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The Lyapunov direct method, as the most effective measure of studying
stability theory for ordinary differential systems and stochastic ordinary
differential systems, has not been generalized to research concerning
stochastic partial differential systems owing to the emptiness of the
corresponding Ito differential formula. The goal of this paper is just
employing the Lyapunov direct method to investigate the stability of Ito
stochastic reaction diffusion systems, including asymptotical stability in
probability and almost sure exponential stability. The obtained results
extend the conclusions of [X.X. Liao, X.R. Mao, Exponential stability and
instability of stochastic neural networks, Stochastic Analysis and
Applications 14 (2) (1996) 165-185; X.X. Liao, S.Z. Yang, S.J. Cheng, Y.L.
Fu, Stability of general neural networks with reaction-diffusion, Science
in China (F) 44 (5) (2001) 389-395].
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