Bifurcations in a Discrete-Time Prey-Predator Model with Hunting Cooperation and Allee Effect in Prey

This paper considers a discrete-time prey–predator model with hunting cooperation and Allee effect in prey. We first discuss the existence and local stability of equilibria for the model. Two codimension-two bifurcations (1:1 strong resonance and fold-flip) are investigated by employing the center manifold theorem and bifurcation theory. We also give the corresponding bifurcation diagrams, phase portraits and diagrams of maximum Lyapunov exponents to verify our theoretical analysis. Besides, we provide some numerical analysis of initial conditions.