Global Dynamics of a Predator-Prey Model with Stage Structure and Delayed Predator Response | Zendy

Lili Wang | Zendy; Rui Xu | Zendy

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Global Dynamics of a Predator-Prey Model with Stage Structure and Delayed Predator Response

Author(s) -

Lili Wang,

Rui Xu

Publication year - 2013

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 - 10.1155/2013/724325

Subject(s) - mathematics , functional response , stability (learning theory) , stability theory , predator , lyapunov function , extinction (optical mineralogy) , dynamics (music) , control theory (sociology) , predation , statistical physics , nonlinear system , physics , economics , computer science , ecology , control (management) , quantum mechanics , machine learning , optics , biology , management , acoustics

A Holling type II predator-prey model with time delay and stage structure for the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. The existence of Hopf bifurcations at the coexistence equilibrium is established. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that the predator-extinction equilibrium is globally asymptotically stable when the coexistence equilibrium is not feasible, and the sufficient conditions are obtained for the global stability of the coexistence equilibrium

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