Survival and ergodicity of a stochastic Holling-III predator–prey model with Markovian switching in an impulsive polluted environment

Abstract

Abstract Based on the effects of white noise and colored noise, we propose a stochastic Holling-III predator–prey model in an impulsive polluted environment. Firstly, we prove an existence and uniqueness theorem of the presented model. Secondly, we establish sufficient criteria of extinction, nonpersistence in mean, and weak persistence in mean for both prey and predator species. Thirdly, with the aid of Lyapunov functions, we prove that this system is ergodic and has a unique stationary distribution under certain conditions. Finally, we verify the theoretical results by performing some numerical simulations.

Keywords

• Stochastic Holling-III predator–prey model
• Markovian switching
• Impulsive polluted environment
• Survival analysis
• Ergodicity