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Abstract and Applied Analysis
Volume 2013, Article ID 432704, 13 pages
http://dx.doi.org/10.1155/2013/432704
Research Article

Asymptotic Behavior of the Stochastic Rayleigh-van der Pol Equations with Jumps

1School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530001, China
2College of Mathematics and Information Science, Guangxi University, Nanning 530004, China

Received 20 May 2013; Revised 2 July 2013; Accepted 2 July 2013

Academic Editor: Józef Banaś

Copyright © 2013 ZaiTang Huang and ChunTao Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the stability, attractors, and bifurcation of stochastic Rayleigh-van der Pol equations with jumps. We first established the stochastic stability and the large deviations results for the stochastic Rayleigh-van der Pol equations. We then examine the existence limit circle and obtain some new random attractors. We further establish stochastic bifurcation of random attractors. Interestingly, this shows the effect of the Poisson noise which can stabilize or unstabilize the system which is significantly different from the classical Brownian motion process.