Exponential stability of numerical solutions to stochastic delay Hopfield neural networks

The main aim of this paper is to investigate the exponential stability of the Euler method and the semi-implicit Euler method for stochastic delay Hopfield neural networks. The definition of MS-stability and GMS-stability of these two numerical methods is introduced. Under the conditions which guarantee the stability of the analytical solution, the Euler scheme is proved to be MS-stable and the semi-implicit scheme is to be MS-stable and GMS-stable. An example is given for illustration.