Birhythmic Behavior in a New Dual Loop Optoelectronic Oscillator

Abstract

AbstractIn the present paper, we report the birhythmic behavior of a time delayed Optoelectronic Oscillator (OEO) with two delays, popularly known as the Dual Loop Optoelectronic Oscillator (DLOEO). The present DLOEO contains a van der Pol Oscillator (VDPO) in its feedback loop, in place of the RF Band Pass Filter (BPF). We derive the system equation of the oscillator using weak nonlinear analysis. Coexistence of the two limit cycle oscillation is known as birhythmicity. Birhythmicity in an oscillator is an intriguing phenomenon. Often, birhythmicity is desirable as it presents us with two possible coexisting stable oscillatory states for common values of system parameters. It can also be a nuisance because a random perturbation may make the system settle onto an unwanted stable state. Therefore, identifying birhythmic behavior in an oscillator is an important task. Through detail analytical and numerical bifurcation analysis, for the first time, our study reveals birhythmic behavior in a DLOEO.KeywordsOptoelectronic OscillatorBirhythmicityTime delayHopf bifurcation