English

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