Almost sure exponential stability of stochastic reaction diffusion systems

作者：Luo Qi; Zhang Yutian^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2009, 71(12): E487-E493.

DOI：10.1016/j.na.2008.11.005

• Stochastic reaction diffusion system
• Lyapunov exponent
• Asymptotical stability in probability
• Almost sure exponential stability

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].

• 出版日期2009-12
• 单位南京信息工程大学