Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model

According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of su...

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Published inDiscrete Dynamics in Nature and Society Vol. 2012; no. 2012; pp. 273 - 293-021
Main Authors Cheng, Huidong, Zhang, Tongqian, Wang, Fang
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2012
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
Hindawi Limited
Subjects
Control systems
Convergence
Differential equations
Dynamical systems
Dynamics
Mathematical analysis
Mathematical models
Pests
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Summary:According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1026-0226
1607-887X
DOI:10.1155/2012/181752