Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations. (English) Zbl 1083.37537

Zhang, Shuwen; Tan, Dejun; Chen, Lansun

Chaos Solitons Fractals 28, No. 2, 367-376 (2006).

Summary: The effect of periodic forcing and impulsive perturbations on a predator-prey model with Holling-type-II functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbation is affected by introducing periodic constant impulsive immigration of the predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can very easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period-doubling cascade, (3) chaos, (4) period-halfing cascade, (5) nonunique dynamics.

MSC:

37N25	Dynamical systems in biology
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
92D25	Population dynamics (general)

Keywords:

periodic forcing; impulsive perturbations; predator-prey model; Holling-type-II functional response; bifurcation diagrams; complex dynamics

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