Horseshoe and entropy in a fractional-order unified system

被引：0
|
作者：
李清都 [1 ,2 ]
陈述 [1 ]
周平 [2 ]
机构：
[1] Key Laboratory of Networked Control and Intelligent Instrument of Ministry of Education,Chongqing University of Posts and Telecommunications
[2] Institute for Nonlinear Systems,Chongqing University of Posts and Telecommunications
来源：
Chinese Physics B | 2011年 / 20卷 / 01期
基金：
中国国家自然科学基金;
关键词：
chaos; topological horseshoe; fractional-order system; generalised Lorenz system;
D O I：
暂无
中图分类号：
O415.5 [混沌理论];
学科分类号：
070201 ;
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 Poincar’e 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.
引用
收藏
页码：179 / 184
页数：6
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