Hunting Cooperation in a Discrete-Time Predator–Prey System

Abstract

The present paper mainly investigates the impact of hunting cooperation in a discrete-time predator–prey system through numerical simulations. We show that without hunting cooperation, an increase in the growth rate of prey population produces chaotic dynamics. We also show that hunting cooperation has the potential to modify the well-known period-doubling route to chaos by reverse period-halving bifurcations and makes the system stable. However, very high hunting cooperation can be detrimental and populations go to extinction. We observe that hunting cooperation induces strong demographic Allee effect in the system, where predator population persists due to hunting cooperation and would go to extinction without hunting cooperation. We perform extensive numerical simulations of the system and draw phase portraits, bifurcation diagrams, maximum Lyapunov exponents, two-parameter stability regions. We also observe the occurrence of flip and Neimark–Sacker bifurcations by taking the hunting cooperation rate as a bifurcation parameter.