Analysis of a stochastic ratio-dependent one-predator and two-mutualistic-preys model with Markovian switching and Holling type III functional response

Advances in Difference Equations

Rensheng He¹  Desheng Hong¹  Zuoliang Xiong²  Hongwei Yin² 

[1] Department of Mathematics, Nanchang University, Nanchang, P.R. China;Numerical Simulation and High-Performance Computing Laboratory, School of Sciences, Nanchang University, Nanchang, P.R. China

关键词: stochastic permanence;    extinction;    Markovian switching;    predator-prey model;    mutualism;   

DOI  :  10.1186/s13662-016-1011-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose a stochastic ratio-dependent one-predator and two-mutualistic-preys model perturbed by white and telegraph noise. By the M-matrix analysis and Lyapunov functions, sufficient conditions of stochastic permanence and extinction are established. These conditions are all dependent on the parameters of subsystems and the stationary probability distribution of the Markov chain. We also obtain the boundary of limit superior and inferior of the average in time of the solution under stochastic permanence. Finally, we give two examples and numerical simulations to illustrate main results.

【 授权许可】

CC BY