A FOOD CHAIN SYSTEM WITH DENSITY-DEPENDENT BIRTH RATE AND IMPULSIVE PERTURBATIONS

Shuwen Zhang (), Fenyan Wang and Lansun Chen
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Shuwen Zhang: College of Science, Jimei University, Xiamen, Fujian 361021, China
Fenyan Wang: College of Science, Jimei University, Xiamen, Fujian 361021, China
Lansun Chen: Department of Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, China

Advances in Complex Systems (ACS), 2006, vol. 09, issue 03, 223-236

Abstract: We investigate a three-species food chain system with density-dependent birth rate and impulsive effect concerning biological and chemical control strategy — periodic releasing of natural enemies or spraying pesticide at different fixed times. Conditions for the extinction of the prey and top predator are given. By using the Floquet theory of impulsive differential equations and small amplitude perturbation skills, we consider the local stability of the prey and top predator eradication periodic solution. Further, we obtain the conditions of permanence of the system.

Keywords: Impulsive perturbation; density-dependent birth; biological control; food chain model; extinction; permanence (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219525906000781

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