Stability and bifurcations analysis on a diusive predator-prey system with nonlocal intraspecic competition and density-dependent diusion

In this paper, the effect of density-dependent dispersal and nonlocal prey competition on the stability and spatiotemporal dynamics of a diffusive Holling-Tanner predator-prey model is investigated. We obtain the possible bifurcation curves by using the linear stability analysis and the stability region of positive equilibrium is shown. It is found that the nonlocal prey competition promotes the linear instability and the occurrence of Hopf bifurcation. However, the addition of density-dependent dispersal increases the possibility of stability, stabilizing the originally unstable equilibrium point. We also perform simulations to verify our results.