Bifurcation Analysis in a Delayed Leslie–Gower Model with Double Allee Effect

This paper focuses on analyzing the complex dynamical behaviors of a delayed Leslie–Gower system with double Allee effect, which encompasses both strong and weak Allee effects. First, the existence and boundedness of the equilibrium point of the model are analyzed, which guarantees the validity of the predator–prey model. Subsequently, the Hopf bifurcation dynamics is obtained in detail for various types of delay, and the property of the Bogdanov–Takens (B–T) bifurcation under multi-delay conditions is researched by the normal form theory and the central manifold theorem. Finally, numerical simulations are conducted to investigate the specific effects of delays and Allee effect, the numerical results are consistent with the theoretical analysis. Interestingly, the results of the thesis indicate that the richness of model dynamics can be achieved by adjusting bifurcation parameters and time delays, which play crucial roles in ecological conservation and quantity control.