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MR ZblA 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.
Keywords: integrated pest management (IPM), mutual interference, permanence, bifurcation, chaos
Zhang, Yujuan; Liu, Bing; Chen, Lansun. Dynamical behavior of Volterra model with mutual interference concerning IPM. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 1, pp. 143-155. doi: 10.1051/m2an:2004007
@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 },
pages = {143--155},
year = {2004},
publisher = {EDP-Sciences},
volume = {38},
number = {1},
doi = {10.1051/m2an:2004007},
mrnumber = {2073934},
zbl = {1081.34042},
language = {en},
url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis PY - 2004 SP - 143 EP - 155 VL - 38 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis %D 2004 %P 143-155 %V 38 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004007/ %R 10.1051/m2an:2004007 %G en %F M2AN_2004__38_1_143_0
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