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Shear diversity prevents collective synchronization.

Ernest Montbrió¹, Diego Pazó

¹Department of Information and Communication Technologies, Universitat Pompeu Fabra, 08018 Barcelona, Spain.

Physical Review Letters

|July 21, 2011

Summary

Collective synchronization in heterogeneous oscillators is hindered by diverse shear, even with strong coupling. A precise threshold for shear distribution width makes synchronization impossible in the Kuramoto model.

Area of Science:

Complex systems
Nonlinear dynamics
Statistical physics

Background:

Heterogeneous oscillators can synchronize through mutual interactions.
Synchronization in systems with distributed frequencies and common shear depends on coupling strength.
The role of shear diversity in synchronization dynamics remains incompletely understood.

Purpose of the Study:

To investigate the impact of distributed shear on collective synchronization in oscillator ensembles.
To derive analytical results for the Kuramoto model with heterogeneous shear.
To determine the conditions under which shear diversity prevents synchronization.

Main Methods:

Analytical treatment of the Kuramoto model incorporating distributed shear.
Mathematical analysis of the transition from incoherence to synchronization.

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Identification of critical thresholds for shear distribution width.

Main Results:

Shear diversity cannot be overcome by diffusive coupling to achieve synchronization.
The first analytical results for the Kuramoto model with distributed shear are presented.
A precise threshold for the width of the shear distribution is identified, beyond which synchronization is impossible.

Conclusions:

Distributed shear presents a fundamental limitation to collective synchronization in heterogeneous oscillator systems.
The findings provide critical insights into the dynamics of complex coupled systems.
The study establishes a theoretical limit for synchronization based on shear heterogeneity.