Dynamic Analysis Of Hopfield Neural Networks And Applications

In this dissertation, the dynamics of continuous-time and discrete-time Hopfieldneural networks (HNNs) are studied, and system designing procedures for construct-ing different neural associative memories are proposed. Furthermore, the applicationsof neural associative memories in information retrieval, pattern recognition and systemassessment are also discussed.In chapter 2, the dynamics of the asymmetric continuous-time Hopfield networksare discussed, and the sufficient conditions for the global and local stability of thenetwork are proposed. Furthermore, two system designing methods for endowing thenetwork with retrieval properties are proposed based on the matrix decomposition andsingle-layer feed forward method, respectively. And the applications of the networkin pattern recognitions and information retrieval are also studied by numerical simula-tions.In chapter 3, the dynamic of unstable continuous-time Hopfield networks is stud-ied. It is found that the solution of the HNN is bounded and the HNN is a dissipativesystem. In addition, some HNNs exhibit two independent limit cycles or chaotic at-tractors which are symmetric to each other with respect to the origin. Furthermore,based on these results, a new chaotic Hopfield network with piecewise linear activa-tion function is presented.In chapter 4, An efficient system designing method for endowing the diluted sym-metric discrete-time Hopfield networks with retrieval properties is proposed based onthe matrix decomposition and connection elimination method. Numerical simulationsshow that the blurred patterns can correctly retrieved, and about 80% wiring cost canbe reduced.In chapter 5, the dynamics of the asymmetric discrete-time Hopfield networks arestudied, and the sufficient conditions for endowing the network with retrieval proper-ties are proposed. In addition, a method for designing efficient diluted networks isproposed based on the matrix decomposition and connection elimination strategy. Nu-merical simulations show that the designed diluted network can act as efficient neural associative memories.In chapter 6, the applications of neural associative memories in color image re-trieval are studied based on a class of reduced Cohen-Grossberg neural networks andcontinuous-time Hopfield network. Numerical simulations show that the designed net-works can perform as efficient noise-reducing systems.In chapter 7, by taking customer satisfaction degree assessment and credit riskevaluation for example, some pioneer works about the applications of neural associa-tive memories in system assessment are presented.