A robust, locally interpretable algorithm for Lyapunov exponents

Grond, Florian; Diebner, Hans H.; Sahle, Sven; Mathias, Adolf; Fischer, Sebastian; Rössler, Otto E.

doi:10.1016/s0960-0779(02)00479-4

Cited by 48 publications

(8 citation statements)

References 4 publications

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“…Convincing evidence for deterministic chaos has come from several recent experiments [23][24][25][26][27]. The results of these experimental studies have confirmed the importance of detecting and exploring chaos.…”

Section: The Largest Lyapunov Exponentmentioning

confidence: 85%

Three-species food web model with impulsive control strategy and chaos

Yu¹,

Zhong²,

Agarwal³

et al. 2011

Communications in Nonlinear Science and Numerical Simulation

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Section: The Largest Lyapunov Exponentmentioning

confidence: 85%

Three-species food web model with impulsive control strategy and chaos

Yu¹,

Zhong²,

Agarwal³

et al. 2011

Communications in Nonlinear Science and Numerical Simulation

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“…Finally, the effect of distributed time delay a on the system (8) is explored. Several recent experiments have become deterministic evidence for chaos, and the results of these literatures show that the study of chaos is very meaningful [37][38][39]. Among them, the largest Lyapunov exponents provide a very effective diagnosis for the chaotic system, and the largest Lyapunov exponent is the average change rate of the two trajectories which are close in phase space as time goes on by exponential separation or polymerization.…”

Section: Examples and Simulationsmentioning

confidence: 99%

On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

Wang

Liu

et al. 2020

Discrete Dynamics in Nature and Society

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In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.

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“…The Lyapunov exponents -also named LCE -are often computed with the Wolf algorithm and its variants (Geist et al 1990;Sandri 1996;Grond et al 2003). Wolf et al (1985) estimated the number of samples required for a good representation of an attractor for the estimation with enough accuracy of the Lyapunov exponents.…”

Section: Geometrical and Statistical Fractal Dimensions: Attractor Chmentioning

confidence: 99%

Characterization of nonlinear dynamic systems for engineering purposes – a partial review

Teodorescu¹

2012

International Journal of General Systems

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A robust, locally interpretable algorithm for Lyapunov exponents

Cited by 48 publications

References 4 publications

Three-species food web model with impulsive control strategy and chaos

Three-species food web model with impulsive control strategy and chaos

On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

Characterization of nonlinear dynamic systems for engineering purposes – a partial review

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