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

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


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