Effects of Non-reciprocity on Coupled Kuramoto Oscillators

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.