Researches On Dynamics Properties Of Some Recurrent Neural Networks

A class of dynamic neural networks known as recurrent neural networks has applications in areas such as optimization and associative memory. Before these neural networks can be put to use, however, their dynamics behaviors must be fully understood. In recent years, the dynamics properties of recurrent neural networks have received considerable attention. This paper is focused on estimating the domains of attraction of equilibrium points for Hopfield neural networks with delays and stabilizing a class of time-delays neural networks via standard feedback control.The first two chapters provide the background knowledge as well as the state-of- the-art of recurrent neural networks.Chapter 3 investigates the estimation of the domains of attraction of equilibrium points for Hopfield neural networks with delays, where Hopfield neural networks with discrete and distributed delays are considered. We derive a sufficient condition for an equilibrium point to be locally exponentially stable. We also present an estimate on the domains of attraction of locally exponentially stable equilibrium points. Our condition and estimate are formulated in terms of the network parameters, the neurons'activation functions and the associated equilibrium point. Hence, they are easily checkable. It is believed that these results are significant and useful for the design and applications of the delayed Hopfield neural networks.Chapter 4 discusses how to stabilize a class of time-delays neural networks via standard feedback control; this kind of neural networks provides a unified view of several well-known neural networks (such as Hopfield neural networks and cellular neural networks) with discrete delays or distributed delays. A stability criterion is given by using the Lyapunov method. All the results obtained in this chapter are stated in simple algebraic forms so that their verifications and applications are straightforward and convenient. Experimental results justify the utility of the proposed result.