Permanence for Lotka-Volterra systems with multiple delays

In this paper, we consider a class of n species LotkaVolterra systems with time delays and establish sufficient conditions which ensure the systems to be permanent. We improve and extend the known conditions of the permanence in Lu and Lu (2008) [4], Lu et al. (2010) [5] and Nakata and Muroya (2010) [7]. Moreover, we give the conditions of the permanence for a class of three species LotkaVolterra predatorprey systems which need no restriction on the size of time delays and improve the result in [2]. Some examples for comparison with the previous results are given to illustrate the main results.