A DELAYED SEMILINEAR PARABOLIC PREDATOR-PREY SYSTEM WITH HABITAT COMPLEXITY AND HARVESTING EFFECTS

In this paper, we propose a delayed reaction-diffusive system with habitat complexity and harvesting effects, and study dynamic behaviors of the system. Firstly, for the system without time delay, the stability of equilibria is studied. It is found that when habitat complexity reaches a certain critical value, the positive equilibrium will change from unstable to locally asymptotically stable. Secondly, time delay effect on the dynamic behaviors of diffusion system is studied. The existence conditions of Hopf bifurcation are given, and the properties of bifurcating periodic solutions are studied by using the center manifold and normal form theories, including the direction of Hopf bifurcation, the stability of bifurcating periodic solutions and the period. Finally, the corresponding numerical simulations and biological interpretation are made to verify the results of theoretical analysis.