Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey | Zendy

Zizhen Zhang | Zendy; Huizhong Yang | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Hopf Bifurcation of a Predator-Prey System with Delays and Stage Structure for the Prey

Author(s) -

Zizhen Zhang,

Huizhong Yang

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 - 10.1155/2012/282908

Subject(s) - center manifold , hopf bifurcation , mathematics , bifurcation , stability (learning theory) , saddle node bifurcation , period doubling bifurcation , population , predation , transcritical bifurcation , control theory (sociology) , mathematical analysis , nonlinear system , physics , ecology , computer science , biology , demography , control (management) , quantum mechanics , machine learning , artificial intelligence , sociology

This paper is concerned with a Holling type III predator-prey system with stage structure for theprey population and two time delays. The main result is given in terms of local stability and bifurcation. By choosing the time delay as a bifurcation parameter, sufficient conditions for the local stability of the positive equilibrium and the existence of periodic solutions via Hopf bifurcation with respect to both delays are obtained. In particular, explicit formulas that can determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established by using the normal form method and center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are also included

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research