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Bifurcations for a predator-prey system with two delays |
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| Authors: | Yongli Song Yahong Peng |
| Institution: | a Department of Mathematics, Tongji University, Shanghai 200092, China b Department of Applied Mathematics, Donghua University, Shanghai 200051, China c Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China |
| Abstract: | 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. |
| Keywords: | Predator-prey system Delay Hopf bifurcation Normal form Periodic solution |
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