Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises

Xiaoling Zou; Dejun Fan; Ke Wang

doi:10.3934/dcdsb.2013.18.1507

Article Contents

2013, Volume 18, Issue 5: 1507-1519. Doi: 10.3934/dcdsb.2013.18.1507

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Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises

1.
Department of Mathematics, Harbin Institute of Technology, Weihai 264209
2.
Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209

Received: May 2012

Revised: October 2012

Published: July 2013

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Abstract

The existence of a stationary distribution and a stochastic Hopf bifurcation phenomenon for a noisy predator-prey system with Beddington-DeAngelis functional response are studied both theoretically and numerically. Considering the qualitative change of the shape of the stationary distribution, the stochastic Hopf bifurcation appears as a change from a peak-like distribution to a crater-like distribution. Results are obtained through the original niosy system rather than approximations based on stochastic averaging or scaling methods.

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Mathematics Subject Classification: Primary: 60H10, 37H20; Secondary: 60E05, 37N25.

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