Multirhythmicity in an optoelectronic oscillator with large delay

TL;DR

This paper investigates multirhythmic behavior in a large-delay optoelectronic oscillator, revealing coexistence of multiple stable square-wave oscillations with different periods, supported by experimental, numerical, and analytical results.

Contribution

It demonstrates the coexistence of multiple stable oscillation regimes in a large-delay optoelectronic oscillator and provides a comprehensive analysis combining experiments, simulations, and theory.

Findings

Multiple square-wave oscillations coexist at the same parameters.

Oscillation periods relate to fractions of the delay depending on phase shift.

Experimental results agree with numerical simulations and analytical stability analysis.

Abstract

An optoelectronic oscillator exhibiting a large delay in its feedback loop is studied both experimentally and theoretically. We show that multiple square-wave oscillations may coexist for the same values of the parameters (multirhythmicity). Depending on the sign of the phase shift, these regimes admit either periods close to an integer fraction of the delay or periods close to an odd integer fraction of twice the delay. These periodic solutions emerge from successive Hopf bifurcation points and stabilize at a finite amplitude following a scenario similar to Eckhaus instability in spatially extended systems. We find quantitative agreements between experiments and numerical simulations. The linear stability of the square-waves is substantiated analytically by determining stable fixed points of a map.