$L^\infty$ estimation of the LDG method for 1-d singularly perturbed convection-diffusion problems
July 2013, 18(5): 1507-1519. doi: 10.3934/dcdsb.2013.18.1507
Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises
Xiaoling Zou 1, , Dejun Fan 1, and Ke Wang 2,
Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China, China
Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
Received May 2012 Revised October 2012 Published March 2013
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.
Keywords: peak-like stationary distribution, numerical simulations., Beddington-DeAngelis functional response, phenomenological bifurcation, crater-like stationary distribution.
Mathematics Subject Classification: Primary: 60H10, 37H20; Secondary: 60E05, 37N2.
Citation: Xiaoling Zou, Dejun Fan, Ke Wang. Stationary distribution and stochastic Hopf bifurcation for a predator-prey system with noises. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1507-1519. doi: 10.3934/dcdsb.2013.18.1507
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