Codimension two 1:1 strong resonance bifurcation in a discrete predator-prey model with Holling Ⅳ functional response

Abstract

In this paper we revisit a discrete predator-prey model with Holling Ⅳ functional response. By using the method of semidiscretization, we obtain new discrete version of this predator-prey model. Some new results, besides its stability of all fixed points and the transcritical bifurcation, mainly for codimension two 1:1 strong resonance bifurcation, are derived by using the center manifold theorem and bifurcation theory, showing that this system possesses complicate dynamical properties.

Keywords

• predator-prey model
• holling ⅳ functional response
• transcritical bifurcation
• 1:1 strong resonance bifurcation
• codimension two