Chaos in a generalized van der Pol system and in its fractional order system

被引：26

作者：

Ge, Zheng-Ming ^{[1
]}

Hsu, Mao-Yuan ^{[1
]}

机构：

[1] Natl Chiao Tung Univ, Dept Mech Engn, Hsinchu 300, Taiwan

来源：

CHAOS SOLITONS & FRACTALS | 2007年 / 33卷 / 05期

关键词：

D O I：

10.1016/j.chaos.2006.03.028

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, chaos of a generalized van der Pol system with fractional orders is studied. Both nonautonomous and autonomous systems are considered in detail. Chaos in the nonautonomous generalized van der Pol system excited by a sinusoidal time function with fractional orders is studied. Next, chaos in the autonomous generalized van der Pol system with fractional orders is considered. By numerical analyses, such as phase portraits, Poincare maps and bifurcation diagrams, periodic, and chaotic motions are observed. Finally, it is found that chaos exists in the fractional order system with the order both less than and more than the number of the states of the integer order generalized van der Pol system. (C) 2006 Elsevier Ltd. All rights reserved.

引用

页码：1711 / 1745

页数：35

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