Global attractivity of a discrete competition model of plankton allelopathy with infinite deviating arguments

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