Emergence of order from chaos: A phenomenological model of coupled oscillators

Abstract

This paper aims to study the transition to order from chaos using a mathematical model of coupled non-identical oscillators. In the course of our analysis, we adopt a different control parameter other than the conventional parameters: coupling strength and frequency-mismatch, generally used in literature to obtain the aforementioned transition. Both the interacting oscillators become periodic, and they lead to the synchronized state as the control parameter changes monotonically. Initially, the participating oscillators, with low amplitude of oscillations, are in the chaotic desynchronized state. Besides, during the periodic oscillations, the oscillators exhibit high amplitude of oscillations. We illustrate the corresponding results using two examples of coupled oscillators. Such emergence of order from chaos with an accompanying increase in amplitude is ascertained in various numerical simulations and experimental observations.