Open AccessStability and Hopf bifurcation in a prey-predator model with memory-based diffusion
Author(s) -
Shu Li,
Zhenzhen Li,
Binxiang Dai
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.2022025
Subject(s) - hopf bifurcation , mathematics , stability (learning theory) , steady state (chemistry) , eigenvalues and eigenvectors , bifurcation , mathematical analysis , predation , pitchfork bifurcation , manifold (fluid mechanics) , center manifold , pure mathematics , physics , nonlinear system , computer science , biology , ecology , mechanical engineering , chemistry , quantum mechanics , machine learning , engineering
In this paper, we consider a predator-prey model with memory-based diffusion. We first analyze the stability of all steady states in detail. Then by analyzing the distribution of eigenvalues, we find that the average memory period can cause the stability change of the positive steady state, and Hopf bifurcation occurs at the positive steady state. Moreover, from the central manifold theorem and the normal form theory, we give the direction and stability of Hopf bifurcation. The results show that, under certain conditions, a family of spatially inhomogeneous periodic solutions will bifurcate from the positive steady state when the average memory period appear.