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Stabilization of stochastic Hopfield neural network with distributed parameters. (English) Zbl 1187.35128
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:
35K57Reaction-diffusion equations
35B35Stability of solutions of PDE
35R60PDEs with randomness, stochastic PDE
37N25Dynamical systems in biology
62M45Neural nets and related approaches (inference from stochastic processes)
82C32Neural nets (statistical mechanics)