Ontology type: schema:ScholarlyArticle Open Access: True
2019-12
AUTHORSZhenzhen Shi, Jianmei Wang, Qingjian Li, Huidong Cheng
ABSTRACTIn this paper, a predator–prey model with ratio-dependent and impulsive state feedback control is constructed, where the pest growth rate is related to an Allee effect. Firstly, the existence condition of the homoclinic cycle is obtained by analyzing the control parameter q. The existence, uniqueness and asymptotic stability of the periodic orbit are discussed by using the geometric theory of the differential equations, the method of successor functions and analog of the Poincaré criterion. Secondly, we formulate a control optimization with a minimal total cost in pest management, and we obtain an optimal economic threshold. Finally, we verify the main results by numerical simulation. More... »
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