Approximation on attraction domain of Cohen-Grossberg neural networks

作者：Jin, Dequan^*; Huang, Zhili; Peng, Jigen

来源：Applied Mathematics and Computation, 2011, 217(21): 8747-8753.

DOI：10.1016/j.amc.2011.03.127

• Cohen-Grossberg neural networks
• Attraction domain
• Lyapunov function
• Nonlinear system

In this paper, approximations of attraction domains of the asymptotically stable equilibrium points of some typical Cohen-Grossberg neural networks are achieved. Most Cohen-Grossberg neural networks are highly nonlinear systems which makes it difficult to approximate their attraction domain. Under some weak assumptions, we are allowed to employ the optimal Lyapunov method to obtain a Lyapunov function for asymptotically stable equilibrium points of a given Cohen-Grossberg neural network. With the help of this Lyapunov function, we approximate the corresponding attraction domain by the iterative expansion approach. Numerical simulations also illustrate that the approximation obtained is really part of the attraction domain.

• 出版日期2011-7-1
• 单位西安交通大学; 广西大学