Hiroyuki Shirahama

Dynamical control of the chaotic state of the current-driven ion acoustic instability in a laboratory plasma using delayed feedback

Controlling chaos caused by the current-driven ion acoustic instability is attempted using delayed feedback, i.e., the time-delay auto synchronization (TDAS) method introduced by Pyragas [Phys. Lett. A 170, 421 (1992)] with flexibility. When the control parameter of the system Vm is increased, the current-driven ion acoustic instability is excited, and then, the system demonstrates chaotic oscillation in a certain range of the parameter. When the electronic circuit to control chaos based on the TDAS method is applied to the chaotic regime, the chaotic orbit changes to a periodic one maintaining the instability, that is, the chaotic state caused by the current-driven ion acoustic instability is well controlled using the TDAS method. Furthermore, it is shown that controlling chaos can be achieved when the delay time τ is chosen to be close to a fundamental frequency of the unstable periodic orbit embedding in the chaotic system.

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 synchronization in a five-star-coupled phase-locked loop system

This paper describes a chaotic synchronization phenomenon observed experimentally in a five-star-coupled phase-locked loop (PLL) oscillator system. This system consists of five PLLs connected in the shape of a star. The state in this system itinerates between the completely synchronized state, in which all PLL oscillators synchronize, and the disordered state, in which all PLLs oscillate individually, via the partially synchronized state. The time-series of the voltage difference between arbitrary two PLL oscillators shows the on-off intermittency. When such a chaotic itinerancy occurs, the distribution function of the duration time of the completely synchronized state is expressed as a \(-\frac{3}{2}\) power law which is quite similar to the distribution function of the laminar duration time in the on-off intermittency.

Circuit Simulation of Conversion of Stability Features near Hopf Bifurcation Using Time-Delayed Feedback Coupling

A circuit simulation of the conversion of the oscillation state near Hopf bifurcation is performed using time-delayed feedback control techniques. The system consists of a target oscillator and a control oscillator coupled with each other. Both the target and controller we used are described by the Landau–Stuart equation. The governing equation is realized in a set of electronic circuits. When the target shows a limit cycle, by adjusting the coupling strength the state can be stabilized to a fixed point, and oppositely the target that is in a state of fixed point can be excited to a limit cycle. The results sufficiently agree with the theory and numerical calculations.

Chaos Control of Fluctuations Caused by Flute Instability in Electron Cyclotron Resonance Plasma

Controlling chaos of density fluctuations observed in electron cyclotron resonance (ECR) plasma is carried out using the time-delayed auto synchronization (TDAS) method introduced by Pyragas. Since the TDAS method, which is a sort of feedback system, requires a feedback signal, the input power of microwaves for ECR discharge is modulated by signals of frequency (<30 kHz) based on the ion-saturation current indicating the electron density. Fluctuations caused by the flute instability reach the chaotic state when the microwave power is increased. It was found that when the TDAS method is applied to the chaotic state, the chaotic state transitions to the periodic state and the correlation dimension changes from a non integer value to an integer value.