Lyapunov exponent

We study the dynamics of a double-well BEC system subjected to oscillating dissipation. The macroscopic model is described within the mean-field approximation while the noise effect due to large reservoir fluctuation has been averaged out to zero. We chose a simple dissipative memory kernel to produce a time-dependent oscillating dissipation. Our numerically calculated phase-space portraits and Lyapunov exponents show an enhanced route to chaos as one increases the driving dissipation amplitude.

14p dianmotminh02 03-05-2024 1 1   Download

The dissertation is divided into four chapters: Chapter 1 - Preliminaries; Chapter 2 - Lyapunov exponents for dynamic equations; Chapter 3 - Bohl exponents for implicit dynamic equations; Chapter 4 - Stability radius for implicit dynamic equations.

117p monsterhunterer 20-06-2021 19 2   Download

In this paper, we investigate the use of a deep learning method, Deep Belief Network (DBN), combined with chaos theory to forecast chaotic time series. DBN should be used to forecast chaotic time series. First, the chaotic time series are analyzed by calculating the largest Lyapunov exponent, reconstructing the time series by phase-space reconstruction and determining the best embedding dimension and the best delay time. When the forecasting model is constructed, the deep belief network is used to feature learning and the neural network is used for prediction.

11p trinhthamhodang9 04-12-2020 22 2   Download

The spread of infectious diseases is so important that changes the demography of the population. Therefore, prevention and intervention measures are essential to control and eliminate the disease. Among the drug and non-drug interventions, vaccination is a powerful strategy to preserve the population from infection.

15p vikentucky2711 24-11-2020 12 1   Download

Memristor is a non-linear circuit element in which voltage-current relationship is determined by the previous values of the voltage and current, generally the history of the circuit. The nonlinearity in this component can be considered as a fractional-order form, which yields a fractional memristor (fracmemristor). In this paper, a fractional-order memristor in a chaotic oscillator is applied, while the other electronic elements are of integer order. The fractional-order range is determined in a way that the circuit has chaotic solutions.

9p dayhoctainha 10-09-2020 8 0   Download

This paper introduces an intensive discussion for the dynamical model of the love triangle in both integer and fractional-order domains. Three different types of nonlinearities soft, hard, and mixed between soft and hard, are used in this study. MATLAB numerical simulations for the different three categories are presented. Also, a discussion for how the kind of personalities affects the behavior of chaotic attractors is introduced. This paper suggests some explanations for the complex love relationships depending on the impact of memory (IoM) principle.

13p dayhoctainha 10-09-2020 25 1   Download

Fractional calculus (FC) is widely used in many interdisciplinary branches of science due to its effectiveness in describing and investigating complicated phenomena. In this work, nonlinear dynamics for a new physical model using nonlocal fractional differential operator with singular kernel is introduced. New Routh-Hurwitz stability conditions are derived for the fractional case as the order lies in [0,2). The new and basic Routh-Hurwitz conditions are applied to the commensurate case. The local stability of the incommensurate orders is also discussed.

12p covid19 14-06-2020 28 2   Download

This paper presents the design of the generalized Double Humped (DH) logistic map, used for pseudorandom number key generation (PRNG). The generalized parameter added to the map provides more control on the map chaotic range. A new special map with a zooming effect of the bifurcation diagram is obtained by manipulating the generalization parameter value. The dynamic behavior of the generalized map is analyzed, including the study of the fixed points and stability ranges, Lyapunov exponent, and the complete bifurcation diagram.

14p trinhthamhodang1 14-11-2019 9 0   Download

An abstract version of Lyapunov exponents is defined for positive homogeneous maps on Homogeneous Lattices and a sufficient condition is given for the asymptotic stability of the map.

5p tuongvidanh 06-01-2019 15 1   Download

We prove that for any s 0 the majority of C s linear cocycles over any hyperbolic (uniformly or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an open dense subset of cocycles and, actually, vanishing Lyapunov exponents correspond to codimension-∞. This open dense subset is described in terms of a geometric condition involving the behavior of the cocycle over certain heteroclinic orbits of the transformation.

39p dontetvui 17-01-2013 40 7   Download

We show that the integrated Lyapunov exponents of C 1 volume-preserving diffeomorphisms are simultaneously continuous at a given diffeomorphism only if the corresponding Oseledets splitting is trivial (all Lyapunov exponents are equal to zero) or else dominated (uniform hyperbolicity in the projective bundle) almost everywhere. We deduce a sharp dichotomy for generic volume-preserving diffeomorphisms on any compact manifold:

64p noel_noel 17-01-2013 33 5   Download

Inspired by Lorenz’ remarkable chaotic flow, we describe in this paper the structure of all C 1 robust transitive sets with singularities for flows on closed 3-manifolds: they are partially hyperbolic with volume-expanding central direction, and are either attractors or repellers. In particular, any C 1 robust attractor with singularities for flows on closed 3-manifolds always has an invariant foliation whose leaves are forward contracted by the flow, and has positive Lyapunov exponent at every orbit, showing that any C 1 robust attractor resembles a geometric Lorenz attractor. ...

59p tuanloccuoi 04-01-2013 53 7   Download

In this paper we consider the upper (lower) - stability of Lyapunov exponents of linear differential equations in Rn . Sufficient conditions for the upper - stability of maximal exponent of linear systems under linear perturbations are given. The obtained results are extended to the system with nonlinear perturbations.

8p tuanlocmuido 19-12-2012 37 2   Download