Dynamics of a Discrete-Time Leslie–Gower Predator–Prey Model with Strong Allee Effect, Hunting Cooperation and Prey Harvesting

In this paper, the dynamical behaviors of a discrete-time Leslie–Gower predator–prey model with strong Allee effect, hunting cooperation and prey harvesting are investigated. Our analysis mainly focuses on the bifurcations of the positive fixed points of this system, which are studied theoretically, including fold bifurcation, fold–flip bifurcation and 1:2, 1:3 and 1:4 strong resonance bifurcations. Moreover, to verify the results, numerical examples that involve the bifurcation diagrams, maximum Lyapunov exponents, bifurcation points detected by MatContM and phase portraits are conducted. By plotting the attraction basins, we display some additional dynamical properties and the influence of parameters on its dynamical behaviors. In addition, two-parameter space plots that are far from the critical values of bifurcation parameters are presented, providing a global view of the dynamics. The results demonstrate that this system exhibits complex dynamical phenomena and the harvesting parameter plays a crucial role in shaping these dynamics, offering valuable insights into the understanding of real ecological systems.