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The Lyapunov exponent is a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions. Estimates of Lyapunov exponents are often used to characterize the qualitative population dynamics of insect time series. The methodology for estimation of the exponent for an observed, noisy, short ecological time series is still under development. Some progress has been made recently in providing measures of error for these exponents. Studies that do not account...

Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators.

Baier, Gerold, Sahle, Sven (1997)

Discrete Dynamics in Nature and Society

Stabilizing the chaotic dynamics of the Lü system.

Tigan, G. (2007)

APPS. Applied Sciences

Stable and non-stable non-chaotic maps of the interval

Tomáš Gedeon (1991)

Mathematica Slovaca

Staircase baker's map generates flaring-type time series.

Hartmann, G.C., Radons, G., Diebner, H.H., Rössler, O.E. (2000)

Discrete Dynamics in Nature and Society

Statistical properties of unimodal maps

Artur Avila, Carlos Gustavo Moreira (2005)

Publications Mathématiques de l'IHÉS

We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition...

Stochastic Stability in Some Chaotic Dynamical Systems.

Gerhard Keller (1982)

Monatshefte für Mathematik

Structural stability of Lorenz attractors

John Guckenheimer, Robert F. Williams (1979)

Publications Mathématiques de l'IHÉS

Structure of mappings of an interval with zero entropy

Michal Misiurewicz (1981)

Publications Mathématiques de l'IHÉS

Sur un aspect numérique de la dimension fractale d'un attracteur chaotique

N. Akroune (2011)

Matematički Vesnik

Symbolic dynamics and Lyapunov exponents for Lozi maps

Diogo Baptista, Ricardo Severino (2012)

ESAIM: Proceedings

Building on the kneading theory for Lozi maps introduced by Yutaka Ishii, in 1997, we introduce a symbolic method to compute its largest Lyapunov exponent. We use this method to study the behavior of the largest Lyapunov exponent for the set of points whose forward and backward orbits remain bounded, and find the maximum value that the largest Lyapunov exponent can assume.

Synchronization in ensembles of coupled maps with a major element.

Omelchenko, Iryna, Maistrenko, Yuri, Mosekilde, Erik (2005)

Discrete Dynamics in Nature and Society

Synchronization with error bound of non-identical forced oscillators

Jian Gen Wang, Jianping Cai, Mihua Ma, Jiuchao Feng (2008)

Kybernetika

Synchronization with error bound of two non-identical forced oscillators is studied in the paper. By introducing two auxiliary autonomous systems, differential inequality technique and active control technique are used to deal with the synchronization of two non-identical forced oscillators with parameter mismatch in external harmonic excitations. Numerical simulations show the effectiveness of the proposed method.

Synchronizing spatiotemporal chaos by introducing a finite flat region in the local map.

Chen, J.Y., Wong, K.W., Zheng, H.Y., Shuai, J.W. (2001)

Discrete Dynamics in Nature and Society

Synthesis of chaotic systems

Antonín Vaněček, Sergej Čelikovský (1994)

Kybernetika

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