Non-Hermitian global synchronization

TL;DR

This paper introduces a novel method to achieve robust global synchronization in nonlinear oscillators by leveraging non-Hermitian physics, demonstrating initial-state independence and topological effects through experimental circuits.

Contribution

It presents a new approach combining non-Hermitian physics with nonlinear dynamics to realize resilient, initial-state-independent global synchronization in physical systems.

Findings

Demonstration of initial-state-independent non-Hermitian skin and topological synchronization

Experimental validation using nonlinear topoelectrical circuits

Identification of anomalous effects like enlarged-size triggered synchronization

Abstract

Synchronization of coupled nonlinear oscillators is a prevalent phenomenon in natural systems and can play important roles in various fields of modern science, such as laser arrays and electric networks. However, achieving robust global synchronization has always been a significant challenge due to its extreme susceptibility to initial conditions and structural perturbations. Here, we present a novel approach to achieve robust global synchronization by manipulating the interplay between non-Hermitian physics and nonlinear dynamics. Remarkably, the initial-state-independent non-Hermitian skin and topological global synchronization are proposed, exhibiting diverse anomalous effects such as the enlarged-size triggered non-Hermitian global synchronization and nonlinear skin states-dominated global synchronization. To validate our findings, we design and fabricate nonlinear topoelectrical circuits for experimental observation of non-Hermitian global synchronization. Our work opens up a promising avenue for establishing resilient global synchronization with potential applications in constructing high-radiance laser arrays and topologically synchronized networks.