Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators

TL;DR

This paper investigates a complex variant of the Kuramoto model with heterogeneous, nonlinear coupling and correlated disorder, revealing diverse collective behaviors and phase transitions in coupled oscillators.

Contribution

It introduces a novel Kuramoto model variant with correlated disorder and nonlinear coupling, providing analytical insights into its rich collective dynamics.

Findings

Discovered explosive and hybrid synchronization transitions.

Identified abrupt irreversible desynchronization phenomena.

Mapped various phase transition types and stability conditions.

Abstract

Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak intensity in synchronizing laser arrays. Here we advance this subject by studying a variant of the Kuramoto model, where the coupling between the phase oscillators is heterogeneous and nonlinear. In particular, the quenched disorder in the coupling strength and the intrinsic frequencies are correlated, and the coupling itself depends on the amplitude of the mean-field of the system. We show that the interplay of these factors leads to a fascinatingly rich collective dynamics, including explosive synchronization transitions, hybrid transitions with hysteresis absence, abrupt irreversible desynchronization transitions, and tiered phase transitions with or without a vanishing onset. We develop an analytical treatment that enables us to determine the observed equilibrium states of the system, as well as to explore their asymptotic stability at various levels. Our research thus provides theoretical foundations for a number of self-organized phenomena that may be responsible for the emergence of collective rhythms in complex systems.