| Issue |
ESAIM: M2AN
Volume 38, Number 1, January-February 2004
|
|
|---|---|---|
| Page(s) | 143 - 155 | |
| DOI | https://doi.org/10.1051/m2an:2004007 | |
| Published online | 15 February 2004 | |
Dynamical behavior of Volterra model with mutual interference concerning IPM
1
Department of Mathematics, Anshan Normal University, Anshan,
Liaoning 114005, P.R. China. yujuanz2000@yahoo.com.
2
Department of Applied Mathematics,
Dalian University of Technology, Dalian, Liaoning 116024,
P.R. China.
Received:
6
July
2003
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.