Stable spatially inhomogeneous periodic solutions for a diffusive Leslie–Gower predator–prey model

The main objective of this thesis is to learn about the dynamics of a diffusive Leslie–Gower predator–prey system with functional response and time delay under homogeneous Neumann boundary conditions. By in-depth analyzing eigenvalues distribution, it proves that there are (diffusion-induced, delay-induced) Turing–Hopf bifurcations around positive equilibrium state. More than this, base on the foundation of the regular modality and the center manifold theory, It is responsible for establishing a precise formula, which is to determine the Turing–Hopf bifurcation property of a diffusive Leslie–Gower predator–prey system with functional response. After that, we applied the formula to a diffusive Leslie–Gower predator–prey system with Beddington–DeAngelis functional response and time delay integrally. Finally, the results have been verified and replenished by numerical simulation adequately.