Permanence and global stability in a discrete n-species competition system with feedback controls

In this paper, we investigate the following discrete n-species competition system with feedback controls: x(i)(k + 1) = x(i)(k)exp{b(i)(k) - (n)Sigma(j=1) a(ij)(k)x(j)(k) - (n)Sigma(j=1, j not equal i) c(ij)(k)x(i)(k)x(j)(k) - d(i)(k)u(i)(k)}, Delta u(i)(k) = r(i)(k) - e(i)(k)u(i)(k) + f(i)(k)x(i)(k), i = 1,2, ..., n which describes the effect of toxic substances and age structures simultaneously. Some sufficient conditions are established on the permanence and the global stability of the system. These results are also applied to some special cases. (C) 2007 Elsevier Ltd. All rights reserved.