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Stability and Hopf bifurcation in a diffusive predator-prey system with Beddington-DeAngelis functional response and time delay. (English) Zbl 1230.35138
Summary: This paper is concerned with a diffusive predator-prey system with Beddington-DeAngelis functional response and delay effect. By analyzing the distribution of the eigenvalues, the stability of the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneous periodic solutions are investigated. Also, it is shown that the small diffusion can affect the Hopf bifurcations. Finally, the direction and stability of Hopf bifurcations are determined by normal form theory and center manifold reduction for partial functional differential equations.
35Q91PDEs in connection with game theory, economics, social and behavioral sciences
35R10Partial functional-differential equations
35B32Bifurcation (PDE)
35B35Stability of solutions of PDE