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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.

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)
Full Text: DOI
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