Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy | Zendy

Qizhen Xiao | Zendy; Binxiang Dai | Zendy

Open Access

Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy

Author(s) -

Qizhen Xiao,

Binxiang Dai

Publication year - 2015

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2015.12.1065

Subject(s) - allee effect , heteroclinic bifurcation , mathematics , heteroclinic cycle , control theory (sociology) , bifurcation , hopf bifurcation , nonlinear system , control (management) , physics , computer science , population , homoclinic orbit , demography , quantum mechanics , artificial intelligence , sociology

In this paper, we analyze a general predator-prey model with state feedback impulsive harvesting strategies in which the prey species displays a strong Allee effect. We firstly show the existence of order-1 heteroclinic cycle and order-1 positive periodic solutions by using the geometric theory of differential equations for the unperturbed system. Based on the theory of rotated vector fields, the order-1 positive periodic solutions and heteroclinic bifurcation are studied for the perturbed system. Finally, some numerical simulations are provided to illustrate our main results. All the results indicate that the harvesting rate should be maintained at a reasonable range to keep the sustainable development of ecological systems.

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