ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

Dynamical behavior of Volterra model with mutual interference concerning IPM

Zhang, Yujuana1a2, Liu, Binga1 and Chen, Lansuna2

a1 Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114005, P.R. China. yujuanz2000@yahoo.com.

a2 Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China.

Abstract

A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication periodic solution by bifurcation theory. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics. Finally, we compare the validity of integrated pest management (IPM) strategy with classical methods and conclude IPM strategy is more effective than classical methods.

(Received July 6 2003)

(Online publication February 15 2004)

Key Words:

  • Integrated pest management (IPM);
  • mutual interference;
  • permanence;
  • bifurcation;
  • chaos.

Mathematics Subject Classification:

  • 34A37;
  • 92D25
Metrics