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

Abstract

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 θth 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.