Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos

TL;DR

This paper investigates how long-range interactions in a chain of nonlinear oscillators influence their collective behavior, revealing transitions from synchronization to chaos depending on the interaction parameter alpha.

Contribution

It introduces a model with a new parameter alpha controlling the complexity of the medium and analyzes its impact on the system's dynamics, including synchronization and chaos.

Findings

Transitions from synchronization to chaos as alpha varies

Long-range interactions significantly alter dynamical regimes

The system's behavior is described by a Ginzburg-Landau equation in the continuum limit

Abstract

We consider a chain of nonlinear oscillators with long-range interaction of the type 1/l^{1+alpha}, where l is a distance between oscillators and 0< alpha <2. In the continues limit the system's dynamics is described by the Ginzburg-Landau equation with complex coefficients. Such a system has a new parameter alpha that is responsible for the complexity of the medium and that strongly influences possible regimes of the dynamics. We study different spatial-temporal patterns of the dynamics depending on alpha and show transitions from synchronization of the motion to broad-spectrum oscillations and to chaos.