Buck, boost, and buck-boost converters constitute large class of dc-dc converters used in practice and are interesting nonlinear dynamical systems. It has been shown earlier that various nonlinear phenomena including subharmonics and chaos can be observed in these converters. In this paper we show that with the simplifying assumption that voltage regulation is achieved in high frequency modulation, a very simple dimensionless model can be derived that explains the dynamic phenomena in both continuous conduction mode as well as the discontinuous conduction mode. Using this model, we analyze some peculiar aspects of the dynamics in discontinuous conduction mode like the occurrence of superstable orbits.

A generalized version of a piece-wise constant (ab. PWC) spiking neuron model is presented. It is shown that the generalization enables the model to reproduce 20 activities in the Izhikevich model. Among the activities, we analyze tonic bursting. Using an analytical one-dimensional iterative map, it is shown that the model can reproduce a burst-related bifurcation scenario, which is qualitatively similar to that of the Izhikevich model. The bifurcation scenario can be observed in an actual hardware.

This paper studies encoding/decoding function of artificial spiking neurons. First, we investigate basic characteristics of spike-trains of the neurons and fix parameter value that can minimize variation of spike-train length for initial value. Second we consider analog-to-digital encoding based upon spike-interval modulation that is suitable for simple and stable signal detection. Third we present a digital-to-analog decoder in which digital input is applied to switch the base signal of the spiking neuron. The system dynamics can be simplified into simple switched dynamical systems and precise analysis is possible. A simple circuit model is also presented.

Collaboration of growing self-organizing maps (GSOM) and adaptive resonance theory maps (ART) is considered through traveling sales-person problems (TSP).The ART is used to parallelize the GSOM: it divides the input space of city positions into subspaces automatically. One GSOM is allocated to each subspace and grows following the input data. After all the GSOMs grow sufficiently they are connected and we obtain a tour. Basic experimental results suggest that we can find semi-optimal solution much faster than serial methods.

The digital spiking neuron (DSN) consists of digital state cells and behaves like a simplified neuron model. By adjusting wirings among the cells, the DSN can generate spike-trains with various characteristics. In this paper we present a theorem that clarifies basic relations between change of wirings and change of characteristics of the spike-train. Also, in order to explore learning potential of the DSN, we propose a learning algorithm for generating spike-trains that are suited to an application example. We then show significances and basic roles of the presented theorem in the learning dynamics.

We present mutually pulse-coupled two relaxation oscillators having refractoriness. The system can be implemented by a simple electrical circuit, and various periodic synchronization phenomena can be observed experimentally. The phenomena are characterized by a ratio of phase locking. Using a return map having a trapping window, the ratio can be analyzed in a parameter subspace rigorously. We then clarify effects of the refractoriness on the pulse coding ability of the system.

We present a novel kind of integrate-and-fire circuit (IFC) with two periodic inputs: a pulse-train stimulation input and a base input. We clarify that the system state is quantized by the pulse-train stimulation input. Then the system dynamics is described by a return map with quantized state (Qmap). By changing the shape of the base input, various Qmaps can be obtained. The Qmap exhibits co-existence state of various super-stable periodic orbits, and the IFC outputs one of corresponding super-stable periodic pulse-trains depending on the initial state. For a typical case, we clarify the number of co-existing periodic pulse-trains theoretically for the stimulation frequencies. Constructing a simple test circuit, typical phenomena can be verified in the laboratory.

This paper presents pulse-coupled two bifurcating neurons. The single neuron is represented by a spike position map and the coupled neurons can be represented by a composition of the spike position maps. Using the composite map, we can analyze basic bifurcation phenomena and can find some interesting phenomena that are caused by the pulse-coupling and are impossible in the single neuron. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

In this paper, an artificial sub-threshold oscillating spiking neuron is presented and its response phenomena to an input spike-train are analyzed. In addition, a dynamic parameter update rule of the neuron for achieving synchronizations to the input spike-train having various spike frequencies is presented. Using an analytical two-dimensional return map, local stability of the parameter update rule is analyzed. Furthermore, a pulse-coupled network of the neurons is presented and its basic self-organizing function is analyzed. Fundamental comparisons are also presented.

An asynchronous sequential logic spiking neuron is an artificial neuron model that can exhibit various bifurcations and nonlinear responses to stimulation inputs. In this paper, a pulse-coupled system of the asynchronous sequential logic spiking neurons is presented. Numerical simulations show that the coupled system can exhibit various lockings and related nonlinear responses. Then, theoretical sufficient parameter conditions for existence of typical lockings are provided. Usefulness of the parameter conditions is validated by comparing with the numerical simulation results as well as field programmable gate array experiment results.

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.

This paper presents a nonlinear model of human brain activity in response to visual stimuli according to Blood-Oxygen-Level-Dependent (BOLD) signals scanned by functional Magnetic Resonance Imaging (fMRI). A BOLD signal often contains a low frequency signal component (trend), which is usually removed by detrending because it is considered a part of noise. However, such detrending could destroy the dynamics of the BOLD signal and ignore an essential component in the response. This paper shows a model that, in the absence of detrending, can predict the BOLD signal with smaller errors than existing models. The presented model also has low Schwarz information criterion, which implies that it will be less likely to overfit the experimental data. Comparison between the various types of artificial trends suggests that the trends are not merely the result of noise in the BOLD signal.

As two simple relaxation oscillators are coupled by periodical and instantaneous switching, the system exhibits rich superstable synchronous phenomena. In order to analyze the phenomena, we derive a hybrid return map of real and binary variables; and give theoretical results for (1) superstability of the synchronous phenomena and (2) period of the synchronous phenomena as a function of the parameters. Using a simple test circuit, typical phenomena are verified in the laboratory.

A digital spiking neuron is a wired system of shift registers that can generate spike-trains having various spike patterns by adjusting the wiring pattern between the registers. Inspired by the ultra-wideband impulse radio, a novel theoretical synthesis method of the neuron for application to spike-pattern division multiplex communications in an artificial pulse-coupled neural network is presented. Also, a novel heuristic learning algorithm of the neuron for realization of better communication performances is presented. In addition, fundamental comparisons to existing impulse radio sequence design methods are given.

In this paper, we consider the Integrate-and-Fire Model (ab. IFM) with two periodic inputs. The IFM outputs a pulse-train which is governed by a one dimensional return map. Using the return map, the relationship between the inputs and the output is clarified: the first input determines the global shape of the return map and the IFM outputs various periodic and chaotic pulse-trains; the second input quantizes the state of the return map and the IFM outputs various periodic pulse-trains. Using a computer aided analysis method, the quantized return map can be analyzed rigorously. Also, some typical phenomena are confirmed in the laboratory.

We present master-slave pulse-coupled bifurcating neurons having refractoriness. The system can exhibit various phenomena, e. g. , periodic and chaotic in-phase synchronizations, and periodic out-of-phase synchronization. We clarify local stabilities of the phenomena and a sufficient condition for the in-phase synchronization. It is suggested that bifurcations of the synchronization phenomena may relate to detection of a master parameter, and the refractoriness may relate to control of the detection accuracy. Using a simple test circuit, typical phenomena are verified in the laboratory.

In this paper a chaotic spiking neuron is presented and its response characteristics to various periodic inputs are analyzed. A return map which can analytically describe the dynamics of the neuron is derived. Using the map, it is theoretically shown that a set of neurons can encode various periodic inputs into a set of spike-trains in such a way that a spike density of a summation of the spike-trains can approximate the waveform of the input. Based on the theoretical results, some potential applications of the presented neuron are also discussed. Using a prototype circuit, typical encoding functions of the neuron are confirmed by experimental measurements.

The mammalian cochlear consists of highly nonlinear components: lymph (viscous fluid), a basilar membrane (vibrating membrane in the viscous fluid), outer hair cells (active dumpers for the basilar membrane), inner hair cells (neural transducers), and spiral ganglion cells (parallel spikes density modulators). In this paper, a novel spiral ganglion cell model, the dynamics of which is described by an asynchronous cellular automaton, is presented. It is shown that the model can reproduce typical nonlinear responses of the spiral ganglion cell in the mammalian cochlea, e.g., spontaneous spiking, parallel spike density modulation, and adaptation. Also, FPGA experiments validate reproductions of these nonlinear responses.