Kazuhiro Fukushima

A New Type of Intermittency in an Electronic Circuit

An intermittency which has a different origin from the Pomeau-Manneville types is studied in a coupled nonlinear LCR circuit. This type of intermittency has a close relation to the multiplicative noise process. The electronic circuit is made up of inductors, resistors and capacitor diodes. An experimental study is done in this system. The results are compared with those of a phenomenological theory based on the multiplicative noise process. More· over, a numerical calculation is also carried out on the equations for the present circuit with observed nonlinear characteristics of diodes. Satisfactory agreement between the exper· imental and calculated results is obtained.

Type-III Intermittency in a Coupled Nonlinear LCR Circuit

Type-III intermittency is experimentally observed in an electronic device. Experimental circuit is considered to be a two-coupled identical oscillator system. Each oscillator consists of an inductor, a resistor and a diode connected in series and is coupled through an inductor. Intermittency takes place in narrow region where the synchronized motion between two oscillators just breaks up. Waveform, maps and power spectrum of intermittent behavior are studied in this paper. Experimental results are compared with those of a numerical calculation based on the equations for this circuit with observed nonlinear characteristics of diode. Good agreements between experiment and numerical calculation are obtained.

Initial condition dependence of the residence time for scattering soliton in a perturbed sine-Gordon equation system

Abstract Behaviors of scattering soliton in a perturbed sine-Gordon equation system are numerically studied. We measure the residence time which is defined as the time that the soliton is trapped by an impurity. The initial condition dependence of the residence time has a self-similar fractal structure and the distribution function of the residence time can be expressed as an exponential function e −βτ , where τ is the residence time. The value of β depends on the amplitude of external periodic force G . Such a dependence is expressed as β ~ ( G − G c ) η , where G c is a critical value defined as the value that the soliton cannot pass over the impurity. The value of the critical exponent η is determined from this relation and we obtain η = 0.328. This relation can be derived from an analysis based on the consideration of critical phenomenological behavior.

On-off intermittency observed in a system of coupled sine-Gordon solitons

Abstract On-off intermittency is numerically observed in a coupled sine-Gordon soliton system. In the present system two solitons are pinned at impurities and couple through inter-chain interaction. The distributions of the burst amplitude and the laminar duration time show a −1 power law and a −3 2 power law, respectively. These power laws agree with the proper statistical features of on-off intermittency. The present type of model is realized in soliton systems such as charge density wave (CDW) and Josephson transmission line ones in which the on-off intermittency can be hopefully observed.

Fluctuation Spectrum for a New Type of Intermittency in a Coupled Electronic Circuit

A new type of intermittency associated with the transition from uniform to nonuniform chaos in a coupled electronic circuit is studied by means of the fluctuation spectrum theory. The time series are constructed by taking the n -th power of original experimental data obtained near the intermittent transition point. The intermittent behavior is enhanced as the power n is increased. Two types of scaling laws are found for the fluctuation spectra σ(α)s.

Chaotic transition in a three-coupled phase-locked loop system

The chaotic transition is observed in a three-coupled phase-locked loop (PLL) system in both experiments and numerical simulations. In this system, three PLL oscillators are connected with the periodic boundary condition. Intermittency is found in partially synchronized phase, in which two of three oscillators synchronize with each other and form a pair, and the chaotic transition occurs due to the recombination of synchronized pairs so that different pair is re-formed. In this phase, on-off intermittency is also observed and statistical analyses are carried out for on-off intermittent time series. This intermittency is considered as a hybrid type of intermittency with both on-off intermittency and intermittency due to the recombination of synchronized pairs present in the same time series. We also show the chaotic transition phenomena in a three-coupled logistic map system. (c) 2001 American Institute of Physics.

Chaotic transition in a five-coupled o 4 -field soliton system

Abstract Cooperative motions of solitons in a cross-shaped system formed by five chains are numerically studied by solving a set of perturbed φ4-field equations with inter-chain couplings. We find the partially synchronized phase, which exists in a region between the completely synchronized phase and the asynchronized phase. We observe the chaotic transition due to the reconstruction of the synchronized state in the partially synchronized phase, in which the solitons make clusters. We investigate the time-evolution of the number of clusters. The distribution function of the duration time of the state in which all solitons synchronize, namely, when the number of clusters is equal to 1, is expressed as a − 3 2 power law. The power spectrum for the time-variation of the number of clusters also shows a power law. When we examine these calculations in a five-coupled logistic map system, good agreement between the results in these systems can be obtained. The chaotic transition phenomenon presented in a five-coupled oscillator system is closely related to the onset of the on–off intermittency.

On–off intermittency in a perturbed φ4-field equation with an inter-chain interaction

Abstract On–off intermittency is observed by numerically solving a perturbed φ4-field equation with an inter-chain interaction. In this system, the distribution function of the burst amplitude shows a −1 power law and also that of laminar duration time a −3/2 power law. In the power spectrum we show a −1/2 power law in the low frequency region. These power laws are the typical characteristics in on–off intermittency. Moreover, in the synchronized state, we confirm the existence of a riddled structure from the calculation of the first passage time. We calculate a distribution function of the first passage time, which has an exponential form for a large time.

Fractal properties of a scattering sine-Gordon soliton

Abstract A perturbed sine-Gordon equation which includes the terms of disspation, inhomogeneity made by impurities and external force is numerically studied. Particularly we investigate a scattering soliton by the impurity potential. The residence time, which is defined as the time that the soliton is trapped by an impurity, strongly depends on the initial conditions and shows self-similar structures. The distribution function of the residence times has a peculiar staircase-like form. The distribution functions for low dimensional mappings are also calculated and compared with the soliton case.

Cooperative phenomena observed in a globally coupled phase-locked loop system

The authors describe cooperative phenomena observed in a globally coupled 8-phase-locked loop (PLL) system in both experiments and simulations by using SPICE. In the present system, each PLL is connected through the coupler that averages the all PLLs output signals. When the frequency modulated external force is applied, three phases are observed such as (1) the coherent phase in which all subsystems are synchronized, (2) the turbulent phase in which all subsystems oscillate independently, and (3) the partially synchronized phase in which creation of clusters and chaotic itineracy due to the reconstruction of clusters occur. In the partially synchronized phase, the time series of voltage difference between arbitrary two subsystems shows an intermittency. From the statistical analysis for this intermittency it is found that the distribution functions of burst amplitude and laminar duration time show the -1 power law and -1.5 power law, respectively. These properties agree with those of the on-off intermittency. We also investigate the variation of number of cluster in the partially synchronized phase. The distribution function of the duration time of one-cluster state, namely the residence time in the state in which all subsystems are synchronized with each other, is also expressed as the -1.5 power law.