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

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      Abstract and Applied Analysis

      Hindawi Limited

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          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.

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          Most cited references 25

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          Fractal system as represented by singularity function

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            An adaptive multi-element generalized polynomial chaos method for stochastic differential equations

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              A note on the fractional-order Chen system

               Jun Lu,  Guanrong Chen (2006)
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                Author and article information

                Journal
                Abstract and Applied Analysis
                Abstract and Applied Analysis
                Hindawi Limited
                1085-3375
                1687-0409
                2014
                2014
                : 2014
                :
                : 1-10
                Article
                10.1155/2014/835482
                © 2014

                http://creativecommons.org/licenses/by/3.0/

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