Research On Stability Of Neural Network And Its Applications In Associative Memories

In recent years, CNNs and HNNs have attracted more and more attention ofresearchers due to their perspectives of applications, such as associative memories andoptimization calculation. Since Hopfield neural networks were proposed in1982,numerous studies on various neural networks have been reported. In1988, CNNs wereproposed by L. O. Chua and L. Yang. CNNs combine advantages of Hopfield’s neuralnetworks with Neumann’s cellular automata (CA). CNNs can be implememted as verylarge scale integrated (VLSI) chips and can be operated at a very high speed.CNNs and HNNs can be used in associative memories. Associative memorymodeling human intelligence as information storage and recovery is a hot research issuein neural computing. Associative memories refer to brainlike devices designed to store aset of prototype patterns such that the stored patterns can be retrieved with the recallingprobes containing sufficient information about contents of the patterns. In neuralnetworks, when given a probe, the retrieval dynamics of the associative memory shouldbe converged to an equilibrium point representing the prototype pattern. Therefore, thestability of neural networks is critical in associative memories.In this dissertation, the stability of cellular neural networks (CNNs) and Hopfieldneural networks (HNNs) and their applications in associative memories are studied.From the stability of CNNs, the regions of the number of equilibrium points of a cell inCNNs are given and some design procedures of associative memories are derived. Inaddition, we get several criteria about stability of asymmetric Hopfield neural networksby use of energy function. Then, a design procedure of Hopfield neural networks forassociative memories is given by use of these criteria and single value decomposition.Specifically, the main contributions of this dissertation are as follows:①The regions of the number of equilibrium points of every cell are considered bythe relationship among parameters of CNNs with unity gain activation function orthresholding activation function. The influence of the values of connection weights ofCNNs on the number of equilibrium points for a cell is found. Some sufficientconditions are obtained by using the relationship among connection weights. Dependingon these sufficient conditions, inputs and outputs of a CNN, the regions of the values ofparameters can be obtained. In addition, the impact of initial states on stability of CNNsis considered； ②In the research process of regions of the number of equilibrium points of everycell, a conjecture is presented which gives a method for computing the number ofdifferent sum-difference values in a set of real numbers. Though we can not give a poof,a large of numerical examples have verified this conjecture；③It is well known that the prototype patterns can be represented by equilibriumpoints of CNNs. Therefore, the stability of equilibrium points of CNNs without timedelay or with time delay is studied and some criteria about the stability of CNNs areestablished. In fact, these criteria give some constraint conditions for the relationship ofparameters of CNNs. Compared with the previous works, our results relax theconservatism of the relationship of parameters and extend the range of the value ofparameters. Through these conditions, we give several design procedures of parametersof CNNs；④The stability of asymmetric Hopfield neural networks with time delay isstudied. Some sufficient conditions about global and local stability of the neuralnetworks are given by m energy functions method. A design procedure of neuralnetworks for associative memories is given by use of these sufficient conditions andsingle value decomposition；⑤A large number of numerical examples are given to verify the above theoriesand methods using MARLAB software platform.