Open AccessThe stability and bifurcation of homogeneous diffusive predator–prey systems with spatio–temporal delays
Author(s) -
Yiwen Tao,
Jing Ren
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.2021038
Subject(s) - uniqueness , mathematics , stability (learning theory) , hopf bifurcation , bifurcation , predation , constant (computer programming) , homogeneous , mathematical analysis , control theory (sociology) , nonlinear system , computer science , physics , combinatorics , ecology , biology , artificial intelligence , control (management) , quantum mechanics , machine learning , programming language
In this paper, we consider a generalized predator-prey system described by a reaction-diffusion system with spatio-temporal delays. We study the local stability for the constant equilibria of predator-prey system with the generalized delay kernels. Moreover, using the specific delay kernels, we perform a qualitative analysis of the solutions, including existence, uniqueness, and boundedness of the solutions; global stability, and Hopf bifurcation of the nontrivial equilibria.