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Permanence criteria for Kolmogorov systems with delays

Published online by Cambridge University Press:  16 May 2014

Zhanyuan Hou
Zhanyuan Hou*
Affiliation:
School of Computing, London Metropolitan University, 166-220 Holloway Road, London N7 8DB, UK, ([email protected])
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Abstract

In this paper, a class of Kolmogorov systems with delays are studied. Sufficient conditions are provided for a system to have a compact uniform attractor. Then Jansen's result for autonomous replicator and Lotka–Volterra systems has been extended to delayed non-autonomous Kolmogorov systems with periodic or autonomous Lotka–Volterra subsystems. Thus, simple algebraic conditions are obtained for partial permanence and permanence. An outstanding feature of all these results is that the conditions are independent of the size and distribution of the delays.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 3 , June 2014 , pp. 511 - 531
Copyright
Copyright © Royal Society of Edinburgh 2014 

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