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

作　　者：李伟 张美婷 赵俊锋 

机构地区：[1]School of Mathematics and Statistics,Xidian University [2]Applied Mathematics Department,School of Science,Northwestern Polytechnical University

出　　处：《Chinese Physics B》2017年第9期62-69,共8页中国物理B（英文版）

基　　金：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);Chinese–Serbian Science and Technology Cooperation for the Years 2015-2016(Grant No.3-19)

摘　　要：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.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.

关 键 词：stochastic bifurcation fractional derivative color noise stochastic averaging method 

分 类 号：O175[理学—数学]