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

Abstract 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 ) - ∑ j = 1 n a ij ( k ) x j ( k ) - ∑ j = 1 , j ≠ i n c ij ( k ) x i ( k ) x j ( k ) - d i ( k ) u i ( k ) , Δ 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.