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

Chen, Yanyan; Luo, Qi

J. Nanjing Univ. Inf. Sci. Technol., Nat. Sci. 1, No. 1, 50-58 (2009).

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

Keywords:

Cohen-Grossberg neural network; global exponential stability; time delay type; neutral type