Analysis of a stochastic predator-prey model with weak Allee effect and Holling-(n+1) functional response

Considering the profound ecological implication of Allee effect, and the effects after incorporating it into models of population dynamics, a stochastic predator-prey model with Holling-(n+1) functional response and weak Allee effect is mainly investigated in this paper. Firstly, we verify the existence of unique global positive solution to the model, and then the boundedness of theta th moment of the solution is studied. Secondly, we investigate the corresponding one-dimensional model, and obtain the explicit density function of the solution to the model. Then, based on the results of the one-dimensional system and a series of appropriate Lyapunov functions, we adopt a new technique to obtain a sufficient and almost necessary condition for the existence of the unique ergodic stationary distribution and extinction. Next, we further study the dynamical behavior of the model with Markovian switching and give some main conclusions. Finally, several numerical simulations are carried out to illustrate the theoretical results. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates a stochastic predator-prey model with weak Allee effect and Holling-(n+1) functional response. Firstly, the existence of unique global positive solution to the model is verified, and the boundedness of the theta-th moment of the solution is studied. Secondly, the corresponding one-dimensional model is investigated, and the explicit density function of the solution is obtained. Then, a new technique is adopted to establish a sufficient and almost necessary condition for the existence of the unique ergodic stationary distribution and extinction based on the results of the one-dimensional system and a series of appropriate Lyapunov functions. Next, the dynamical behavior of the model with Markovian switching is analyzed and some main conclusions are derived. Finally, numerical simulations are conducted to illustrate the theoretical results.