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Explosive synchronization in a general complex network.

Xiyun Zhang¹, Xin Hu, J Kurths

¹Department of Physics, East China Normal University, Shanghai, 200062, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 16, 2013

Summary

This summary is machine-generated.

We present a new framework for explosive synchronization (ES) in complex networks, identifying a key condition related to coupling strengths and natural frequencies. This deepens the understanding of synchronization mechanisms beyond previous requirements.

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Area of Science:

Physics
Complex Systems
Network Science

Background:

Explosive synchronization (ES) requires scale-free networks and frequency-degree correlations.
Previous studies on ES have focused on specific network conditions.

Purpose of the Study:

To propose a generalized framework for explosive synchronization in complex networks.
To identify a new necessary condition for ES based on coupling strengths and natural frequencies.

Main Methods:

Developed a theoretical framework for ES in general complex networks.
Assumed a positive correlation between oscillator coupling strengths and the absolute of their natural frequencies.
Employed rigorous analytical treatment using a mean-field approach.

Main Results:

The new framework encompasses previous ES conditions as specific cases.
A single, unified condition replaces the two previously necessary conditions for ES.
The mean-field analysis explains the underlying mechanism of ES in the proposed framework.

Conclusions:

The study fundamentally deepens the understanding of the microscopic mechanisms driving synchronization.
The generalized framework offers broader applicability for studying explosive synchronization.
The findings provide new insights into synchronization phenomena in complex systems.