Multi‐State Dependent Impulsive Control for Holling I Predator‐Prey Model | Zendy

Huidong Cheng | Zendy; Fang Wang | Zendy; Tongqian Zhang | Zendy

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

Author(s) -

Huidong Cheng,

Fang Wang,

Tongqian Zhang

Publication year - 2012

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2012/181752

Subject(s) - mathematics , convergence (economics) , functional response , ordinary differential equation , control theory (sociology) , differential equation , sequence (biology) , order (exchange) , predation , mathematical optimization , control (management) , computer science , mathematical analysis , predator , artificial intelligence , ecology , genetics , economics , biology , economic growth , finance

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

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