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Complexity Of An Ivlev'S Predator-Prey Model With Pulse

Author

Listed:
  • GUOPING PANG

    (Department of Mathematics and Computer Science, Yulin Normal University, Yulin Guangxi 537000, China;
    Department of Applied Mathematics, Dalian University of Technology, Dalian Liaoning 116024, China)

  • LANSUN CHEN

    (Department of Applied Mathematics, Dalian University of Technology, Dalian Liaoning 116024, China;
    Minnan Science and Technology Institute Fujian Normal University, Nan'an Fujian 362332, P. R. China)

Abstract

In this paper, we investigate the extinction, permanence and dynamic complexity of the two-prey, one-predator system with Ivlev's functional response and impulsive perturbation on the predator at fixed moments. Conditions for the extinction and permanence of the system are established via the comparison theorem. Numerical simulations are carried out to explain the conclusions we obtain. Furthermore, the resulting bifurcation diagrams clearly show that the impulsive system takes on many forms of complexity including period-doubling bifurcation, period-halving bifurcation, and chaos.

Suggested Citation

  • Guoping Pang & Lansun Chen, 2007. "Complexity Of An Ivlev'S Predator-Prey Model With Pulse," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 217-231.
    • Handle: RePEc:wsi:acsxxx:v:10:y:2007:i:02:n:s0219525907001021
    DOI: 10.1142/S0219525907001021
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