Bifurcations for a predator-prey system with two delays ✩

By Yongli Song, Yahong Peng, Junjie Wei. 2008

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In this paper, a predator–prey system with two delays is investigated. By choosing the sum τ of two delays as a bifurcation parameter, we show that Hopf bifurcations can occur as τ crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Using a global Hopf bifurcation result of [J. Wu, Symmetric functional differential equations and neural networks with memory, Trans. Amer. Math. Soc. 350 (1998) 4799–4838], we may show the global existence of periodic solutions.

Subfields: Computer Networks and Communications, Numerical Analysis, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/9335bec784239653da0645948dc5dcf6e26ce710