Stochastic bifurcations of generalized Duffing-van der Pol system with fractional derivative under colored noise

doi:10.1088/1674-1056/26/9/090501

Abstract The stochastic bifurcation of a generalized Duffing-van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation.

Keywords: stochastic bifurcation fractional derivative color noise stochastic averaging method

Received: 01 March 2017
Revised: 08 May 2017
Accepted manuscript online:

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.10.Gg	(Stochastic analysis methods)
	05.10.Ln	(Monte Carlo methods)
	05.40.Ca	(Noise)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11302157), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2015JM1028), the Fundamental Research Funds for the Central Universities, China (Grant No. JB160706), and Chinese-Serbian Science and Technology Cooperation for the Years 2015-2016 (Grant No. 3-19).

Corresponding Authors: Wei Li
E-mail: liweilw@mail.xidian.edu.cn

Cite this article:

Wei Li(李伟), Mei-Ting Zhang(张美婷), Jun-Feng Zhao(赵俊锋) Stochastic bifurcations of generalized Duffing-van der Pol system with fractional derivative under colored noise 2017 Chin. Phys. B 26 090501

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Stochastic bifurcations of generalized Duffing-van der Pol system with fractional derivative under colored noise

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