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Related Experiment Video

Updated: Oct 29, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks.

Anil Kumar¹, Sarika Jalan¹

¹Complex Systems Lab, Department of Physics, Indian Institute of Technology Indore, Khandwa Road, Simrol, Indore 453552, India.

Chaos (Woodbury, N.Y.)

|July 12, 2021

Summary

Introducing a phase shift in coupled Kuramoto oscillators can induce explosive synchronization (ES) and hysteresis. This phenomenon is robust and extends to single networks with phase-shifted links.

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Area of Science:

Complex systems
Nonlinear dynamics
Network science

Background:

Explosive synchronization (ES) is a phenomenon observed in coupled oscillator systems.
Previous methods for inducing ES in Kuramoto oscillators have been explored.
Multiplex networks offer complex interaction structures for studying synchronization dynamics.

Purpose of the Study:

To investigate the role of interlayer coupling phase shifts in inducing explosive synchronization in a two-layer multiplex network of Kuramoto oscillators.
To analyze the emergence of hysteresis and its dependence on system parameters.
To extend the findings to single networks with phase-shifted interactions.

Main Methods:

Numerical simulations of a two-layer multiplex network of Kuramoto oscillators.
Introduction of a phase shift (α) in interlayer coupling terms.
Mean-field analysis to support numerical results.
Testing robustness against network topology and natural frequency distribution variations.

Main Results:

A phase shift (α) in interlayer coupling can instigate explosive synchronization (ES) in both layers of a multiplex network.
As α approaches π/2, ES emerges with hysteresis.
Hysteresis width is dependent on the phase shift, coupling strength, and natural frequency mismatch.
Suppression of synchronization is identified as the cause of ES, consistent with prior research.
ES demonstrates robustness against changes in network topology and natural frequency distribution.

Conclusions:

Phase-shifted interlayer coupling is a novel mechanism for inducing explosive synchronization and hysteresis in multiplex Kuramoto oscillator networks.
The findings can be extended to single networks by incorporating phase-shifted links.
This research provides insights into controlling synchronization dynamics in complex systems.