Chimeras on a social-type network

TL;DR

This paper studies a social-type network of coupled oscillators, revealing that passive units strongly correlate with active ones in a chimera pattern due to negative transversal Lyapunov exponents.

Contribution

It introduces a model with active and passive units on a ring with long-range coupling, demonstrating the emergence of correlated passive units in a chimera state.

Findings

Passive units are strongly correlated with active units.

Negative transversal Lyapunov exponents explain the correlation.

Active oscillators form a fluctuating chimera pattern.

Abstract

We consider a social-type network of coupled phase oscillators. Such a network consists of an active core of mutually interacting elements, and of a flock of passive units, which follow the driving from the active elements, but otherwise are not interacting. We consider a ring geometry with a long-range coupling, where active oscillators form a fluctuating chimera pattern. We show that the passive elements are strongly correlated. This is explained by negative transversal Lyapunov exponents.