期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 374, 期 2, 页码 644-654出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2010.08.029
关键词
Density dependence; Beddington-DeAngelis functional response; Permanence; Stability; Lyapunov function
资金
- National Natural Science Foundation of China [60774041]
- Japan Society for the Promotion of Science [22540122]
Two models of a density dependent predator-prey system with Beddington-DeAngelis functional response are systematically considered. One includes the time delay in the functional response and the other does not. The explorations involve the permanence, local asymptotic stability and global asymptotic stability of the positive equilibrium for the models by using stability theory of differential equations and Lyapunov functions. For the permanence, the density dependence for predators is shown to give some negative effect for the two models. Further the permanence implies the local asymptotic stability for a positive equilibrium point of the model without delay. Also the global asymptotic stability condition, which can be easily checked for the model is obtained. For the model with time delay, local and global asymptotic stability conditions are obtained. (C) 2010 Elsevier Inc. All rights reserved.
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