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.
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)
