Analysis of a Leslie-Gower model with Alle effects, cooperative hunting, and constant placement rates

Abstract: This paper investigates the dynamical properties of the Leslie-Gower model with Alle effects, cooperative hunting, and constant placement rates. The conditions for the existence of the triple equilibrium point of the model are first analyzed. Subsequently, the canonical type theory and the qualitative theory of planar systems are applied to obtain that the triple equilibrium point can be a node with a residual dimension of 2 and an equilibrium point with a residual dimension of 3 under different parameter conditions. Finally, it is proved that the system bifurcates with a residual dimension of 2 in the vicinity of the node with cooperative hunting and placement rate as branching parameters.