Stability of a stochastic reaction-diffusion Hopfield neural network with time-varying delays. (English) Zbl 1240.60192

Zhang, Zifang; Deng, Jin

J. Sichuan Univ., Nat. Sci. Ed. 47, No. 3, 451-456 (2010).

Summary: The main aim of this paper is to discuss moment exponential stability for a stochastic reaction-diffusion Hopfield neural network with time-varying delays. Using the Itô formula, a delay differential inequality and the characteristics of the neural network, the algebraic conditions of the moment exponential stability for non-constant equilibrium solutions are derived. An example is also given for illustration.

MSC:

60H15	Stochastic partial differential equations (aspects of stochastic analysis)
35B35	Stability in context of PDEs
35R60	PDEs with randomness, stochastic partial differential equations

Keywords:

time-varying delays; non-constant equilibrium solution; moment exponential stability; reaction-diffusion neural network