a1 Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114005, P.R. China. email@example.com.
a2 Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China.
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)
Mathematics Subject Classification: