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.
Mots clés : integrated pest management (IPM), mutual interference, permanence, bifurcation, chaos
@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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {143--155},
publisher = {EDP-Sciences},
volume = {38},
number = {1},
year = {2004},
doi = {10.1051/m2an:2004007},
mrnumber = {2073934},
zbl = {1081.34042},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004007/}
}
TY - JOUR AU - Zhang, Yujuan AU - Liu, Bing AU - Chen, Lansun TI - Dynamical behavior of Volterra model with mutual interference concerning IPM JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 143 EP - 155 VL - 38 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004007/ DO - 10.1051/m2an:2004007 LA - en ID - M2AN_2004__38_1_143_0 ER -
%0 Journal Article %A Zhang, Yujuan %A Liu, Bing %A Chen, Lansun %T Dynamical behavior of Volterra model with mutual interference concerning IPM %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 143-155 %V 38 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004007/ %R 10.1051/m2an:2004007 %G en %F M2AN_2004__38_1_143_0
Zhang, Yujuan; Liu, Bing; Chen, Lansun. Dynamical behavior of Volterra model with mutual interference concerning IPM. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 1, pp. 143-155. doi : 10.1051/m2an:2004007. http://www.numdam.org/articles/10.1051/m2an:2004007/
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