Hopf Bifurcation of Compound Stochastic van der Pol System

Shaojuan Ma and Qianling Zhang

Mathematical Problems in Engineering, 2016, vol. 2016, 1-7

Abstract:

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 and noise intensity on stochastic Hopf bifurcation in compound stochastic system is discussed. At last we found that increased can relocate the critical value of bifurcation parameter forward while increased makes it backward and the influence of is more sensitive than . The results are verified by numerical simulations.

Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2016/4246916.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2016/4246916.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:4246916

DOI: 10.1155/2016/4246916

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().