Dynamics of Oscillators Coupled by a Medium with Adaptive Impact

TL;DR

This paper investigates how coupled oscillators, modeled by metronomes on a moving base with adaptive feedback, evolve towards specific dynamic regions, revealing transitions with increased frequency complexity.

Contribution

It introduces a model of adaptive feedback controlling the base movement, demonstrating how oscillator dynamics evolve towards specific regions with spectral transitions.

Findings

Oscillators tend to evolve towards a specific dynamic region.

Adaptive feedback influences the frequency spectrum of oscillators.

Transitions involve the emergence of more frequencies in the spectra.

Abstract

In this article we study the dynamics of coupled oscillators. We use mechanical metronomes that are placed over a rigid base. The base moves by a motor in a one-dimensional direction and the movements of the base follow some functions of the phases of the metronomes (in other words, it is controlled to move according to a provided function). Because of the motor and the feedback, the phases of the metronomes affect the movements of the base while on the other hand, when the base moves, it affects the phases of the metronomes in return. For a simple function for the base movement (such as $y = \gamma_{x} [r \theta_1 + (1 - r) \theta_2]$ in which $y$ is the velocity of the base, $\gamma_{x}$ is a multiplier, $r$ is a proportion and $\theta_1$ and $\theta_2$ are phases of the metronomes), we show the effects on the dynamics of the oscillators. Then we study how this function changes in time when its parameters adapt by a feedback. By numerical simulations and experimental tests, we show that the dynamic of the set of oscillators and the base tends to evolve towards a certain region. This region is close to a transition in dynamics of the oscillators; where more frequencies start to appear in the frequency spectra of the phases of the metronomes.