Effects of Non-reciprocity on Coupled Kuramoto Oscillators

TL;DR

This paper investigates how non-reciprocal interactions influence the dynamics of coupled Kuramoto oscillators, revealing new states and significant modifications to chimera states, with implications for understanding asymmetric interactions in complex systems.

Contribution

It introduces a non-reciprocal Kuramoto model and demonstrates how non-reciprocity creates novel dynamical states and alters chimera state behavior.

Findings

Non-reciprocity significantly changes the chimera state diagram.

New dynamical states such as traveling chimera and run-and-chase emerge.

Non-reciprocal interactions lead to coexistence phases.

Abstract

All the fundamental interactions (such as gravity or electromagnetic interactions) are reciprocal in nature. However, in the macroscopic world, in particular outside equilibrium, non-reciprocal or non-mutual interactions are quite ubiquitous. Understanding the impact of such non-reciprocal interactions has drawn a significant amount of interest in physics and other fields of sciences in recent years. We explore a non-reciprocal version of coupled oscillators (known as the Kuramoto model) with the aim of understanding the role of non-reciprocity, particularly in relation to chimera states, where oscillators spontaneously break into mutually synchronous and asynchronous groups. Our findings suggest that non-reciprocity not only alters the state diagram of the chimera state significantly but can also lead to new dynamical states, such as traveling chimera, run-and-chase and coexistence phases.