Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion | Zendy

Li Shu | Zendy; Zhenzhen Li | Zendy; Binxiang Dai | Zendy

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Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion

Author(s) -

Li Shu,

Zhenzhen Li,

Binxiang Dai

Publication year - 2022

Publication title -

discrete and continuous dynamical systems - 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 , stability (learning theory) , mathematics , steady state (chemistry) , eigenvalues and eigenvectors , bifurcation , mathematical analysis , manifold (fluid mechanics) , diffusion , predation , pure mathematics , physics , computer science , thermodynamics , nonlinear system , 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.

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