HOPF BIFURCATION IN A PREDATOR-PREY MODEL WITH MEMORY EFFECT AND INTRA-SPECIES COMPETITION IN PREDATOR

This paper investigates the spatiotemporal dynamics of a reac-tion diffusion predator-prey model that incorporates memory delay and intra-species competition in predator. We provide rigorous results of the model including the local stability of positive equilibrium, the existence and the prop-erty of Hopf bifurcation. We show that increasing the intra-species competition is not beneficial to the stability of the positive equilibrium. Moreover, we ob-tain that the stable region of the positive equilibrium will decrease with the increase of memory-based diffusion coefficient when it larger than the critical value. In addition, the memory delay may also affect the stability of the posi-tive equilibrium. When the memory delay crosses the critical value, the stable positive equilibrium becomes unstable, and the stably inhomogeneous periodic solutions appears. These results indicate that the memory delay and intra-species competition play an important role in the spatiotemporal dynamics of predator-prey model.