G. A. Johnson

SYNCHRONIZATION STABILITY IN COUPLED OSCILLATOR ARRAYS: SOLUTION FOR ARBITRARY CONFIGURATIONS

The stability of the state of motion in which a collection of coupled oscillators are in identical synchrony is often a primary and crucial issue. When synchronization stability is needed for many different configurations of the oscillators the problem can become computationally intense. In addition, there is often no general guidance on how to change a configuration to enhance or diminsh stability, depending on the requirements. We have recently introduced a concept called the Master Stability Function that is designed to accomplish two goals: (1) decrease the numerical load in calculating synchronization stability and (2) provide guidance in designing coupling configurations that conform to the stability required. In doing this, we develop a very general formulation of the identical synchronization problem, show that asymptotic results can be derived for very general cases, and demonstrate that simple oscillator configurations can probe the Master Stability Function.

Keeping chaos at bay

The use of electronic circuits in studying chaotic dynamics and control are reviewed. Since all chaotic systems have several properties in common, simple circuits are analogous to much more complicated ones, such as lasers. Consequently, the methods developed to control chaos in electronic circuits are applicable to many diverse physical systems. The controlling device itself is a high-speed analog circuit. In applying perturbations, no calculations are made; instead, trial-and-error adjustments are used to locate the desired behavior. The initial observations of chaos in electronics, the development of the Ott-Grebogi-Yorke method for calculating the perturbations needed to stabilize a periodic orbit in a chaotic system and the occasional proportional feedback method, and their applications are discussed.<<ETX>>

CONTROLLING CHAOS IN CHUA'S CIRCUIT

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chuas circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbits and multiple-correction, high-period orbits. Also, by employing two control circuits, we are able to stabilize orbits that visit both regions of Chuas circuits double-scroll attractor, applying corrections in each of these regions during a single orbit.

Stochastic resonance in coupled nonlinear dynamic elements

We investigate the response of a linear chain of diffusively coupled diode resonators under the influence of thermal noise. We also examine the connection between spatiotemporal stochastic resonance and the presence of kink-antikink pairs in the array. The interplay of nucleation rates and kink speeds is briefly addressed. The experimental results are supplemented with simulations on a coupled map lattice. We furthermore present analytical results for the synchronization and signal processing properties of a Phi(4) field theory and explore the effects of various forms of nonlinear coupling. (c) 1998 American Institute of Physics.

CONTROLLING CHAOS IN A SIMPLE AUTONOMOUS SYSTEM: CHUA’S CIRCUIT

The occasional proportional feedback (OPF) control technique has been successful in stabilizing periodic orbits in both periodically driven and autonomous systems undergoing chaotic behavior. By applying this technique to the well-known Chua’s circuit, we are able to control a variety of periodic orbits including single-correction, low-period orbits and multiple-correction, high-period orbits. Also, by employing two control circuits, we are able to stabilize orbits that visit both regions of Chua’s circuit’s double-scroll attractor, applying corrections in each of these regions during a single orbit.

PARAMETER-INSENSITIVE AND NARROW-BAND SYNCHRONIZATION OF CHAOTIC CIRCUITS

There have been many proposals to use chaotic signals for communications. There are many practical problems with transmitting chaotic signals, however: transmitter and receiver must match, and chaotic signals are affected by phase or amplitude distortion and additive noise. We describe ways to reduce the parameter sensitivity of chaotic synchronization and reduce the bandwidth of chaotic signals.

Modular fiber optic hull monitoring system with real time signal processing

We demonstrate a modular semi-autonomous system for permanent ship hull structural health monitoring based on fiber Bragg gratings, Fabry-Perot interrogation, and a distributed software system for acquisition, real-time signal processing and visualization.

Stability analysis of fixed points via chaos control.

This paper reviews recent advances in the application of chaos control techniques to the stability analysis of two-dimensional dynamical systems. We demonstrate how the systems response to one or multiple feedback controllers can be utilized to calculate the characteristic multipliers associated with an unstable periodic orbit. The experimental results, obtained for a single and two coupled diode resonators, agree well with the presented theory. (c) 1997 American Institute of Physics.

Stable states and kink dynamics in a system of coupled diode resonators

Abstract We investigate the origin of stable spatially extended waveforms in an open flow system consisting of unidirectionally coupled chaotic oscillators. Results are obtained for an experimental system consisting of coupled diode resonators as well as for a coupled map lattice, a numerical model comprised of logistic maps. Under the conditions studied, spatially coherent or laminar states in both systems are convectively unstable, typically inducing high-dimensional, complex spatio-temporal dynamics. In each system stable spatial waveforms are shown to exist and are stabilized by either anchoring the first oscillator onto specific temporal orbits or by employing periodic boundary conditions. The latter case combined with a reduced drive amplitude also allows for travelling phase-kink solutions which move with constant velocity. This velocity is roughly inversely proportional to the coupling resistance and also depends on the number of kinks present in the system. We show evidence that the stable states of the system are associated with travelling kinks.

A system for high-frequency and quasi-static fiber bragg grating interrogation

A method for tracking interferometer drift is presented, enabling the development of a system for interrogating fiber Bragg gratings both for very low-frequency measurements and for applications requiring sampling rates into the kilohertz range.