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Horseshoe and entropy in a fractional-order unified system 被引量:1

Horseshoe and entropy in a fractional-order unified system
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摘要 This paper studies chaotic dynamics in a fractional-order unified system by means of topological horseshoe theory and numerical computation. First it finds four quadrilaterals in a carefully-chosen Poincare section, then shows that the corresponding map is semiconjugate to a shift map with four symbols. By estimating the topological entropy of the map and the original time-continuous system, it provides a computer assisted verification on existence of chaos in this system, which is much more convincible than the common method of Lyapunov exponents. This new method can potentially be used in rigorous studies of chaos in such a kind of system. This paper may be a start for proving a given fractional-order differential equation to be chaotic. This paper studies chaotic dynamics in a fractional-order unified system by means of topological horseshoe theory and numerical computation. First it finds four quadrilaterals in a carefully-chosen Poincare section, then shows that the corresponding map is semiconjugate to a shift map with four symbols. By estimating the topological entropy of the map and the original time-continuous system, it provides a computer assisted verification on existence of chaos in this system, which is much more convincible than the common method of Lyapunov exponents. This new method can potentially be used in rigorous studies of chaos in such a kind of system. This paper may be a start for proving a given fractional-order differential equation to be chaotic.
出处 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期175-180,共6页 中国物理B(英文版)
基金 Project supported by the National Natural Science Foundation of China(Grant Nos.10926072 and 10972082) Chongqing Municipal Education Commission(Grant No.KJ080515) Natural Science Foundation Project of CQ CSTC,China(GrantNo.2008BB2409)
关键词 CHAOS topological horseshoe fractional-order system generalised Lorenz system chaos, topological horseshoe, fractional-order system, generalised Lorenz system
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