# 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

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topZhang, 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 -

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