CHAOTIC BEHAVIOR OF A PERIODICALLY FORCED PREDATOR–PREY SYSTEM WITH BEDDINGTON–DEANGELIS FUNCTIONAL RESPONSE AND IMPULSIVE PERTURBATIONS

Shuwen Zhang (), Dejun Tan and Lansun Chen
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Shuwen Zhang: College of Science, Jimei University, Xiamen, Fujian 361021, China
Dejun Tan: College of Education of Teachers, Jimei University, Xiamen, Fujian 361021, China
Lansun Chen: Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, China

Advances in Complex Systems (ACS), 2006, vol. 09, issue 03, 209-222

Abstract: The effects of periodic forcing and impulsive perturbations on the predator–prey model with Beddington–DeAngelis functional response are investigated. We assume periodic variation in the intrinsic growth rate of the prey as well as 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 quasi-periodic oscillating, a period-doubling cascade, chaos, a period-halving cascade, non-unique dynamics, and period windows.

Keywords: Predator–prey system; impulsive perturbation; periodic forcing; bifurcation; chaos; complexity (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219525906000811

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