Stabilization of stochastic Hopfield neural network with distributed parameters. (English) Zbl 1187.35128

Luo, Qi; Deng, Feigi; Bao, Jundong; Zhao, Birong; Fu, Yuli

Sci. China, Ser. F 47, No. 6, 752-762 (2004).

Summary: In this paper, the stability of stochastic Hopfield neural network with distributed parameters is studied. To discuss the stability of systems, the main idea is to integrate the solution to systems in the space variable. Then, the integration is considered as the solution process of corresponding neural networks described by stochastic ordinary differential equations. A Lyapunov function is constructed and Itô formula is employed to compute the derivative of the mean Lyapunov function along the systems, with respect to the space variable. It is difficult to treat stochastic systems with distributed parameters since there is no corresponding Itô formula for this kind of system. Our method can overcome this difficulty. Till now, the research of stability and stabilization of stochastic neural networks with distributed parameters has not been considered.

MSC:

35K57	Reaction-diffusion equations
35B35	Stability in context of PDEs
35R60	PDEs with randomness, stochastic partial differential equations
37N25	Dynamical systems in biology
62M45	Neural nets and related approaches to inference from stochastic processes
82C32	Neural nets applied to problems in time-dependent statistical mechanics

Keywords:

Hopfield neural networks; distributed parameters; average exponential stability in mean square