Dynamics of a Mutualistic Model with Diffusion  

作　　者：Mei Li 

机构地区：[1]School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210023,China

出　　处：《Analysis in Theory and Applications》2017年第3期206-218,共13页分析理论与应用（英文刊）

基　　金：supported by the NSFC Grant(No.11171158);Project of Graduate Education Innovation of Jiangsu Province(No.KYLX 0719);Project of Natural Science Research of Higher Education Institutions of Jiangsu Province(No.15KJB110008)

摘　　要：This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.This article is concerned with a system of semilinear parabolic equations with no-flux boundary condition in a mutualistic ecological model. Stability result of the equilibrium about relevant ODE problem is proved by discussing its Jacobian matrix, we give two priori estimates and prove that the model is permanent when ε1 ＋ε2≠ 0. Moreover sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the model are obtained. Nonexistence of nonconstant positive steady states of the model is also given. When ε1 ＋ε2 = 0, grow up property is derived if the geometric mean of the interaction coefficients is greater than I （a1a2 〉 1）, while if the geometric mean of the interaction coefficients is less than I （a1a2 〈 1）, there exists a global solution. Finally, numerical simulations are given.

关 键 词：Reaction-diffusion systems mutualistic model EQUILIBRIUM PERMANENCE grow-up. 

分 类 号：O175[理学—数学]