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Modeling and implementation approaches for the reproduction of input-output relationships in biological nervous tissues contribute to the development of engineering and clinical applications. However, because of high nonlinearity, the traditional modeling and implementation approaches encounter difficulties in terms of generalization ability (i.e., performance when reproducing an unknown data set) and computational resources (i.e., computation time and circuit elements). To overcome these difficulties, asynchronous cellular automaton-based neuron (ACAN) models, which are described as special kinds of cellular automata that can be implemented as small asynchronous sequential logic circuits have been proposed. This paper presents a novel type of such ACAN and a theoretical analysis of its excitability. This paper also presents a novel network of such neurons, which can mimic input-output relationships of biological and nonlinear ordinary differential equation model neural networks. Numerical analyses confirm that the presented network has a higher generalization ability than other major modeling and implementation approaches. In addition, Field-Programmable Gate Array-implementations confirm that the presented network requires lower computational resources.

Spike-timing-dependent plasticity (STDP) is a form of synaptic modification that depends on the relative timings of presynaptic and postsynaptic spikes. In this letter, we proposed a calcium-based simple STDP model, described by an ordinary differential equation having only three state variables: one represents the density of intracellular calcium, one represents a fraction of open state NMDARs, and one represents the synaptic weight. We shown that in spite of its simplicity, the model can reproduce the properties of the plasticity that have been experimentally measured in various brain areas (e.g., layer 2/3 and 5 visual cortical slices, hippocampal cultures, and layer 2/3 somatosensory cortical slices) with respect to various patterns of presynaptic and postsynaptic spikes. In addition, comparisons with other STDP models are made, and the significance and advantages of the proposed model are discussed.

A generalized asynchronous cellular automaton-based neuron model is a special kind of cellular automaton that is designed to mimic the nonlinear dynamics of neurons. The model can be implemented as an asynchronous sequential logic circuit and its control parameter is the pattern of wires among the circuit elements that is adjustable after implementation in a field-programmable gate array (FPGA) device. In this paper, a novel theoretical analysis method for the model is presented. Using this method, stabilities of neuron-like orbits and occurrence mechanisms of neuron-like bifurcations of the model are clarified theoretically. Also, a novel learning algorithm for the model is presented. An equivalent experiment shows that an FPGA-implemented learning algorithm enables an FPGA-implemented model to automatically reproduce typical nonlinear responses and occurrence mechanisms observed in biological and model neurons.

A novel rotate-and-fire digital spiking neuron is presented. The digital neuron is a wired system of shift registers and thus it is suited to on-chip learning unlike many other analog spiking neuron models. By adjusting the wiring pattern among the registers, the digital neuron can generate spike trains with various spike patterns and can exhibit related bifurcations. A discrete-continuous hybrid map, which describes the neuron dynamics without any approximation, is derived analytically. Using the hybrid map, it is shown that the digital spiking neuron can mimic typical bifurcation phenomena and various nonlinear responses of biological neurons.

A novel chaotic spiking neuron is presented and its nonlinear dynamics and encoding functions are analyzed. A set of paralleled N neurons accepts a common analog input and outputs a set of N chaotic spike-trains. Three theorems which guarantee that the neurons can encode the analog input into a summation of the N chaotic spike-trains are derived: (1) a spike histogram of the summed spike-train can mimic waveforms of various inputs, (2) the spike-trains do not synchronize to each other and thus the summed spike-train can have N times higher encoding resolution than each single spike-train, and (3) firing rates of the neurons can be adjusted by internal parameters. The theorems are proven by using nonlinear iterative maps and are confirmed by numerical simulations as well. Electronic circuit implementation methods of the paralleled neurons are also presented and typical paralleled encoding functions are confirmed by both experimental measurements and SPICE simulations.

A digital spiking neuron is a wired system of shift registers and can generate various spike-trains by adjusting the wiring pattern. In this paper we analyze the basic relations between the wiring pattern and characteristics of the spike-train. Based on the relations, we present a learning algorithm which utilizes successive changes of the wiring pattern. It is shown that the neuron can reproduce spike-trains of another neuron which has an unknown wiring pattern. It is also shown that the neuron can approximate various spike-trains of a chaotic analog spiking neuron.

This paper presents a spiking neuron circuit with a triangular base signal. The circuit can output rich pulse-trains and the dynamics can be analyzed using a piecewise linear one-dimensional pulse-position map. Applying cross-switching to two neurons we construct a pulse-coupled system whose dynamics can be integrated into a composite map of the pulse position maps of two neurons. The composite map is piecewise linear and precise analysis is possible. We can clarify various interesting phenomena caused by the pulse-coupling. For example, periodic behavior of each neuron is changed into chaotic behavior and chaotic behavior of each neuron is changed into periodic behavior. These results provide basic information to construct flexible pulse-coupled neural networks.