期刊
APPLIED MATHEMATICAL MODELLING
卷 33, 期 11, 页码 4049-4061出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2009.02.008
关键词
Predator-prey system; Delay; Stability; Hopf bifurcation; Periodic solution
资金
- Doctoral Fund of Ministry of Education of China [200802471024]
- National Nature Science Foundation of China [10871129]
- Innovation Program of Shanghai Municipal Education Commission [09ZZ33]
In this paper, the delayed Leslie-Gower predator-prey system is investigated. By choosing the delay as a bifurcation parameter, we show that Hopf bifurcations can Occur as the delay 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 Wu [J. Wu, Symmetric functional differential equations neural networks with memory, Trans. Am. Math. Soc. 350 (1998) 4799-4838] for functional differential equations, we may show the global existence of periodic Solutions. (C) 2009 Elsevier Inc. All rights reserved.
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