Exponential stability of neutral reaction diffusion systems with Brownian noise

A major motivation for this paper is to address the problem of exponential stability for neutral reaction diffusion systems with Brownian noise. The underlying relationship is revealed between the reaction diffusion system with Brownian noise and the associated stochastic ordinary differential system. Thereby, Lyapunov method is employed to investigate the asymptotic behavior of reaction diffusion systems with Brownian noise. To conclude, some sufficient conditions for the mean-square exponential stability are proposed through Ito formula together with a constructed average Lyapunov function regarding spatial variables.