Natural Science Research Center, The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Nan-Gang District, Harbin 150080, China
Copyright © 2010 Shengqiang Liu. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We discuss a general -species discrete Kolmogorov system with time lags. We build some
new results about the sufficient conditions for permanence, extinction, and balancing survival.
When applying these results to some Lotka-Volterra systems, we obtain the criteria on
harmless delay for the permanence as well as profitless delay for balancing survival.