## Global exponential stability in Lagrange sense for a class of neural networks.(Chinese. English summary)Zbl 1212.93238

Summary: Considering three types of bounded activation functions, and employing appropriate Lyapunov functions and the inequality analyzing technique, this paper studies the global exponential stability in Lagrange sense for a class of neutral-type Cohen-Grossberg neural networks with time-varying delays. Then, several global exponential attractive sets in which all trajectories converge are obtained and structural demonstrations of the system model are also presented. These results are applied to the analysis of both monostable and multistable neural networks. Finally, some numerical examples as well as simulations are given to verify our results.

### MSC:

 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 34D23 Global stability of solutions to ordinary differential equations 92B20 Neural networks for/in biological studies, artificial life and related topics 93D20 Asymptotic stability in control theory