Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure | Zendy

Lingshu Wang | Zendy; Guanghui Feng | Zendy

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Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure

Author(s) -

Lingshu Wang,

Guanghui Feng

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/431671

Subject(s) - mathematics , hopf bifurcation , stability (learning theory) , invariant (physics) , functional response , lyapunov function , control theory (sociology) , bifurcation , predation , predator , nonlinear system , control (management) , computer science , physics , mathematical physics , quantum mechanics , machine learning , artificial intelligence , biology , paleontology

A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results

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