Stability Analysis of a Self-Memory Prey-Predator Diffusion Model Based on Bazykin Functional Response  

作　　者：Yanzhe Han Fuqin Sun Yanzhe Han;Fuqin Sun(School of Sciences, Tianjin University of Technology and Education, Tianjin, China)

机构地区：[1]School of Sciences, Tianjin University of Technology and Education, Tianjin, China

出　　处：《Journal of Applied Mathematics and Physics》2023年第5期1391-1403,共13页应用数学与应用物理（英文）

摘　　要：To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.

关 键 词：Bazykin Functional Response Lyapunov Function BOUNDEDNESS UNIQUENESS Stability 

分 类 号：O17[理学—数学]