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.
@article{M2AN_2004__38_1_143_0,
author = {Zhang, Yujuan and Liu, Bing and Chen, Lansun},
title = {Dynamical behavior of Volterra model with mutual interference concerning IPM},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {38},
year = {2004},
pages = {143-155},
doi = {10.1051/m2an:2004007},
mrnumber = {2073934},
zbl = {1081.34042},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2004__38_1_143_0}
}
Zhang, Yujuan; Liu, Bing; Chen, Lansun. Dynamical behavior of Volterra model with mutual interference concerning IPM. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 38 (2004) pp. 143-155. doi : 10.1051/m2an:2004007. http://gdmltest.u-ga.fr/item/M2AN_2004__38_1_143_0/
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