Algebraic conditions of stability for Hopfield neural network. (English) Zbl 1186.82060

Liao, Xiaoxin; Mao, Xuerong; Wang, Jun; Zeng, Zhigang

Sci. China, Ser. F 47, No. 1, 113-125 (2004).

Summary: Using the relationship between the resistance, capacitance and current in Hopfield neural network, and the properties of sigmoid function, this paper gives the terse, explicit algebraical criteria of global exponential stability, global asymptotical stability and instability. Then this paper makes clear the essence of the stability that Hopfield defined, and provides a theoretical foundation for the design of a network.

MSC:

82C32	Neural nets applied to problems in time-dependent statistical mechanics
34D20	Stability of solutions to ordinary differential equations

Keywords:

Hopfield neural network; physical parameter; activation function; stability