Effects of generalist predation and group defense on dynamics and bifurcations of a Leslie type predator–prey system

In this study, we explore the effects of generalist predation and group defense on the dynamics and bifurcations of a Leslie-type predator–prey model. By using qualitative theory and bifurcation theory, as well as some algebraic and symbolic computation methods, we demonstrate that the model can undergo a nilpotent focus bifurcation of codimension 4 and a degenerate Hopf bifurcation of codimension up to 2 as the parameters vary. Moreover, some sufficient conditions are derived for the global stability of the prey-free equilibrium or the unique positive equilibrium. Our results indicate that the joint interaction of generalist predation and prey group defense can induce richer dynamics and bifurcations. Generalist predation can lead to the extinction of the prey population, whereas prey group defense has a stabilizing effect on both populations. Finally, some numerical simulations, such as three limit cycles or tristability, are provided to illustrate the theoretical results.