Exponential synchronization and polynomial synchronization of recurrent neural networks with and without proportional delays

Abstract

In this paper, synchronization problems of drive-response recurrent neural networks (RNNs) with and without proportional delays are studied, which include exponential synchronization and polynomial synchronization. Here the control input is an unidirectional coupled term. The concept of polynomial synchronization for RNNs is first proposed. By constructing Lyapunov functionals, applying some inequality analysis techniques, several appropriate control inputs are designed, and several delay-dependent sufficient conditions for ensuring exponential synchronization and polynomial synchronization of the considered drive-response systems are obtained. Moreover, the relationship between exponential synchronization and polynomial synchronization is revealed. Numerical examples show that the proposed method is effective and less conservative than the previous result.