DELAY INDUCED INSTABILITIES IN COUPLED SEMICONDUCTOR LASERS AND MACKEY-GLASS ELECTRONIC CIRCUITS

Abstract

We describe two experimental systems where a time-delayed feedback mechanism plays an important role in inducing instabilities. The first system consists of two cross-coupled semiconductor lasers with time-delayed negative optoelectronic feedback. This system is described by coupled delay-differential equations, and we explore the dynamics near the onset of oscillations as the coupling strength is varied. We study the influence of asymmetric coupling strengths on the onset of oscillations and the dependence of the amplitudes of oscillations on the coupling strengths. In-phase oscillations with a period of twice the delay time emerge as the product of coupling strengths increases above a critical value. A scaling relationship is observed between rescaled amplitudes of oscillations and the product of the coupling strengths. We also study the dependence of the periodicity and the phase relations of the oscillations as we adjust the delay time.

The second system is an electronic circuit with time-delayed nonlinear feedback which simulates the Mackey-Glass model described by a delay-differential equation. First we study the dynamics of the Mackey-Glass system in various parameter regimes and then we study the synchronization of two unidirectionally coupled Mackey-Glass circuits. The change of the quality of the synchronization with parameter mismatch as well as bandwidth limitations in the transmission channel is investigated. With a low pass filter in the transmission line, we find that the inclusion of the dominant frequency component of the original driver signals is crucial to achieve synchronization between the driver and receiver circuits, both numerically and experimentally.