A generalized version of sequential logic circuit based neuron models is presented, where the dynamics of the model is modeled by an asynchronous cellular automaton. Thanks to the generalizations in this paper, the model can exhibit various neuron-like waveforms of the membrane potential in response to excitatory and inhibitory stimulus. Also, the model can reproduce four groups of biological and model neurons, which are classified based on existence of bistability and subthreshold oscillations, as well as their underlying bifurcations mechanisms.

A number of studies have recently been published concerning chaotic neuron models and asynchronous neural networks having chaotic neuron models. In the case of large-scale neural networks having chaotic neuron models, the neural network should be constructed using analog hardware, rather than by computer simulation via software, due to the high speed and high integration of analog circuits. In the present study, we discuss the circuit structure of a chaotic neuron model, which is constructed on the basis of the mathematical model of an asynchronous chaotic neuron. We show that the pulse-type hardware chaotic neuron model can be constructed on the basis of the mathematical model of an asynchronous chaotic neuron. The proposed model is an effective model for the cell body section of the pulse-type hardware chaotic neuron model for ICs. In addition, we show the bifurcation structure of our composed model, and discuss the bifurcation routes and return maps thereof.

In this study, we show how changing a frequency in one of N chaotic circuits coupled by a resistor effects our system by means of both circuit experiment and computer calculation. In these N chaotic circuits, N-1 circuits are completely identical, and the remaining one has altered the value of the oscillation frequency. It is found that for the case of N = 3 when a value of a coupling resistor is gradually increased, only one circuit with different frequency exhibits bifurcation phenomena including inverse period-doubling bifurcation, and for larger value of coupling resistor, the chaotic circuit with different frequency suddenly stops oscillating and the remaining two chaotic circuits exhibit completely anti-phase synchronization.

Dynamic behavior of a distributed parameter system described by the one-dimensional wave equation with a nonlinear boundary condition is examined in detail using a graphical method proposed by Witt on a digital computer. The bifurcation diagram, homoclinic orbit and one-dimensional map are obtained and examined. Results using an analog simulator are introduced and compared with that of the graphical method. The discrepancy between these results is considered, and from the comparison among the bifurcation diagrams obtained by the graphical method, it is denoted that the energy dissipation in the system considerably restrains the chaotic state in the bifurcation process.