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Dynamical behavior of Volterra model with mutual interferenceconcerning IPM

Published online by Cambridge University Press:  15 February 2004

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2004

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