摘要：We consider a discrete competition model of plankton allelopathy with infinite deviating arguments of the form x 1 ( k + 1 ) = x 1 ( k ) exp { K 1 − α 1 x 1 ( k ) − β 12 ∑ s = − ∞ n K 12 ( n − s ) x 2 ( s ) − γ 1 x 1 ( k ) ∑ s = − ∞ n f 12 ( n − s ) x 2 ( s ) } , x 2 ( k + 1 ) = x 2 ( k ) exp { K 2 − β 21 ∑ s = − ∞ n K 21 ( n − s ) x 1 ( s ) − α 2 x 2 ( k ) − γ 2 x 2 ( k ) ∑ s = − ∞ n f 21 ( n − s ) x 1 ( s ) } . $$\begin{aligned} x_)(k+1)={}& x_)(k)\exp \Biggl\{ K_)-\alpha_) x_)(k)-\beta_{12} \sum_{s=-\infty}^{n}K_{12}(n-s)x_,(s) \\ &{}-\gamma_) x_)(k) \sum_{s=-\infty }^{n}f_{12}(n-s)x_,(s) \Biggr\} , \\ x_,(k+1)={}& x_,(k)\exp \Biggl\{ K_,- \beta_{21} \sum_{s=-\infty }^{n}K_{21}(n-s)x_)(s) -\alpha_,x_,(k) \\ &{}-\gamma_, x_,(k)\sum_{s=-\infty }^{n}f_{21}(n-s)x_)(s) \Biggr\} . \end{aligned}$$ By using an iterative method we investigate the global attractivity of the interior equilibrium point of the system.
