期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 230, 期 1, 页码 187-203出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2008.11.009
关键词
Ratio-dependence; Time delay; Stability; Hopf bifurcation
资金
- National Natural Science Foundation of China [10671209, 10471066, 10531030]
- China Postdoctoral Science Foundation [20060391010]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
A ratio-dependent predator-prey model with time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and a semi-trivial boundary equilibrium is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. Using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semi-trivial equilibrium is also addressed. Numerical simulations are carried out to illustrate the main results. (C) 2008 Elsevier B.V. All rights reserved.
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