Abstract
The present paper puts forward and probes a stochastic single-species model with predation effect in a polluted environment. We propose a threshold between extermination and weak persistence of the species and provide sufficient conditions for the stochastic persistence of the species. In addition, we evaluate the growth rates of the solution. Theoretical findings are expounded by some numerical simulations.
Highlights
Environmental pollution because of industry, commerce, agriculture, and the rapid growth of human population has been increasingly prominent and has become an global problem
In the 1980s, Hallam and his co-workers [4,5,6] first constructed a series of deterministic models with pollution and uncovered that environmental pollution has serious influence on the persistence and extermination of the species
We offer a threshold between extermination and weak persistence of the species and provide conditions under which the species is stochastically persistent in Sect
Summary
Environmental pollution because of industry, commerce, agriculture, and the rapid growth of human population has been increasingly prominent and has become an global problem. In the 1980s, Hallam and his co-workers [4,5,6] first constructed a series of deterministic models with pollution and uncovered that environmental pollution has serious influence on the persistence and extermination of the species. These results were improved and extended [7,8,9,10,11,12,13,14,15,16,17]. Motivated by the fact that the evolution of populations often encounters environmental perturbations [18], several authors (see, e.g., [9, 12,13,14,15,16,17]) paid attention to stochastic population models with pollution and uncovered that environmental perturbations have vital functions on the persistence and extermination of the species
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