Dynamical behavior of Volterra model with mutual interference concerning IPM
Department of Mathematics, Anshan Normal University, Anshan,
Liaoning 114005, P.R. China. email@example.com.
2 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.
Mathematics Subject Classification: 34A37 / 92D25
Key words: Integrated pest management (IPM) / mutual interference / permanence / bifurcation / chaos.
© EDP Sciences, SMAI, 2004