Hopf Bifurcations of a Stochastic Fractional-Order Van der Pol SystemReport as inadecuate




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Abstract and Applied AnalysisVolume 2014 2014, Article ID 835482, 10 pages

Research Article

State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China

School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001, China

Received 27 March 2014; Revised 21 May 2014; Accepted 21 May 2014; Published 9 June 2014

Academic Editor: Juan J. Trujillo

Copyright © 2014 Xiaojun Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.





Author: Xiaojun Liu, Ling Hong, and Lixin Yang

Source: https://www.hindawi.com/



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