期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 296, 期 2, 页码 521-537出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2004.04.051
关键词
predator-prey system; time delay; stability; Hopf bifurcation; normal form
We consider a delayed predator-prey system with Beddington-DeAngelis functional response. The stability of the interior equilibrium will be studied by analyzing the associated characteristic transcendental equation. By choosing the delay tau as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay tau crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhaes. An example is given and numerical simulations are performed to illustrate the obtained results. (C) 2004 Elsevier Inc. All rights reserved.
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