Qualitative analysis of a degenerate fixed point of a discrete predator–prey model with cooperative hunting

Abstract

This paper investigates the qualitative properties near a degenerate fixed point of a discrete predator–prey model with cooperative hunting derived from the Lotka–Volterra model where the eigenvalues of the corresponding linear operator are ±1. Applying the theory of the normal form and the Takens's theorem, we change the problem of this discrete model into the one of an ordinary differential system. With the technique of desingularization to blow up the degenerate equilibrium of the ordinary differential system, we obtain its qualitative properties. Utilizing the conjugacy between the discrete model and the time‐one mapping of the vector field, we obtain the qualitative structures of this discrete model.