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

SHUWEN ZHANG

College of Science, Jimei University, Xiamen, Fujian 361021, China

Corresponding author.

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DEJUN TAN

College of Education of Teachers, Jimei University, Xiamen, Fujian 361021, China

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, and

LANSUN CHEN

Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, China

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https://doi.org/10.1142/S0219525906000811Cited by:5 (Source: Crossref)

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.

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