Time-delay effect on a diffusive predator–prey model with habitat complexity

Abstract Based on the predator–prey system with a Holling type functional response function, diffusive digest delay and habitat complexity is proposed. Firstly, stability of equilibrium diffusion without studied. Secondly, under Neumann boundary conditions, taking time as bifurcation parameter, by analyzing eigenvalues linearized operator using normal form theory center manifold method partial differential equations, effect studied conditions which Hopf occurs are given. In addition, calculation formulas direction bifurcating periodic solutions derived. Finally, accuracy theoretical analysis results verified numerical simulations biological explanation given for results.