Exponential synchronization for stochastic neural networks driven by fractional Brownian motion.

In this paper, we investigate the exponential synchronization problem for a new class of stochastic neural networks driven by fractional Brownian motion (fBm). In order to deal with the problem of stability for the error system, we propose the mild solution of system equation with respect to fractional Brownian motion based on the space of Hilbert–Schmidt operator law. By using the infinitesimal generator on analytic semigroup principle and associating with the well-known Hölder inequality, Gronwall inequality, we obtain the exponential synchronization criteria for the drive system and response system driven by fBm. Finally, two numerical examples as well as some evolution figures are implemented to demonstrate the effectiveness and feasibility of the proposed exponential synchronization schemes.