Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators

TL;DR

This paper introduces a flexible delayed-feedback nonlinear oscillator capable of diverse dynamical behaviors, explores synchronization conditions between coupled oscillators, and presents an experimental method for Lyapunov exponent estimation and adaptive synchronization control.

Contribution

It presents a novel modular oscillator design, a model-free Lyapunov exponent measurement technique, and an adaptive control method for maintaining synchronization under changing coupling.

Findings

Oscillator can generate periodic to chaotic dynamics.

Synchronization conditions are identified experimentally.

Adaptive control maintains synchronization despite coupling changes.

Abstract

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital-signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions under which they will synchronize. By examining the rates of divergence or convergence between two coupled oscillators, we quantify the maximum Lyapunov exponents or transverse Lyapunov exponents of the system, and we present an experimental method to determine these rates that does not require a mathematical model of the system. Finally, we demonstrate a new adaptive control method that keeps two oscillators synchronized even when the coupling between them is changing unpredictably.