Jingan Cui, Mingna Guo
Abstract:
In this paper, we consider the effect of dispersal on the
permanence of single and interacting populations modelled by
systems of integro differential equations. Different from
former studies, our discussion here includes the important
situation when species live in a weak patchy environment;
i.e., species in some isolated patches will become extinct
without the contribution from other patches.
For the single population model considered in this paper,
we show that the same species can persist for some
dispersal rates and the species will vanish in some isolated
patches. Based on the results for a single population model, we
derive sufficient conditions for the permanence of two interacting
competitive and predator-prey dispersing systems.
Submitted November 24, 2004. Published June 10, 2005.
Math Subject Classifications: 92D25, 34C60, 34K20.
Key Words: Logistic equation; Lotka-Volterra system; dispersal;
permanence; extinction; time delay.
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| Jingan Cui Department of Mathematics Nanjing Normal University Nanjing 210097, China email: cuija@njnu.edu.cn |
| Mingna Guo Department of Mathematics Nanjing Normal University Nanjing 210097, China |
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