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This paper studies basic dynamics from a novel pulse-coupled network (PCN). The unit element of the PCN is an integrate-and-fire circuit (IFC) that exhibits chaos. We an give an iff condition for the chaos generation. Using two IFC, we construct a master-slave PCN. It exhibits interesting chaos synchronous phenomena and their breakdown phenomena. We give basic classification of the phenomena and their existence regions can be elucidated in the parameter space. We then construct a ring-type PCN and elucidate that the PCN exhibits interesting grouping phenomena based on the chaos synchronization patterns. Using a simple test circuit, some of typical phenomena can be verified in the laboratory.

Harmonic competition is a learning strategy based upon winner-take-all or winner-take-quota with respect to a composite of heterogeneous subcosts. This learning is unsupervised and organizes itself. The subcosts may conflict with each other. Thus, the total learning system realizes a self-organizing multiple criteria optimization. The subcosts are combined additively and multiplicatively using adjusting parameters. For such a total cost, a general successive learning algorithm is derived first. Then, specific problems in the Euclidian space are addressed. Vector quantization with various constraints and traveling salesperson problems are selected as test problems. The former is a typical class of problems where the number of neurons is less than that of the data. The latter is an opposite case. Duality exists in these two classes. In both cases, the combination parameters of the subcosts show wide dynamic ranges in the course of learning. It is possible, however, to decide the parameter control from the structure of the total cost. This method finds a preferred solution from the Pareto optimal set of the multiple object optimization. Controlled mutations motivated by genetic algorithms are proved to be effective in finding near-optimal solutions.

Chaos and fractal responses from an artificial neural cell stimulated by a periodic square wave are discussed. The dynamics are described by an autonomous equation, and the one-dimensional return map is derived explicitly. The relation between the exciting pulse-width tau(1), and the excited rate gamma(e) which is the number ratio of input pulses and output pulses investigated. Mathematical evidence for gamma(e) to be Cantor function for tau(1) is given. It corresponds to fractal responses. A condition for observable chaos generation in responses from the cell is proved. This condition is described only by parameters. Some of the theoretical results are verified by laboratory experiments.

A typical image processing neuro chip consists of a regular array of very simple cell circuits. When it is implemented by a CMOS process, two stability issues naturally arise. First, parasitic capacitors of MOS transistors induce temporal dynamics. Since a processed image is given as the stable limit point of the temporal dynamics, a temporally unstable chip is unusable. Second, because of the array structure, the node voltage distribution induces spatial dynamics, and it could behave in a wild manner, e.g. oscillatory. The main contributions are: (i) a clarification of the spatial stability issue; (ii) explicit if and only if conditions for the temporal and the spatial stability in terms of circuit parameters; (iii) a rigorous explanation of the fact that even though the spatial stability is stronger than the temporal stability, the set of parameter values for which the two stability issues disagree is of (Lebesgue) measure zero; and (iv) theoretical estimates of the processing speed.