Analysis of the Dynamics of a Predator-Prey Model with Holling Functional Response (Journal of Nonlinear Modeling and Analysis, 2024)
A diffusive predator-prey system with Holling functional responseis considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, theexistence conditions for Turing instability and Hopf bifurcations of a systemwith Holling II functional response are established. Next, the existence of thehydra effect is demonstrated, when the system is undergoing non-homogeneoussteady-state solutions. Finally, numerical simulations are illustrated to support our theory results.
Keywords: Predator-prey model; Turing instability; Hopf bifurcation; Hydra effect.