Permanence, extinction and balancing survival in nonautonomous Lotka–Volterra system with delays

摘要

In this paper, the periodic n-species Lotka–Volterra competition systems with time delays are considered. The sufficient conditions are derived for the permanence, extinction and balancing survival of the system. Some known results are improved and unified. Further, our results suggest that under some conditions, the introduction and the variance of the time delays will be either harmless or “useless”. Conjecture about the effect of time delays on some global behaviors of the system is advanced.