Criteria for exponential [corrected] stability of Cohen-Grossberg neural networks.

Abstract

In this paper, the Cohen-Grossberg neural network models without and with time delays are considered. By constructing several novel Lyapunov functionals, some sufficient criteria for the existence of a unique equilibrium and global exponential stability of the network are derived. These results are fairly general and can be easily verified. Besides, the approach of the analysis allows one to consider different types of activation functions, including piecewise linear, sigmoids with bounded activations as well as C1-smooth sigmoids. In the meantime, our approach does not require any symmetric assumption of the connection matrix. It is believed that these results are significant and useful for the design and applications of the Cohen-Grossberg model.