Apparent remote synchronization of amplitudes: a demodulation and interference effect

TL;DR

This paper reveals that apparent remote synchronization in nonlinear oscillators is caused by a demodulation and interference effect, showing that true synchronization decreases monotonically with distance despite apparent non-trivial patterns.

Contribution

The study uncovers the mechanism behind apparent remote synchronization, demonstrating it results from amplitude modulation and interference rather than genuine synchronization.

Findings

Destructive interference causes the observed dip in amplitude correlations.

Synchronization and causality decrease monotonically with distance when properly measured.

The mechanism involves amplitude modulation and spectral overlap, leading to false impressions of remote synchronization.

Abstract

A form of "remote synchronization" was recently described wherein amplitude fluctuations across a ring of non-identical, non-linear electronic oscillators become entrained into spatially-structured patterns. According to linear models and mutual information, synchronization and causality dip at a certain distance, then recover before eventually fading. Here, the underlying mechanism is finally elucidated through novel experiments and simulations. The system non-linearity is found to have a dual role: it supports chaotic dynamics, and it enables energy exchange between the lower and higher sidebands of a predominant frequency. This frequency acts as carrier signal in an arrangement resembling standard amplitude modulation, wherein the lower sideband and the demodulated baseband signals spectrally overlap. Due to a spatially-dependent phase relationship, at a certain distance near-complete destructive interference occurs between them, causing the observed dip. Methods suitable for detecting non-trivial entrainment, such as transfer entropy and the auxiliary system approach, nevertheless reveal that synchronization and causality actually decrease with distance monotonically. Remoteness is, therefore, arguably only apparent, as also reflected in the propagation of external perturbations. These results demonstrate a complex mechanism of dynamical interdependence, and exemplify how it can lead to incorrectly inferring synchronization and causality.