Analysis Of The Stability Of A Class Of Stochastic Differential Equations

This paper investigates the stability of stochastic delyed Hopfield neural networks and stochastic delayed cellular neural networks. The thesis consists of four chapters.Chaper 1 gives an introduction to some basic concepts of stochastic different- ial equations.It also introduces some investigation methods on the stability anal- ysis of stochastic differential equations.In Chapter 2, the stability for stochastic delyed Hopfield neural networks is studied. By Lyapunov function, Ito?'s formula,Burkholder-Davids-Gundy inequality and Borel- Canteli's lemma,some new criteria of the 1-exponential stability, mean square expone- ntial stability and almost surely exponential stability for the system are obtained.Chapter 3 studies the exponential stability for stochastic delayed cellular neural net- works.Fistly, the 1-exponential stability for the system is investigated with the familiar method as in Chapter 2.The linear matrix equality (LMI) method,frequently used in Robust control, is applied to the stability analysis of stochastic differential equations, and some useful stability criteria are concluded via LMI method.Since the Hopfield neural networks and cellular neural networks are representative recurrent neural networks,in Chapter 4, the stabilty of the stochastic delayed recurrent neural networks is investigated with the familiar method as in Chapter 3. According to the stability criteria obtained in this chapter, the stability for stochastic delyed Hopfield neural networks and stochastic delayed cellular neural networks can be easily derived.