Abstract
A stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response is proposed, the existence of a global positive solution and stochastically ultimate boundedness are derived. Sufficient conditions for extinction, non-persistence in the mean, weak persistence in the mean and strong persistence in the mean are established. The global attractiveness of the solution is also considered. Finally, numerical simulations are carried out to support our findings. MSC:92B05, 34F05, 60H10, 93E03.
Highlights
In population dynamics, the relationship between predator and prey plays an important role due to its universal existence
We introduce a non-autonomous predator-prey model with Beddington-DeAngelis functional response:
We show that the solution of system ( ) is globally positive and stochastically bounded
Summary
The relationship between predator and prey plays an important role due to its universal existence. 3 Persistence in the mean and extinction Lemma The solutions of system ( ) with initial value (x , y ) ∈ R + have the following properties: lim sup ln x(t) ≤ , t→∞ t lim sup ln y(t) ≤ , a.s. t→∞ t (II) If there are positive constants λ , T and λ ≥ such that t n ln x(t) ≥ λt – λ x(s) ds + βiBi(t) for t ≥ T , where βi is a constant, ≤ i ≤ n, x ∗ ≥ λ/λ , a.s. In the following, we give the result about weak persistence in the mean and extinction of the prey and predator population.
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