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

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 stochast...

Full description

Saved in:
Bibliographic Details
Published inChinese physics B Vol. 26; no. 9; pp. 62 - 69
Main Author 李伟 张美婷 赵俊锋
Format Journal Article
LanguageEnglish
Published 01.08.2017
Subjects
l系统
van
分数阶导数
广义
有色噪声
概率密度
随机分岔
Online AccessGet full text
ISSN1674-1056
2058-3834
DOI10.1088/1674-1056/26/9/090501

Cover

More Information
Summary: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.
Bibliography:stochastic bifurcation fractional derivative color noise stochastic averaging method
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.
11-5639/O4
ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/26/9/090501