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ESAIM: Mathematical Modelling and Numerical Analysis ESAIM: Mathematical Modelling and Numerical Analysis

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Dynamical behavior of Volterra model with mutual interferenceconcerning IPM

Published online by Cambridge University Press:  15 February 2004

Yujuan Zhang ,
Bing Liu  and
Lansun Chen
Yujuan Zhang
Affiliation:
Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114005, P.R. China. yujuanz2000@yahoo.com. Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China.
Bing Liu
Affiliation:
Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114005, P.R. China. yujuanz2000@yahoo.com.
Lansun Chen
Affiliation:
Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China.
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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.

Keywords

Integrated pest management (IPM) mutual interference permanence bifurcation chaos.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 1 , January 2004 , pp. 143 - 155
Copyright
© EDP Sciences, SMAI, 2004

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