Abstract
In this paper, stochastic non-autonomous predator–prey models with and without impulses are investigated. The effects of generalized nonlinear harvesting for prey and predator populations are considered. For the stochastic system without impulses, the existence and uniqueness of the positive solution is proven and sufficient conditions that guarantee the extinction and persistence of the population in the mean are achieved. We show the existence of a nontrivial positive periodic solution by constructing appropriate Lyapunov functions and using Khasminskii’s theory. Moreover, the global attractiveness and stochastic persistence in probability of the stochastic model are discussed. Results show that the stronger noises and nonlinear harvesting component can significantly influence the dynamics of the system and lead to the extinction of the predator population. Additionally, for the stochastic predator–prey system with impulsive effect, we prove that there exists a positive periodic solution. Numerical simulations are conducted to show the effectiveness and feasibility of the obtained results.
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