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Complex dynamics of Holling type II Lotka–Volterra predator–prey system with impulsive perturbations on the predator. (English) Zbl 1085.34529
The authors consider the so called Holling-type II predator-prey model with logistic term, subjected to an impulsive periodic perturbation that corresponds to punctuated predator in-migration. In the first part of the paper, the authors give conditions for the existence of bounded nontrivial soutions of the perturbed system. In the second part of the paper, a numerical exploration of the system is given, with the forcing amplitude as a parameter. The bifurcation diagram exhibits complex dynamical behaviour characteristic for periodically forced nonlinear oscillators.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
34C15Nonlinear oscillations, coupled oscillators (ODE)
37N25Dynamical systems in biology
34A37Differential equations with impulses
34C23Bifurcation (ODE)
34C28Complex behavior, chaotic systems (ODE)