Recently, we have discovered wave propagation phenomena which are continuously existing waves of changing phase states between two adjacent oscillators from in-phase to anti-phase or from anti-phase to in-phase in van der Pol oscillators coupled by inductors as a ladder. We named the phenomena as "phase-inversion waves." In this study, phase-inversion waves which exist in the state of in-and-anti-phase synchronization have been found. We observe the phenomena by circuit experiments and computer calculations, and investigate them.

In this study, nonlinear wave phenomena related to transmissions and reflections of the phase-inversion waves around a discontinuity of a coupled system consisting of two kinds of arrays of van der Pol oscillators are investigated. By computer simulations, behavior of the phase-inversion waves around the discontinuity in the coupled system is classified into eight types. Further, the mechanisms of the transmission and the reflection of a phase-inversion wave at the discontinuity are explained. Circuit experiments confirm the simulated results.

In this paper, a simple chaotic circuit using two RC phase shift oscillators and a diode is proposed and analyzed. By using a simpler model of the original circuit, the mechanism of generating chaos is explained and the exact solutions are derived. The exact expression of the Poincare map and its Jacobian matrix make it possible to confirm the generation of chaos using the Lyapunov exponents and to investigate the related bifurcation phenomena.

In this study, wave propagation phenomena of phase differences observed in van der Pol oscillators coupled by inductors as a ladder are investigated. The phenomena are called "phase waves. " We classify the observed phenomena and analyze the difference in detail. We observe that the behavior of the phase waves generated by giving a phase difference of positive value is different from the behavior of those generated by giving a phase difference of negative value. We can also observe the generation of two pairs of phase waves. We clarify the mechanisms of these complicated phenomena. Finally, for the case of nine oscillators, we carry out both computer calculations and circuit experiments. Circuit experimental results agree well with computer calculated results qualitatively.

We propose here a time-domain shooting algorithm for calculating the steady-state responses of nonlinear RF circuits containing parasitic elements that is based on both a modified Newton and a secant methods. Bipolar transistors and MOSFETs in ICs have small parasitic capacitors among their terminals. We can not neglect them because they will gives large effects to the shooting algorithm at the high frequency. Since our purpose is to develop a user friendly simulator, we mainly take into account the relatively large normal capacitors such as coupling and/or by-pass capacitors and so on, because the parasitic capacitors are usually smaller and contained in the device models. We have developed a very simple simulator only using the fundamental tools of SPICE, which can be applied to relatively large scale ICs, efficiently.

In this study, a ring of simple chaotic circuits coupled by inductors is investigated. An extremely simple three-dimensional autonomous circuit is considered as a chaotic subcircuit. By carrying out circuit experiments and computer calculations for two, three or four subcircuits case, various synchronization phenomena of chaos are confirmed to be stably generated. For the three subcircuits case, two different synchronization modes coexist, namely in-phase synchronization mode and three-phase synchronization mode. By investigating Poincar map, we can see that two types of synchronizations bifurcate to quasi-synchronized chaos via different bifurcation route, namely in-phase synchronization undergoes period-doubling route while three-phase synchronization undergoes torus breakdown. Further, we investigate the effect of the values of coupling inductors to bifurcation phenomena of two types of synchronizations.

Cellular Neural Networks (CNNs) are nonlinear dynamic array processors with mainly local interconnections. In most of the applications, the local interconnection pattern, called cloning template, is translation invariant. In this paper, an optimal ring-coding method for rotation invariant description of given set of objects, is introduced. The design methodology of the templates based on the ring-codes and the synthesis of CNN analogic algorithms to detect standing and moving objects in a rotationally invariant way, discussed in detail. It is shown that the algorithms can be implemented using the CNN Universal Machine, the recently invented analogic visual microprocessor. The estimated time performance and the parallel detecting capability is emphasized, the limitations are also thoroughly investigated.

We consider oscillators consisting of a reactance circuit and a negative resistor. They may happen to have multi-mode oscillations around the anti-resonant frequencies of the reactance circuit. This kind of oscillators can be easily synthesized by setting the resonant and anti-resonant frequencies of the reactance circuits. However, it is not easy to analyze the oscillation phenomena, because they have multiple oscillations whose oscillations depend on the initial guesses. In this paper, we propose a Spice-oriented solution algorithm combining the harmonic balance method with Newton homotopy method that can find out the multiple solutions on the homotopy paths. In our analysis, the determining equations from the harmonic balance method are given by modified equivalent circuit models of "DC," "Cosine" and "Sine" circuits. The modified circuits can be solved by a simulator STC (solution curve tracing circuit), where the multiple oscillations are found by the transient analysis of Spice. Thus, we need not to derive the troublesome circuit equations, nor the mathematical transformations to get the determining equations. It makes the solution algorithms much simpler.

In this study, wave propagation phenomena of phase states are observed at van der Pol oscillators coupled by inductors as a ladder. For the case of 17 oscillators, interesting wave propagation phenomena of phase states are found. By using the relationship between phase states and oscillation frequencies, the mechanisms of the propagation and the reflection of wave are explained. Circuit experimental results agree well with computer calculated results qualitatively.

There are many kinds of transmission lines such as uniform, nonuniform and nonlinear ones terminated by linear and/or nonlinear subnetworks. The nonuniform transmission lines are crucial in integrated circuits and printed circuit boards, because these circuits have complex geometries and layout between the multi layers, and most of the transmission lines possess nonuniform characteristics. On the other hand, the nonlinear transmission line have been focused in the fields of communication and instrumentation. Here, we present a new numerical method for analyzing nonuniform and nonlinear transmission lines with linear and/or nonlinear terminations. The waveforms at any points along the lines are described by the Fourier expansions. The partial differential equations representing the circuit are transformed into a set of ordinary differential equations at each frequency component, where for nonlinear transmission line, the perturbation technique is applied. The method is efficiently applied to weakly nonlinear transmission line. The nonuniform transmission lines terminated by a nonlinear subnetwork are analyzed by hybrid frequency-domain method. The stability for stiff circuit is improved by introducing compensation element. The efficiency of our method is illustrated by some examples.

In this paper, the performance of some communication systems using chaos synchronization is evaluated and compared. A new channel model taking the attenuation, impedance mismatch and noise into account, is proposed for the performance evaluation. The evaluation of bit error rate is done for both ideal and non-ideal conditions using the channel model. It is confirmed that some chaos-based communication systems have a good performance compared with conventional analog communication schemes.

A fast time-domain simulation technique of plane circuits via two-layer Cellular Neural Network (CNN)-based modeling, which is necessary for power/signal integrity evaluation in VLSIs, printed circuit boards, and packages, is presented. Using the new notation expressed by the two-layer CNN, 1,553 times faster simulation is achieved, compared with Berkeley SPICE (ngspice). In CNN community, CNNs are generally simulated by explicit numerical integration such as the forward Euler and Runge-Kutta methods. However, since the two-layer CNN is a stiff circuit, we cannot analyze it by using an explicit numerical integration method. Hence, to analyze the two-layer CNN and reduce the computational cost, the leapfrog method is introduced. This procedure would open an application of CNN to electronic design automation area.

In this paper, four coupled chaotic circuits generating four-phase quasi-synchronization of chaos are proposed. By tuning the coupling parameter, chaotic wandering over the phase states characterized by the four-phase synchronization occurs. In order to analyze chaotic wandering, dependent variables corresponding to phases of solutions in subcircuits are introduced. Combining the variables with hysteresis decision of the phase states enables statistical analysis of chaotic wandering.

In this study, a modeling method of the intermittency chaos using the Markov chain is proposed. The performances of the intermittency chaos and the Markov chain model are investigated when they are injected to the Hopfield Neural Network for a quadratic assignment problem or an associative memory. Computer simulated results show that the proposed modeling is good enough to gain similar performance of the intermittency chaos.

In this paper we present a predictor-corrector tracing curve algorithm for analysis of nonlinear circuits. In order to tracing the curves having sharp turning points efficiently, we introduce a norm Σd i/ds as the parameter to control the tracing step size. This parameter more precisely reflects the sharp degree of the turning points on a curve. In addition that, the Hermite polynomial is used for extrapolation in predictor stage, and the Brown iteration method is used to solve the system of equation in corrector stage. The numerical examples show which computational efficiency is greatly improved, so that this algorithm can be used for DC analysis of nonlinear circuits, efficiently.

Distortion analysis of nonlinear circuits is very important for designing analog integrated circuits and communication systems. In this letter, we propose an efficient frequency-domain approach for calculating frequency response curves, which is based on HB (harmonic balance) method combining with ABMs (Analog Behavior Models) of Spice. Firstly, nonlinear devices such as bipolar transistors and MOSFETs are transformed into the HB device modules executing the Fourier transformations. Using these modules, the determining equation of the HB method is formed by the equivalent sine-cosine circuit in the schematic form or net-list. It consists of the coupled resistive circuits, so that it can be efficiently solved by the DC analysis of Spice. In our algorithm, we need not to derive any troublesome circuit equations, and any kinds of the transformations.

This paper discusses pulse responses of multi-conductor transmission lines terminated by linear and nonlinear subnetworks. At first step, the circuit is partitioned into a linear transmission lines and nonlinear subnetworks by the substitution voltage sources. Then, the linear subnetworks are solved by a well-known phasor technique, and the nonlinear subnetworks by a numerical integration technique. The variational value at each iteration is calculated by a frequency domain relaxation method to the associated linearized time-invariant sensitivity circuit. Although the algorithm can be efficiently applied to weakly nonlinear circuits, the convergence ratio for stiff nonlinear circuits becomes very small. Hence, we recommend to introduce a compensation element which plays very important role to weaken the nonlinearity. Thus, our algorithm is very simple and can be efficiently applied to wide classes of nonlinear circuits.

In this study, synchronization phenomena in chaotic oscillators coupled by a transmission line are investigated. In particular investigation using real circuits is done for the first time. It is confirmed that the chaotic subsystems synchronize, although signals propagating along the transmission line are affected by the time delay. Further the period-doubling bifurcation with varying the time delay and anti-phase synchronization phenomena are observed in our circuit model. Also the voltage distribution of transmission line is simulated in order to investigate whether the current flowing through the transmission line is constant or not. It is found that the subsystems synchronize although the current through the transmission line keeps on varying.

The paper discusses the spatio-temporal phenomena in autonomous two-layer Cellular Neural Networks (CNNs) with mutually coupled templates between two layers. By computer calculations, we show how pattern formations, autowaves and classical waves can be regenerated in the networks, and describe the properties of these phenomena in detail. In particular, we focus our discussion on the necessary conditions for generating these spatio-temporal phenomena. In addition, the influences of the template parameters and initial state conditions of CNNs on the spatio-temporal phenomena are investigated.