Dynamics of a stochastic non-autonomous predator-prey system with Beddington-DeAngelis functional response

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

Coexistence and extinction of a periodic stochastic predator–prey model with general functional response

“…(2) Theorem 1 refines and evolves the above results in the periodic case: firstly, model (1) is more general; secondly, we provide the coexistence-and-extinction threshold while there is a gap in [8]; thirdly, we provide the conditions for UWPIM, the authors [8] provided conditions for WPIM.…”

“…in thee nonautonomous case. When their results are restricted to the periodic case, Li and Zhang [8] testified that -If Λ 1 > 0 and…”

“…Theorem 1 refines and evolves the work of [20]: firstly, the model in [20] is a special case of model (1); secondly, there is a gap in [20] while we provide the coexistence-and-extinction threshold; thirdly, we provide the conditions for UWPIM which indicates WPIM, however, WPIM does not indicate UWPIM. [8] delved into model (1) with…”

On the small-time behavior of stochastic logistic models

“…The existence of positive solutions to the system (19) and its long-time behaviors have been recently discussed in [8]. Our aim here is to establish the small-time behavior of the solutions.…”

Dynamics of a single predator multiple prey model with stochastic perturbation and seasonal variation

“…Meng et al [24] studied a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal model, and proved the uniformly persistent of population by using the comparison theorem and fundamental theory of delay differential equation. More related stochastic non-autonomous or periodic population models can be found in [25,26] and the references therein.…”