On a model of competition in periodic environments

摘要

Sufficient conditions are obtained for the existence and global attractivity of a positive periodic solution of the system xi(n+1) = bi(n)xi(n)1 + ∑j=1mcij(n)xj(n), i = 1,2,…, m; n ∈ N in which bi(n), cij(n) (i, j = 1,2,…, m), n ∈ N denote positive periodic sequences with a common period. Also, a method is proposed for the derivation of the discrete system from a continuous time analogue modelling competition in periodic environments with time delays in the stabilizing negative feedback effects.