Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System

被引：1
|
作者：
Liu, Xiaojun [1 ,2 ]
Hong, Ling [1 ]
Yang, Lixin [1 ,2 ]
机构：
[1] Xi An Jiao Tong Univ, State Key Lab Strength & Vibrat Mech Struct, Xian 710049, Peoples R China
[2] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2014年
基金：
中国国家自然科学基金;
关键词：
GENERALIZED POLYNOMIAL CHAOS; DUFFING SYSTEM; DIFFERENTIAL-EQUATIONS; VANDERPOL OSCILLATOR; SYNCHRONIZATION; APPROXIMATION; UNCERTAINTY; EXPANSIONS;
D O I：
10.1155/2014/835482
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Hopf bifurcation of a fractional-order Van der Pol (VDP for short) system with a random parameter is investigated. Firstly, the Chebyshev polynomial approximation is applied to study the stochastic fractional-order system. Based on the method, the stochastic system is reduced to the equivalent deterministic one, and then the responses of the stochastic system can be obtained by numerical methods. Then, according to the existence conditions of Hopf bifurcation, the critical parameter value of the bifurcation is obtained by theoretical analysis. Then, numerical simulations are carried out to verify the theoretical results.
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收藏
页数：10
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