Partial locking in phase-oscillator populations with heterogenous coupling

Author:

Xu Can1ORCID,Wu Yonggang2,Zheng Zhigang1ORCID,Tang Longkun2ORCID

Affiliation:

1. Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China

2. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Abstract

We consider a variant of the mean-field model of coupled phase oscillators with uniform distribution of natural frequencies. By establishing correlations between the quenched disorder of intrinsic frequencies and coupling strength with both in- and out-coupling heterogeneities, we reveal a generic criterion for the onset of partial locking that takes place in a domain with the coexistence of phase-locked oscillators and drifters. The critical points manifesting the instability of the stationary states are obtained analytically. In particular, the bifurcation mechanism of the equilibrium states is uncovered by the use of frequency-dependent version of the Ott–Antonsen reduction consistently with the analysis based on the self-consistent approach. We demonstrate that both the manner of coupling heterogeneity and correlation exponent have influence on the emergent patterns of partial locking. Our research could find applicability in better understanding the phase transitions and related collective phenomena involving synchronization control in networked systems.

Funder

National Natural Science Foundation of China

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Reference43 articles.

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3. From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

4. The Kuramoto model: A simple paradigm for synchronization phenomena

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