Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

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• 作者：N.V. Kuznetsov ; T.N. Mokaev ; P.A. Vasilyev
• 关键词：Rö ; ssler system ; Lyapunov dimension ; Strange attractor ; Lyapunov exponent ; Chaos ; Leonov&rsquo ; s conjecture
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：April, 2014
• 年：2014
• 卷：19
• 期：4
• 页码：1027-1034
• 全文大小：880 K

文摘

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