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Hopf bifurcation in a diffusive predator-prey model with herd behavior and prey harvesting
Heping Jiang,Xiaosong Tang
Keywords:Hopf bifurcation; Predator-Prey model; Herd behavior; Prey harvesting; Delay
Abstract:
      In this paper, the dynamics of a diffusive delayed predator-prey model with herd behavior and prey harvesting subject to the homogeneous Neumann boundary condition is considered. Firstly, using the harvesting term as a bifurcation parameter, we obtain the existence and the stability of the equilibrium by analyzing the distribution of the roots of associated characteristic equation. Secondly, regarding time delay as a bifurcation parameter, and using the normal form theory and center manifold theorem, the existence, stability and direction of bifurcating periodic solutions are demonstrated. Finally, numerical simulations are conducted to illustrate the theoretical analysis.