Hopf bifurcation of compound stochastic van der Pol system
type: Item
instance of: scholarly article
title: Hopf bifurcation of compound stochastic van der Pol system
zbMATH Open document ID: 1400.34098
DOI: 10.1155/2016/4246916
author: Qianling Zhang
author: Shao-juan Ma
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: Hopf bifurcation analysis for compound stochastic van der Pol system with a bound random parameter and Gaussian white noise is investigated in this paper. By the Karhunen-Loeve (K-L) expansion and the orthogonal polynomial approximation, the equivalent deterministic van der Pol system can be deduced. Based on the bifurcation theory of nonlinear deterministic system, the critical value of bifurcation parameter is obtained and the influence of random strength \(\delta\) and noise intensity \(\sigma\) on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased \(\delta\) can relocate the critical value of bifurcation parameter forward while increased \(\sigma\) makes it backward and the influence of \(\delta\) is more sensitive than \(\sigma\). The results are verified by numerical simulations.
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 70L05
zbMATH DE Number: 6953172
MaRDI profile type: Publication
Wikidata QID: Q59131273
full work available at URL: https://doi.org/10.1155/2016/4246916
OpenAlex ID: W2416054124
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description: scientific article; zbMATH DE number 6953172