# Dynamical behavior of Volterra model with mutual interference concerning IPM

• Volume: 38, Issue: 1, page 143-155
• ISSN: 0764-583X

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## Abstract

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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.

## How to cite

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Zhang, Yujuan, Liu, Bing, and Chen, Lansun. "Dynamical behavior of Volterra model with mutual interference concerning IPM." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 38.1 (2004): 143-155. <http://eudml.org/doc/244821>.

@article{Zhang2004,
abstract = {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.},
author = {Zhang, Yujuan, Liu, Bing, Chen, Lansun},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {integrated pest management (IPM); mutual interference; permanence; bifurcation; chaos; mutual interference, permanence, bifurcation},
language = {eng},
number = {1},
pages = {143-155},
publisher = {EDP-Sciences},
title = {Dynamical behavior of Volterra model with mutual interference concerning IPM},
url = {http://eudml.org/doc/244821},
volume = {38},
year = {2004},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2004
PB - EDP-Sciences
VL - 38
IS - 1
SP - 143
EP - 155
AB - 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.
LA - eng
KW - integrated pest management (IPM); mutual interference; permanence; bifurcation; chaos; mutual interference, permanence, bifurcation
UR - http://eudml.org/doc/244821
ER -

## References

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