Stability Property for the Predator-Free Equilibrium Point of Predator-Prey Systems with a Class of Functional Response and Prey Refuges

We investigate the stability property for the predator-free equilibrium point of predator-prey systems with a class of functional response and prey refuges by using the analytical approach. Under some very weakly assumption, we show that conditions that ensure the locally asymptotically stable of th...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2012-01, Vol.2012 (2012), p.143-147-012
Main Authors: Chen, Fengde, Ma, Zhaozhi, Wu, Yumin
Format: Article
Language:English
Subjects:
Asymptotic properties
Dynamical systems
Dynamics
Endangered & extinct species
Inequality
Mathematical analysis
Mathematical problems
Power plants
Refuges
Risk premiums
Stability
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Summary:We investigate the stability property for the predator-free equilibrium point of predator-prey systems with a class of functional response and prey refuges by using the analytical approach. Under some very weakly assumption, we show that conditions that ensure the locally asymptotically stable of the predator-free equilibrium point are consistent with that of the globally asymptotically stable ones. Our result supplements the corresponding result of Ma et al., 2009.
ISSN:1026-0226
1607-887X
DOI:10.1155/2012/148942