Abstract
In this paper, a delayed diffusive modified Leslie–Gower-type predator–prey model with Beddington–DeAngelis functional response subject to Neumann boundary condition is considered. The stability/instability of the non-negative equilibria and a detailed Hopf bifurcation analysis are investigated. And explicit formulas for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived by the theory of normal form and center manifold. In addition, some numerical simulations are carried out.
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