Open AccessDynamical behavior of a stochastic predator-prey model with general functional response and nonlinear jump-diffusion
Author(s) -
Xinhong Zhang,
Qingxiong Yang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021177
Subject(s) - ergodicity , ergodic theory , mathematics , nonlinear system , extinction (optical mineralogy) , functional response , stationary distribution , statistical physics , jump , diffusion , exponential function , predation , predator , mathematical analysis , statistics , markov chain , physics , ecology , thermodynamics , quantum mechanics , optics , biology
In this paper, we consider a stochastic predator-prey model with general functional response, which is perturbed by nonlinear Lévy jumps. Firstly, We show that this model has a unique global positive solution with uniform boundedness of \begin{document}$ \theta\in(0,1] $\end{document} -th moment. Secondly, we obtain the threshold for extinction and exponential ergodicity of the one-dimensional Logistic system with nonlinear perturbations. Then based on the results of Logistic system, we introduce a new technique to study the ergodic stationary distribution for the stochastic predator-prey model with general functional response and nonlinear jump-diffusion, and derive the sufficient and almost necessary condition for extinction and ergodicity.