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.

In this study, multimode chaos observed from two coupled chaotic oscillators with hard nonlinearities is investigated. At first, a simple chaotic oscillator with hard nonlinearities is realized. It is confirmed that in this chaotic oscillator the origin is always asymptotically stable and that the solution, which is excited by giving relatively large initial conditions, undergoes period-doubling bifurcations and bifurcates to chaos. Next, the coexistence of four different modes of oscillations are observed from two coupled chaotic oscillators with hard nonlinearities by both of circuit experiments and computer calculations. One of the modes of oscillation is a nonresonant double-mode oscillation and this oscillation is stably generated even in the case that oscillation is chaotic. Namely, for this oscillation mode, chaotic oscillation and periodic oscillation can be simultaneously excited. This phenomenon has not been reported yet, and we name this phenomenon as double-mode chaos. Finally, the beat frequency of the double-mode chaos is confirmed to be changed by varying the value of the coupling capacitor.

In this study, some oscillators with different oscillation frequencies, N - 1 oscillators have the same oscillation frequency and only the Nth oscillator has different frequency, coupled by a resistor are investigated. At first we consider nonresonance. By carrying out circuit experiments and computer calculations, we observe that oscillation of the Nth oscillator stops in some range of the frequency ratio and that others are synchronized as if the Nth oscillator does not exist. These phenomena are also analyzed theoretically by using the averaging method. Secondly, we investigate the resonance region where the fiequency ratio is nearly equal to 1. For this region we can observe interesting double-mode oscillation, that is, synchronization of envelopes of the double-mode oscillation and change of oscillation amplitude of the Nth oscillator.

In this article, a new analogic CNN algorithm to extract features of postage stamps in gray-scale images Is introduced. The Gradient Controlled Diffusion method plays an important role in the approach. In our algorithm, it is used for smoothing and separating Arabic figures drawn with a color which is similar to the background color. We extract Arabic figures in postage stamps by combining Gradient Controlled Diffusion with nearest neighbor linear CNN template and logic operations. Applying the feature extraction algorithm to different test images it has been verified that it is also effective in complex segmentation problems

In this paper, we investigate bifurcation phenomena ovserved from two autonomous three-dimensional chaotic circuits coupled by an inductor. Two types of synchronization modes are ovserved in this coupled system, i.e., in-phase synchronization and anti-phase synchronization. For the purpose of detailed analysis, we consider the case that the diodes in the subcircuits are assumed to operate as ideal switches. In this case Poincare map is derived as a three-dimensional map, and Lyapunov exponents can be calculated by using exact solutions. Various bifurcation phenomena related with chaos synchronization are clarified. We confirm that various bifurcation phenomena are observed from circuit experiments.

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.

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. In this article, an efficient numerical method for analyzing nonuniform transmission lines has been presented by using the Chebyshev expansion method and moment techniques. Efficiency on computational cost is demonstrated by numerical example.

In this paper, a middle-mapping learning algorithm for cellular associative memories is presented. This algorithm makes full use of the properties of the cellular neural network so that the associative memory has some advantages compared with the memory designed by the ourter product method. It can guarantee each prototype is stored at an equilibrium point. In the practical implementation, it is easy to build up the circuit because the weight matrix presenting the connection between cells is not symmetric. The synchronous updating rule makes its associative speed very fast compared to the Hopfield associative memory.

Template learning has potential application in several areas of Cellular Neural Network research, including texture recognition, pattern detection and so on. In this letter, a recently-developed algorithm called Adaptive Simulated Annealing is investigated for learning CNN templates, as a superior alternative to the Genetic Algorithm.

In this paper, we propose a new algorithm for calculating the exact poles of the admittance matrix of RLCG interconnects. After choosing dominant poles and corresponding residues, each element of the exact admittance matrix is approximated by partial fraction. A procedure to obtain the residues that guarantee the passivity is also provided, based on experimental studies. In the procedure the residues are calculated by using the least squares method so that the partial fraction matches each element of the exact admittance matrix in the frequency-domain. From the partial fraction representation, the asymptotic equivalent circuit models which can be easily simulated with SPICE are synthesized. It is shown that an efficient model-order reduction is possible for short-length interconnects.

In this paper, we discuss computational methods for obtaining the bifurcation points and the branch directions at branching points of solution curves for the nonlinear resistive circuits. There are many kinds of the bifurcation points such as limit point, branch point and isolated point. At these points, the Jacobian matrix of circuit equation becomes singular so that we cannot directly apply the usual numerical techniques such as Newton-Raphson method. Therefore, we propose a simple modification technique such that the Newton-Raphson method can be also applied to the modified equations. On the other hand, a curve tracing algorithm can continuously trace the solution curves having the limit points and/or branching points. In this case, we can see whether the curve has passed through a bifurcation point or not by checking the sign of determinant of the Jacobian matrix. We also propose two different methods for calculating the directions of branches at branching point. Combining these algorithms, complicated solution curves will be easily traced by the curve tracing method. We show the example of a Hopfield network in Sect.5.

In this article, a new type of diffusion template and an analogic CNN algorithm using this diffusion template for detecting some lung cancer symptoms in X-ray films are proposed. The performance of the diffusion template is investigated and our CNN algorithm is verified to detect some key lung cancer symptoms, successfully.

Analysis of frequency-dependent lossy transmission lines is very important for designing the high-speed VLSI, MCM and PCB. The frequency-dependent parameters are always obtained as tabulated data. In this paper, a new curve fitting technique of the tabulated data for the moment matching technique in the interconnect analysis is presented. This method based on Chebyshev interpolation enhances the efficiency of the moment matching technique.

In this paper some new results for analog hardware realization of secure communication system using chaos synchronization have been presented. In particular the effect of the use of transmission line as channel has been considered assuming practical implementation. The influence of the loss of transmission line and mismatching on synchronization has been investigated in chaotic systems based on the Pecora-Carroll concept. It has been shown that desynchronization due to loss can be checked by using an amplifier with appropriate gain. Moreover the bit error rate (BER) has been evaluated in a digital communication system based on the principle of chaotic masking.

In this study, a simple chaos communication system including modulation-demodulation circuits is studied. The influence of modulation-demodulation circuits to chaos synchronization is investigated. For the estimation of communication quality, bit error rate (BER) is calculated by computer simulation when a sequential random pulse information signal is transmitted via this proposed system.