Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

•Exact Lyapunov dimension of many classical attractors is known.•Exact Lyapunov dimension for Rossler system has not been known.•Leonov conjecture: it is equal to local Lyapunov dimension in stationary point.•In this work Leonov’s conjecture is checked numerically. Exact Lyapunov dimension of attrac...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2014-04, Vol.19 (4), p.1027-1034
Main Authors: Kuznetsov, N.V., Mokaev, T.N., Vasilyev, P.A.
Format: Article
Language:English
Subjects:
Chaos
Chaos theory
Computer simulation
Leonov’s conjecture
Lyapunov dimension
Lyapunov exponent
Mathematical models
Nonlinearity
Rössler system
Strange attractor
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Summary:•Exact Lyapunov dimension of many classical attractors is known.•Exact Lyapunov dimension for Rossler system has not been known.•Leonov conjecture: it is equal to local Lyapunov dimension in stationary point.•In this work Leonov’s conjecture is checked numerically. 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.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2013.07.026