Dynamics of modified Leslie–Gower-type prey–predator model with seasonally varying parameters

A modified Leslie–Gower-type prey–predator model composed of a logistic prey with Holling’s type II functional response is studied. The axial point (1, 0) is found to be globally asymptotically stable in a domain. Condition for stability of the non-trivial equilibrium point is obtained. The existence of stable limit cycle of the system is also established. The analysis for Hopf bifurcation is carried out. The numerical simulations are carried out to study the effects of seasonally varying parameters of the model. The system shows the rich dynamic behavior including bifurcation and chaos.