Dynamical behavior of Volterra model with mutual interference concerning IPM
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 1, p. 143-155

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.

DOI : https://doi.org/10.1051/m2an:2004007
Classification:  34A37,  92D25
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {1},
     year = {2004},
     pages = {143-155},
     doi = {10.1051/m2an:2004007},
     zbl = {1081.34042},
     mrnumber = {2073934},
     language = {en},
     url = {http://www.numdam.org/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, Volume 38 (2004) no. 1, pp. 143-155. doi : 10.1051/m2an:2004007. http://www.numdam.org/item/M2AN_2004__38_1_143_0/

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