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Spatiotemporal dynamics in a predator-prey model with a functional response increasing in both predator and prey densities
Ruizhi Yang,Ting Ding
Keywords:Predator-prey; Delay; Turing instability; Hopf bifurcation
Abstract:
      In this paper, we studied a diffusive predator-prey model with a functional response increasing in both predator and prey densities. The Turing instability and local stability are studied by analyzing the eigenvalue spectrum. Delay induced Hopf bifurcation is investigated by using time delay as bifurcation parameter. Some conditions for determining the property of Hopf bifurcation are obtained by utilizing the normal form method and center manifold reduction for partial functional differential equation.