Quantum mechanics

Phase (matter)

Metallurgy

Materials science

Phase transition

Coupling (piping)

Telecommunications

Computer science

Kuramoto model

Anthropology

Statistical physics

Collective behavior

Physics

Hysteresis

Nonlinear system

Amplitude

Mathematics

Synchronization networks

Sociology

Condensed matter physics

Synchronization (alternating current)

Jump

Combinatorics

Transmission (telecommunications)

Topology (electrical circuits)

Mean field theory

Synchronizing

Physical Review Research

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.

Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators