This paper proposes and characterizes an A/D converter (ADC) based on a spiking neuron model with a rectangular threshold signal. The neuron repeats an integrate-and-fire process and outputs a superstable spike sequence. The dynamics of this system are closely related to those of rate-encoding ADCs. We propose an ADC system based on the spiking neuron model. We derive a theoretical parameter region in a limited time interval of the digital output sequence. We analyze the conversion characteristics in this region and verify that they retain the monotonic increase and rate encoding of an ADC.

This paper studies synchronization phenomena in a ring-coupled system of digital spiking neurons. The neuron consists of two shift registers connected by a wiring circuit and can generate various spike-trains. Applying a spike based connection, the ring-coupled system is constructed. The ring-coupled system can generate multi-phase synchronization phenomena of various periodic spike-trains. Using a simple dynamic model, existence and stability of the synchronization phenomena are analyzed. Presenting a FPGA based test circuit, typical synchronization phenomena are confirmed experimentally.

We studied complicated superstable periodic orbits (SSPOs) in a spiking neuron model with a rectangular threshold signal. The neuron exhibited SSPOs with various periods that changed dramatically when we varied the parameter space. Using a one-dimensional return map defined by the spike phase, we evaluated period changes and showed its complicated distribution. Finally, we constructed a test circuit to confirm the typical phenomena displayed by the mathematical model.

A digital map is a simple dynamical system that is related to various digital dynamical systems including cellular automata, dynamic binary neural networks, and digital spiking neurons. Depending on parameters and initial condition, the map can exhibit various periodic orbits and transient phenomena to them. In order to analyze the dynamics, we present two simple feature quantities. The first and second quantities characterize the plentifulness of the periodic phenomena and the deviation of the transient phenomena, respectively. Using the two feature quantities, we construct the steady-versus-transient plot that is useful in the visualization and consideration of various digital dynamical systems. As a first step, we demonstrate analysis results for an example of the digital maps based on analog bifurcating neuron models.

This paper studies spike-train dynamics of the bifurcating neuron and its pulse-coupled system. The neuron has periodic base signal that is given by applying a periodic square wave to a basic low-pass filter. As key parameters of the filter vary, the systems can exhibit various bifurcation phenomena. For example, the neuron exhibits period-doubling bifurcation through which the period of spike-train is doubling. The coupled system exhibits two kinds of (smooth and non-smooth) tangent bifurcations that can induce “chaos + chaos = order”: chaotic spike-trains of two neurons are changed into periodic spike-train by the pulse-coupling. Using the mapping procedure, the bifurcation phenomena can be analyzed precisely. Presenting simple test circuits, typical phenomena are confirmed experimentally.

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 presents a digital spike map and its learning algorithm of spike-trains. The map is characterized by a swarm of particles on lattice points. As a teacher signal is applied, the algorithm finds a winner particle. The winner and its neighbor particles move in a similar way to the self-organizing maps. A new particle can born and the particle swarm can grow depending on the property of teacher signals. If learning parameters are selected suitably, the map can evolve to approximate a class of teacher signals. Performing basic numerical experiments, the algorithm efficiency is confirmed.

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.

This letter studies a pulse-coupled system constructed by delayed cross-switching between two bifurcating neurons. The system can exhibit an interesting bifurcation: the delay-coupling can change chaotic behavior of single neurons into stable periodic behavior. Using the 1D phase map, it is clarified that the phenomenon is caused by the tangent bifurcation for the delay parameter. Presenting a simple test circuit, the phenomenon can be 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.

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 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.

In this paper, we propose an analog CMOS circuit which achieves spiking neural networks with spike-timing dependent synaptic plasticity (STDP). In particular, we propose a STDP circuit with symmetric function for the first time, and also we demonstrate associative memory operation in a Hopfield-type feedback network with STDP learning. In our spiking neuron model, analog information expressing processing results is given by the relative timing of spike firing events. It is well known that a biological neuron changes its synaptic weights by STDP, which provides learning rules depending on relative timing between asynchronous spikes. Therefore, STDP can be used for spiking neural systems with learning function. The measurement results of fabricated chips using TSMC 0.25 µm CMOS process technology demonstrate that our spiking neuron circuit can construct feedback networks and update synaptic weights based on relative timing between asynchronous spikes by a symmetric or an asymmetric STDP circuits.

This paper studies a simple spiking oscillator having piecewise constant vector field. Repeating vibrate-and-fire dynamics, the system exhibits various spike-trains and we pay special attention to chaotic spike-trains having line-like spectrum in distribution of inter-spike intervals. In the parameter space, existence regions of such phenomena can construct infinite window-like structures. The system has piecewise linear trajectory and we can give theoretical evidence for the phenomena. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

This letter studies response of a chaotic spiking oscillator to chaotic spike-train inputs. The circuit can exhibits a variety of synchronous/asynchronous phenomena and we show an interesting phenomenon "consistency": the circuit can exhibit random response that is identical in steady steady state for various initial values. Presenting a simple test circuit, the consistency is confirmed experimentally.

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.

This paper studies a spiking neuron circuit with triangular base signal. The circuit can output rich spike-trains and the dynamics can be analyzed using a one-dimensional piecewise linear map. This system exhibits period doubling bifurcation, tangent bifurcation, super-stable periodic orbit bifurcation and so on. These phenomena can be characterized based on the inter-spike intervals. Using the maps, we can analyze the phenomena precisely. By presenting a simple test circuit, typical phenomena are confirmed experimentally.

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.

An integrate-and-fire-type spiking feedback network is discussed in this paper. In our spiking neuron model, analog information expressing processing results is given by the relative relation of spike firing. Therefore, for spiking feedback networks, all neurons should fire (pseudo-)periodically. However, an integrate-and-fire-type neuron generates no spike unless its internal potential exceeds the threshold. To solve this problem, we propose negative thresholding operation. In this paper, this operation is achieved by a global excitatory unit. This unit operates immediately after receiving the first spike input. We have designed a CMOS spiking feedback network VLSI circuit with the global excitatory unit for Hopfield-type associative memory. The circuit simulation results show that the network achieves correct association operation.

This letter studies a simple nonautonomous chaotic circuit constructed by adding an impulsive switch to the RCL circuit. The switch operation depends on time and on state variable through a refractory threshold. The circuit exhibits various chaotic attractors, periodic attractors and related bifurcation phenomena. The dynamics can be analyzed using 1-D return map focusing on the time-dependent switching moments. Using a simple test circuit model typical phenomena are verified in PSPICE simulations.