Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-Varying Delays and Continuously Distributed Delays

Abstract

In this paper, we investigate the global exponential stability for a class of Cohen-Grossberg neural networks (CGNN) with time-varying delays and continuously distributed delays. CGNN herein is a general neural networks model which includes some well-known neural networks as its special cases. Firstly, applying the homeomorphism theory, we establish the new sufficient condition of existence and uniqueness of the equilibrium point to CGNN. Then, the sufficient criteria of global exponential stability of CGNN, which are easy to verify, are given by M-matrix. Our results imply and generalize some existed ones in previous literature. Furthermore, it is convenient to estimate the exponential convergence rates of the neural networks by using the criteria. Compared with the previous methods, our method does not resort to any Lyapunov functions or functionals. Finally, a example is given to illustrate the effective of our results.