Permanence criteria for Kolmogorov systems with delays
Dynamical Systems
2013-03-08 v1
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 (J. Math. Biol. Vol. 25 (1987) 411-422) for autonomous replicator and Lotka-Volterra systems has been extended to delayed nonautonomous 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 irrelevant of the size and distribution of the delays.
Keywords
Cite
@article{arxiv.1303.1668,
title = {Permanence criteria for Kolmogorov systems with delays},
author = {Zhanyuan Hou},
journal= {arXiv preprint arXiv:1303.1668},
year = {2013}
}
Comments
To be published in Proceedings of Royal Society of Edinburgh