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Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations. (English) Zbl 1083.37537
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:
37N25Dynamical systems in biology
37D45Strange attractors, chaotic dynamics
92D25Population dynamics (general)