Stability for a class of difference equations (Q1019659)

The authors consider the gobal asymptotical stability of the zero of the following nonlinear difference equations with unbounded delays: \[ x_{i+1}=qx_i-\sum^i_{j=-\infty}a_{ij}f_{i-j}(x_j),\quad i=0,1,\dots, \] \[ x_j=\phi_j,\quad -\infty<j\leq 0. \] where \(0<q<1\) and \(f_j(x)\), \(0\leq j<\infty\) are suitable functions. Moreover, the authors apply their main results to the discrete versions of Wazewska-Czyzewska and Lasota model, and Nicolson's blowfies model, and a single-species growth model.