The LLEs describe the growth of infinitesimal perturbations due to internal variability, and are a measure of the immediate predictive uncertainty at any given point in the system phase-space. The LLE-derived predictability estimates are compared with those obtained from the error growth in a set of re-forecast experiments with CM2.1. It is shown that the LLEs underestimate the error growth for short forecast lead times (less than 8 months), while they overestimate it for longer lead times. The departure of LLE-derived error growth rates from the re-forecast rates is a linear function of forecast lead time, and is also sensitive to the length of the time series used for the LLE calculation. The LLE-derived error growth rate is closer to that estimated from the re-forecasts for a lead time of 4 months. In the 2,000-year long simulation, the LLE-derived predictability at the 4-month lead time varies (multi)decadally only by 9-18 %. Active ENSO periods are more predictable than inactive ones, while epochs with regular periodicity and moderate magnitude are classified as the most predictable by the LLEs. Events with a deeper thermocline in the west Pacific up to five years prior to their peak, along with an earlier deepening of the thermocline in the east Pacific in the months preceding the peak, are classified as more predictable. Also, the GCM is found to be less predictable than nature under this measure of predictability.

  12. Finite-time Lyapunov exponent-based analysis for compressible flows.

    PubMed

    González, D R; Speth, R L; Gaitonde, D V; Lewis, M J

    2016-08-01

    The finite-time Lyapunov exponent (FTLE) technique has shown substantial success in analyzing incompressible flows by capturing the dynamics of coherent structures. Recent applications include river and ocean flow patterns, respiratory tract dynamics, and bio-inspired propulsors. In the present work, we extend FTLE to the compressible flow regime so that coherent structures, which travel at convective speeds, can be associated with waves traveling at acoustic speeds. This is particularly helpful in the study of jet acoustics. We first show that with a suitable choice of integration time interval, FTLE can extract wave dynamics from the velocity field. The integration time thus acts as a pseudo-filter separating coherent structures from waves. Results are confirmed by examining forward and backward FTLE coefficients for several simple, well-known acoustic fields. Next, we use this analysis to identify events associated with intermittency in jet noise pressure probe data. Although intermittent events are known to be dominant causes of jet noise, their direct source in the turbulent jet flow has remained unexplained. To this end, a Large-Eddy Simulation of a Mach 0.9 jet is subjected to FTLE to simultaneously examine, and thus expose, the causal relationship between coherent structures and the corresponding acoustic waves. Results show that intermittent events are associated with entrainment in the initial roll up region and emissive events downstream of the potential-core collapse. Instantaneous acoustic disturbances are observed to be primarily induced near the collapse of the potential core and continue propagating towards the far-field at the experimentally observed, approximately 30° angle relative to the jet axis. PMID:27586608

  13. Stability evaluation and improvement of adaptive optics systems by using the Lyapunov stability approach

    NASA Astrophysics Data System (ADS)

    Wang, Liang; Chen, Tao; Liu, Xin-yue; Lin, Xu-dong; Yang, Xiao-xia; Li, Hong-zhuang

    2016-02-01

    In this research, investigations on the closed-loop control stability of adaptive optics systems are conducted by using the Lyapunov approach. As an direct metric of the control stability, the error propagator includes the effects of both the integral gain and the influence matrix and is effective for control-stability evaluation. An experimental 97-element AO system is developed for the control-stability investigation, and the Southwell sensor-actuator configuration rather than the Fried geometry is adopted so as to suppress the potential waffle mode. Because filtering out small singular values of the influence matrix can be used to improve the control stability, the effect of the influence matrix and the effect of the integral gain are considered as a whole by using the error propagator. Then, the control stability of the AO system is evaluated for varying the integral gains and the number of filtered-out singular values. Afterwards, an analysis of the evaluations of the error propagator is made, and a conclusion can be drawn that the control stability can be improved by filtering out more singular values of the influence matrix when the integral gain is high. In other words, the error propagator is useful for trading off the bandwidth error and the fitting error of AO systems in a control-stability approach. Finally, a performance measurement of the experimental AO system is conducted when 13 smaller singular values of the influence matrix are filtered out, and the results show that filtering out a small fraction of the singular values has a minor influence on the performance of this AO system.

  14. Image-Based Visual Servoing for Robotic Systems: A Nonlinear Lyapunov-Based Control Approach

    SciTech Connect

    Dixon, Warren

    2004-06-01

    There is significant motivation to provide robotic systems with improved autonomy as a means to significantly accelerate deactivation and decommissioning (D&D) operations while also reducing the associated costs, removing human operators from hazardous environments, and reducing the required burden and skill of human operators. To achieve improved autonomy, this project focused on the basic science challenges leading to the development of visual servo controllers. The challenge in developing these controllers is that a camera provides 2-dimensional image information about the 3-dimensional Euclidean-space through a perspective (range dependent) projection that can be corrupted by uncertainty in the camera calibration matrix and by disturbances such as nonlinear radial distortion. Disturbances in this relationship (i.e., corruption in the sensor information) propagate erroneous information to the feedback controller of the robot, leading to potentially unpredictable task execution. This research project focused on the development of a visual servo control methodology that targets compensating for disturbances in the camera model (i.e., camera calibration and the recovery of range information) as a means to achieve predictable response by the robotic system operating in unstructured environments. The fundamental idea is to use nonlinear Lyapunov-based techniques along with photogrammetry methods to overcome the complex control issues and alleviate many of the restrictive assumptions that impact current robotic applications. The outcome of this control methodology is a plug-and-play visual servoing control module that can be utilized in conjunction with current technology such as feature recognition and extraction to enable robotic systems with the capabilities of increased accuracy, autonomy, and robustness, with a larger field of view (and hence a larger workspace). The developed methodology has been reported in numerous peer-reviewed publications and the

  15. Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities

    NASA Astrophysics Data System (ADS)

    Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher

    2013-06-01

    We compute and compare the three types of vectors frequently used to explore the instability properties of dynamical models, namely Lyapunov vectors (LVs), singular vectors (SVs) and bred vectors (BVs) in two systems, using the Wolfe-Samelson (2007 Tellus A 59 355-66) algorithm to compute all of the Lyapunov vectors. The first system is the Lorenz (1963 J. Atmos. Sci. 20 130-41) three-variable model. Although the leading Lyapunov vector, LV1, grows fastest globally, the second Lyapunov vector, LV2, which has zero growth globally, often grows faster than LV1 locally. Whenever this happens, BVs grow closer to LV2, suggesting that in larger atmospheric or oceanic models where several instabilities can grow in different areas of the world, BVs will grow toward the fastest growing local unstable mode. A comparison of their growth rates at different times shows that all three types of dynamical vectors have the ability to predict regime changes and the duration of the new regime based on their growth rates in the last orbit of the old regime, as shown for BVs by Evans et al (2004 Bull. Am. Meteorol. Soc. 520-4). LV1 and BVs have similar predictive skill, LV2 has a tendency to produce false alarms, and even LV3 shows that maximum decay is also associated with regime change. Initial and final SVs grow much faster and are the most accurate predictors of regime change, although the characteristics of the initial SVs are strongly dependent on the length of the optimization window. The second system is the toy ‘ocean-atmosphere’ model developed by Peña and Kalnay (2004 Nonlinear Process. Geophys. 11 319-27) coupling three Lorenz (1963 J. Atmos. Sci. 20 130-41) systems with different time scales, in order to test the effects of fast and slow modes of growth on the dynamical vectors. A fast ‘extratropical atmosphere’ is weakly coupled to a fast ‘tropical atmosphere’ which is, in turn, strongly coupled to a slow ‘ocean’ system, the latter coupling imitating the

  16. Joining consensus of networked multi-agent systems with nonlinear couplings and weighting constraints

    NASA Astrophysics Data System (ADS)

    Wang, Bohui; Wang, Jingcheng; Zhang, Langwen; Ge, Yang

    2016-04-01

    This paper studies the joining consensus of networked multi-agent systems subject to nonlinear couplings and weighted directed graphs via pinning control. A weighted-average consensus protocol is proposed to achieve the collective decision by interacting with the local information of some pinned agents. By proposing a novel joining consensus protocol, average consensus and general consensus strategies are joined to achieve an agreement for the weighting networked system. Furthermore, by calculating a proper consensus gain and using finite control Lyapunov controllers, an efficient joining consensus protocol is presented to improve the consensus speed. Sufficient conditions for achieving the consensuses asymptotically are proved. Finally, theoretical results are validated via simulations.

  17. Nonadiabatic transition path sampling

    NASA Astrophysics Data System (ADS)

    Sherman, M. C.; Corcelli, S. A.

    2016-07-01

    Fewest-switches surface hopping (FSSH) is combined with transition path sampling (TPS) to produce a new method called nonadiabatic path sampling (NAPS). The NAPS method is validated on a model electron transfer system coupled to a Langevin bath. Numerically exact rate constants are computed using the reactive flux (RF) method over a broad range of solvent frictions that span from the energy diffusion (low friction) regime to the spatial diffusion (high friction) regime. The NAPS method is shown to quantitatively reproduce the RF benchmark rate constants over the full range of solvent friction. Integrating FSSH within the TPS framework expands the applicability of both approaches and creates a new method that will be helpful in determining detailed mechanisms for nonadiabatic reactions in the condensed-phase.

  18. Nonadiabatic transition path sampling.

    PubMed

    Sherman, M C; Corcelli, S A

    2016-07-21

    Fewest-switches surface hopping (FSSH) is combined with transition path sampling (TPS) to produce a new method called nonadiabatic path sampling (NAPS). The NAPS method is validated on a model electron transfer system coupled to a Langevin bath. Numerically exact rate constants are computed using the reactive flux (RF) method over a broad range of solvent frictions that span from the energy diffusion (low friction) regime to the spatial diffusion (high friction) regime. The NAPS method is shown to quantitatively reproduce the RF benchmark rate constants over the full range of solvent friction. Integrating FSSH within the TPS framework expands the applicability of both approaches and creates a new method that will be helpful in determining detailed mechanisms for nonadiabatic reactions in the condensed-phase. PMID:27448877

  19. Four paths of competition

    SciTech Connect

    Studness, C.M.

    1995-05-01

    The financial community`s focus on utility competition has been riveted on the proceedings now in progress at state regulatory commissions. The fear that something immediately damaging will come out of these proceedings seems to have diminished in recent months, and the stock market has reacted favorably. However, regulatory developments are only one of four paths leading to competition; the others are the marketplace, the legislatures, and the courts. Each could play a critical role in the emergence of competition.

  20. Teleconnection Paths via Climate Network Direct Link Detection.

    PubMed

    Zhou, Dong; Gozolchiani, Avi; Ashkenazy, Yosef; Havlin, Shlomo

    2015-12-31

    Teleconnections describe remote connections (typically thousands of kilometers) of the climate system. These are of great importance in climate dynamics as they reflect the transportation of energy and climate change on global scales (like the El Niño phenomenon). Yet, the path of influence propagation between such remote regions, and weighting associated with different paths, are only partially known. Here we propose a systematic climate network approach to find and quantify the optimal paths between remotely distant interacting locations. Specifically, we separate the correlations between two grid points into direct and indirect components, where the optimal path is found based on a minimal total cost function of the direct links. We demonstrate our method using near surface air temperature reanalysis data, on identifying cross-latitude teleconnections and their corresponding optimal paths. The proposed method may be used to quantify and improve our understanding regarding the emergence of climate patterns on global scales. PMID:26765033

  1. Teleconnection Paths via Climate Network Direct Link Detection

    NASA Astrophysics Data System (ADS)

    Zhou, Dong; Gozolchiani, Avi; Ashkenazy, Yosef; Havlin, Shlomo

    2015-12-01

    Teleconnections describe remote connections (typically thousands of kilometers) of the climate system. These are of great importance in climate dynamics as they reflect the transportation of energy and climate change on global scales (like the El Niño phenomenon). Yet, the path of influence propagation between such remote regions, and weighting associated with different paths, are only partially known. Here we propose a systematic climate network approach to find and quantify the optimal paths between remotely distant interacting locations. Specifically, we separate the correlations between two grid points into direct and indirect components, where the optimal path is found based on a minimal total cost function of the direct links. We demonstrate our method using near surface air temperature reanalysis data, on identifying cross-latitude teleconnections and their corresponding optimal paths. The proposed method may be used to quantify and improve our understanding regarding the emergence of climate patterns on global scales.

  2. Spirit's Path to Bonneville

    NASA Technical Reports Server (NTRS)

    2004-01-01

    Scientists created this overlay map by laying navigation and panoramic camera images taken from the surface of Mars on top of one of Spirit's descent images taken as the spacecraft descended to the martian surface. The map was created to help track the path that Spirit has traveled through sol 44 and to put into perspective the distance left to travel before reaching the edge of the large crater nicknamed 'Bonneville.'

    The area boxed in yellow contains the ground images that have been matched to and layered on top of the descent image. The yellow line shows the path that Spirit has traveled and the red dashed line shows the intended path for future sols. The blue circles highlight hollowed areas on the surface, such as Sleepy Hollow, near the lander, and Laguna Hollow, the sol 45 drive destination. Scientists use these hollowed areas - which can be seen in both the ground images and the descent image - to correctly match up the overlay.

    Field geologists on Earth create maps like this to assist them in tracking their observations.

  3. PATHS groundwater hydrologic model

    SciTech Connect

    Nelson, R.W.; Schur, J.A.

    1980-04-01

    A preliminary evaluation capability for two-dimensional groundwater pollution problems was developed as part of the Transport Modeling Task for the Waste Isolation Safety Assessment Program (WISAP). Our approach was to use the data limitations as a guide in setting the level of modeling detail. PATHS Groundwater Hydrologic Model is the first level (simplest) idealized hybrid analytical/numerical model for two-dimensional, saturated groundwater flow and single component transport; homogeneous geology. This document consists of the description of the PATHS groundwater hydrologic model. The preliminary evaluation capability prepared for WISAP, including the enhancements that were made because of the authors' experience using the earlier capability is described. Appendixes A through D supplement the report as follows: complete derivations of the background equations are provided in Appendix A. Appendix B is a comprehensive set of instructions for users of PATHS. It is written for users who have little or no experience with computers. Appendix C is for the programmer. It contains information on how input parameters are passed between programs in the system. It also contains program listings and test case listing. Appendix D is a definition of terms.

  4. A Deterministic Approximation Algorithm for Maximum 2-Path Packing

    NASA Astrophysics Data System (ADS)

    Tanahashi, Ruka; Chen, Zhi-Zhong

    This paper deals with the maximum-weight 2-path packing problem (M2PP), which is the problem of computing a set of vertex-disjoint paths of length 2 in a given edge-weighted complete graph so that the total weight of edges in the paths is maximized. Previously, Hassin and Rubinstein gave a randomized cubic-time approximation algorithm for M2PP which achieves an expected ratio of 35/67 - ε ≈ 0.5223 - ε for any constant ε > 0. We refine their algorithm and derandomize it to obtain a deterministic cubic-time approximation algorithm for the problem which achieves a better ratio (namely, 0.5265 - ε for any constant ε > 0).

  5. Scuba Weights

    NASA Technical Reports Server (NTRS)

    1995-01-01

    The Attitude Adjuster is a system for weight repositioning corresponding to a SCUBA diver's changing positions. Compact tubes on the diver's air tank permit controlled movement of lead balls within the Adjuster, automatically repositioning when the diver changes position. Manufactured by Think Tank Technologies, the system is light and small, reducing drag and energy requirements and contributing to lower air consumption. The Mid-Continent Technology Transfer Center helped the company with both technical and business information and arranged for the testing at Marshall Space Flight Center's Weightlessness Environmental Training Facility for astronauts.

  6. Bred vectors, singular vectors, and Lyapunov vectors in simple and complex models

    NASA Astrophysics Data System (ADS)

    Norwood, Adrienne

    We compute and compare three types of vectors frequently used to explore the instability properties of dynamical models, Lyapunov vectors (LVs), singular vectors (SVs), and bred vectors (BVs). The first model is the Lorenz (1963) three-variable model. We find BVs align with the locally fastest growing LV, which is often the second fastest growing global LV. The growth rates of the three types of vectors reveal all predict regime changes and durations of new regimes, as shown for BVs by Evans et al. (2004). The second model is the toy 'atmosphere-ocean model' developed by Pena and Kalnay (2004) coupling three Lorenz (1963) models with different time scales to test the effects of fast and slow modes of growth on the dynamical vectors. A fast 'extratropical atmosphere' is weakly coupled to a fast 'tropical atmosphere' which is strongly coupled to a slow 'ocean' system, the latter coupling imitating the tropical El Nino--Southern Oscillation. BVs separate the fast and slow modes of growth through appropriate selection of the breeding parameters. LVs successfully separate the fast 'extratropics' but cannot completely decouple the 'tropics' from the 'ocean,' leading to 'coupled' LVs that are affected by both systems but mainly dominated by one. SVs identify the fast modes but cannot capture the slow modes until the fast 'extratropics' are replaced with faster 'convection.' The dissimilar behavior of the three types of vectors degrades the similarities of the subspaces they inhabit (Norwood et al. 2013). The third model is a quasi-geostrophic channel model (Rotunno and Bao 1996) that is a simplification of extratropical synoptic-scale motions with baroclinic instabilities only. We were unable to successfully compute LVs for it. However, randomly initialized BVs quickly converge to a single vector that is the leading LV. The last model is the SPEEDY model created by Molteni (2003). It is a simplified general atmospheric circulation model with several types of instabilities

  7. Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus-response curves.

    PubMed

    Duc, Luu Hoang; Chávez, Joseph Páez; Son, Doan Thai; Siegmund, Stefan

    2016-01-01

    In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape. PMID:27416142

  8. Critical Path Web Site

    NASA Technical Reports Server (NTRS)

    Robinson, Judith L.; Charles, John B.; Rummel, John A. (Technical Monitor)

    2000-01-01

    Approximately three years ago, the Agency's lead center for the human elements of spaceflight (the Johnson Space Center), along with the National Biomedical Research Institute (NSBRI) (which has the lead role in developing countermeasures) initiated an activity to identify the most critical risks confronting extended human spaceflight. Two salient factors influenced this activity: first, what information is needed to enable a "go/no go" decision to embark on extended human spaceflight missions; and second, what knowledge and capabilities are needed to address known and potential health, safety and performance risks associated with such missions. A unique approach was used to first define and assess those risks, and then to prioritize them. This activity was called the Critical Path Roadmap (CPR) and it represents an opportunity to develop and implement a focused and evolving program of research and technology designed from a "risk reduction" perspective to prevent or minimize the risks to humans exposed to the space environment. The Critical Path Roadmap provides the foundation needed to ensure that human spaceflight, now and in the future, is as safe, productive and healthy as possible (within the constraints imposed on any particular mission) regardless of mission duration or destination. As a tool, the Critical Path Roadmap enables the decisionmaker to select from among the demonstrated or potential risks those that are to be mitigated, and the completeness of that mitigation. The primary audience for the CPR Web Site is the members of the scientific community who are interested in the research and technology efforts required for ensuring safe and productive human spaceflight. They may already be informed about the various space life sciences research programs or they may be newcomers. Providing the CPR content to potential investigators increases the probability of their delivering effective risk mitigations. Others who will use the CPR Web Site and its content

  9. Critical Path Web Site

    NASA Technical Reports Server (NTRS)

    Robinson, Judith L.; Charles, John B.; Rummel, John A. (Technical Monitor)

    2000-01-01

    Approximately three years ago, the Agency's lead center for the human elements of spaceflight (the Johnson Space Center), along with the National Biomedical Research Institute (NSBRI) (which has the lead role in developing countermeasures) initiated an activity to identify the most critical risks confronting extended human spaceflight. Two salient factors influenced this activity: first, what information is needed to enable a "go/no go" decision to embark on extended human spaceflight missions; and second, what knowledge and capabilities are needed to address known and potential health, safety and performance risks associated with such missions. A unique approach was used to first define and assess those risks, and then to prioritize them. This activity was called the Critical Path Roadmap (CPR) and it represents an opportunity to develop and implement a focused and evolving program of research and technology designed from a "risk reduction" perspective to prevent or minimize the risks to humans exposed to the space environment. The Critical Path Roadmap provides the foundation needed to ensure that human spaceflight, now and in the future, is as safe, productive and healthy as possible (within the constraints imposed on any particular mission) regardless of mission duration or destination. As a tool, the Critical Path Roadmap enables the decision maker to select from among the demonstrated or potential risks those that are to be mitigated, and the completeness of that mitigation. The primary audience for the CPR Web Site is the members of the scientific community who are interested in the research and technology efforts required for ensuring safe and productive human spaceflight. They may already be informed about the various space life sciences research programs or they may be newcomers. Providing the CPR content to potential investigators increases the probability of their delivering effective risk mitigations. Others who will use the CPR Web Site and its

  10. Path Integrals and Supersolids

    NASA Astrophysics Data System (ADS)

    Ceperley, D. M.

    2008-11-01

    Recent experiments by Kim and Chan on solid 4He have been interpreted as discovery of a supersolid phase of matter. Arguments based on wavefunctions have shown that such a phase exists, but do not necessarily apply to solid 4He. Imaginary time path integrals, implemented using Monte Carlo methods, provide a definitive answer; a clean system of solid 4He should be a normal quantum solid, not one with superfluid properties. The Kim-Chan phenomena must be due to defects introduced when the solid is formed.