The Stable Periodic Solutions of a Discrete Neural Network System

Abstract

In this paper, a nonlinear difference system

$$ \left\{ {{}^{{x_{n} = \beta x_{{n - 1}} + f{\left( {y_{{n - k}} } \right)},}}_{{y_{n} = \beta y_{{n - 1}} + f{\left( {x_{{n - k}} } \right)},}} } \right.\;n \in N $$

is considered and sufficient conditions for the existence of the stable 2k + 1 periodic solution are obtained.