Numerical Stability analysis of two step maruyama methods of stochastic delay Hopfield neural networks

Abstract

This thesis is mainly concerned with some kind of stability analysis of the two-step Maruyama schemes for the stochastic delay Hopfield neural networks. Stochastic differential equations many times result in modeling of problems like population dynamics, financial and neural networks etc. In many situations, the explicit form of the solutions of such equations cannot be acquired. Many real world applications are based on the stochastic delay Hopfield neural networks. This thesis consists of four parts. The first part of this thesis is the study of the mean square stability of the two step Maruyama methods of the stochastic delay Hopfield neural networks. The second part of the thesis is the study of the almost sure exponential stability of two-step Maruyama methods of the stochastic delay Hopfield neural networks. The third chapter of the thesis is the study about the trajectory stability of numerical methods of stochastic delay Hopfield neural networks. The last chapter of the thesis deals with the T-stability of two-step Maruyama methods of the stochastic delay Hopfield neural networks. newlineKey Words Neural networks newline newline