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2014 Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System
Xiaojun Liu, Ling Hong, Lixin Yang
Abstr. Appl. Anal. 2014: 1-10 (2014). DOI: 10.1155/2014/835482


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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Xiaojun Liu. Ling Hong. Lixin Yang. "Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol System." Abstr. Appl. Anal. 2014 1 - 10, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07023163
MathSciNet: MR3224323
Digital Object Identifier: 10.1155/2014/835482

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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