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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. [email protected]. 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. [email protected].
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 interferenceconcerning integrated pest management is proposed and analyzed. Byusing Floquet theorem and small amplitude perturbation method andcomparison theorem, we show the existence of a globallyasymptotically stable pest-eradication periodic solution. Further,we prove that when the stability of pest-eradication periodicsolution is lost, the system is permanent and there exists alocally stable positive periodic solution which arises from thepest-eradication periodic solution by bifurcation theory. When theunique positive periodic solution loses its stability, numericalsimulation shows there is a characteristic sequence ofbifurcations, leading to a chaotic dynamics. Finally, we comparethe validity of integrated pest management (IPM) strategy withclassical methods and conclude IPM strategy is more effective thanclassical methods.

Keywords

Integrated pest management (IPM)mutual interferencepermanencebifurcationchaos.
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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