Dynamics Analysis of a Stochastic Leslie–Gower Predator‐Prey Model with Feedback Controls

Abstract

This study focuses on the investigation of a stochastic Leslie–Gower predator-prey model with feedback controls and Holling type II functional responses. First, the existence and uniqueness of a global positive solution to the system under white noise interference are proved. Second, the conditions for the existence of the system’s positive recurrence are established by constructing suitable Lyapunov functions. Additionally, the persistence and extinction of prey and predator in the system are discussed, and the impacts of noise interference and feedback controls on the system are revealed. Finally, we validate the theoretical results by numerical simulations.

Periodic Solution of a Neutral Delay Leslie Predator-Prey Model and the Effect of Random Perturbation on the Smith Growth Model

“…On the contrary, biological populations multiply and thrive in nature, which will inevitably be affected by various environmental noise, so it is important to consider the effects of random disturbances on population dynamics [21][22][23][24][25][26][27][28][29]. In [30], the asymptotic stability of a stochastic May mutualism system was studied.…”