Mathematical modeling reveals that environmental noise and time delays regulate population persistence and extinction in predator-prey systems, highlighting complex ecological dynamics.
This paper incorporates the effects of the stochastic perturbations and multiple time-delays into a generalized predator-prey system. The presented system includes two types of perturbations: one is a nonlinear comprehensive perturbation, and the other is a perturbation on the predator’s attacking rate. Firstly, the unique existence of the global positive solutions and various boundedness properties of the proposed system are considered. Secondly, the mean persistence and extinction of predator and prey populations are investigated. The results demonstrate that stochastic perturbations and multiple time-delays have an important effects on the dynamical behaviors of the considered system. Finally, all theoretical results are verified by numerical simulations.
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Ma et al. (2026) studied this question.
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