Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang; Bing Liu; Lansun Chen

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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 38.1 (2010): 143-155. <http://eudml.org/doc/194203>.

@article{Zhang2010,
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},
keywords = {Integrated pest management (IPM); mutual interference; permanence; bifurcation; chaos.; integrated pest management (IPM); mutual interference, permanence, bifurcation},
language = {eng},
month = {3},
number = {1},
pages = {143-155},
publisher = {EDP Sciences},
title = {Dynamical behavior of Volterra model with mutual interference concerning IPM},
url = {http://eudml.org/doc/194203},
volume = {38},
year = {2010},
}

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
DA - 2010/3//
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.; integrated pest management (IPM); mutual interference, permanence, bifurcation
UR - http://eudml.org/doc/194203
ER -

References

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