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A Food Chain System With Density-Dependent Birth Rate And Impulsive Perturbations

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shuwen Zhang & Fenyan Wang & Lansun Chen, 2006. "A Food Chain System With Density-Dependent Birth Rate And Impulsive Perturbations," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 223-236.
    • Handle: RePEc:wsi:acsxxx:v:09:y:2006:i:03:n:s0219525906000781
    DOI: 10.1142/S0219525906000781
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