Periodicity in a class of systems of delay difference equations

We study a system of delay difference equations modeling four-dimensional discrete-time delayed neural networks with no internal decay. such a discrete-time system can be regarded as the discrete analog of a differential equation with piecewise constant argument. by using semicycle analysis method,it is shown that every bounded solution of this discrete-time system is eventually periodic. the obtained results are new,and they complement previously known results. © copyright 2011 zhijian wei.