Exponential stability of numerical solutions to stochastic delay Hopfield neural networks

Abstract

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.