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Analysis of the Dynamics of a Predator-prey Model with Holling Functional Response
  
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KeyWord:Predator-prey model; Turing instability; Hopf bifurcation; Hydra effect
Author NameAffiliation
Hongyu Chen School of Science, Northeast Forestry University, Harbin, Heilongjiang 150040, China 
Chunrui Zhang School of Science, Northeast Forestry University, Harbin, Heilongjiang 150040, China 
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Abstract:
      A diffusive predator-prey system with Holling functional response is considered. Firstly, existence of positive equilibrium of this reaction diffusion model under Neumann boundary condition is obtained. Meanwhile, the existence conditions for Turing instability and Hopf bifurcations of a system with Holling \uppercase\expandafter{\romannumeral2} functional response are established. Next, the existence of the hydra effect is demonstrated, when the system is undergoing non-homogeneous steady-state solutions. Finally, numerical simulations are illustrated to support our theory results.