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The stability and bifurcation of homogeneous diffusive predator–prey systems with spatio–temporal delays

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  • 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.

    Mathematics Subject Classification: Primary: 35K57.


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  • Figure 1.  Some examples of $ f(u) $ and $ g(u) $. (a). Logistic effect (blue), weak Allee effect (red), strong Allee effect (green). (b). Type I function (blue), Type Ⅱ function (red), Type Ⅲ function (green)

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