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https://doi.org/10.1016/j.jde.2021.10.021

has been cited by the following article:

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

  AUTHORS: Yanzhe Han, Fuqin Sun

  KEYWORDS: Bazykin Functional Response, Lyapunov Function, Boundedness, Uniqueness, Stability

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.5, May 29, 2023

  ABSTRACT: 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.