Bifurcation analysis of a diffusive predator-prey model with hyperbolic mortality and prey-taxis

In this paper, we study a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition. We first analyze the influence of prey-taxis on the local stability of constant equilibria. It turns out that prey-taxis has influence on the stability of the unique positive constant equilibrium, but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium. We then derive Hopf bifurcation and steady state bifurcation related to prey-taxis, which imply that the prey-taxis plays an important role in the dynamics.

Automated summary

In this paper, a diffusive predator-prey model with hyperbolic mortality and prey-taxis under homogeneous Neumann boundary condition is studied. The influence of prey-taxis on the local stability of constant equilibria is analyzed. Prey-taxis is found to affect the stability of the unique positive constant equilibrium, but has no influence on the stability of the trivial equilibrium and the semi-trivial equilibrium. Hopf bifurcation and steady state bifurcation related to prey-taxis are then derived, indicating the important role of prey-taxis in the dynamics.