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Persistence, extinction and global asymptotical stability of a non-autonomous predator-prey model with random perturbation. (English) Zbl 1254.34074
Summary: A two-species stochastic non-autonomous predator-prey model is investigated. Sufficient criteria for extinction, non-persistence in the mean and weak persistence in the mean are established. The critical value between persistence and extinction is obtained for each species in many cases. It is also shown that the system is globally asymptotically stable under some simple conditions. Some numerical simulations are introduced to illustrate the main results.
MSC:
34D23Global stability of ODE
92D25Population dynamics (general)
34D10Stability perturbations of ODE
34F05ODE with randomness
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