The Stability Of Certain Types Of Neural Network Analysis

Since neural networks have enormous potential in wide varieties of applications,many specialists and scholars apply themselves to the research of the theory andachieve many perfect productions. In this dissertation, we perform the stabilityresearch of Hopfield neural networks (HNNs) and cellular neural networks (CNNs).The main contents of this dissertation include: the stability analysis for a class offirst-order and a class of second-order HNNs without and with delays, respectively;the stability analysis for a class of generalized CNNs with constant delays.The main originalities in this paper can be summarized as follows:1. Firstly, in the first section of the second chapter, we clear up thedevelopmental process of the stability research about the first order HNNs, and thenlist the investigational productions of internal and external literatures in this field. Inthe following section we analyze the stability of a class of HNNs with delays. In thissection we discard the demand that the activation functions must be derivable andonly request them to be Lipschitz continuous. The necessary and sufficient conditionfor the existence of a unique equilibrium of this system is achieved by applying thematrices analysis and Brouwer theorem. In addition, we adopt the method ofvariations of the parameters, though constructing Lyapunov function was a usual oneto investigate stability. Consequently, another kind of condition ensuring the stabilityof the system is achieved. Accordingly, the fundamental set of solution of the linearpart of the original system can be used to control the nonlinear part and then make thesystem stable.2. In the third chapter the high-order HNNs model to which is scarcely referredin the internal and external literatures will be talk about. As the high-order neuralnetworks are more complex than the first-order ones, by far, the derivative of theactivity functions in system are usually assumed be limitary and monotonicincreasing even. Similarly, after modifying the precondition we assume that theactivity functions are limitary and Lipschitz continuous only. Consequently, thesufficient condition for the existence of a unique equilibrium of this system will beachieved. In the third section a kind of condition ensuring the global asymptotic...