Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model

Prosenjit Kundu, Pitambar Khanra, Chittaranjan Hens, Pinaki Pal

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27 Scopus citations

Abstract

We investigate transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto (SK) model on complex networks both analytically and numerically. We analytically derive self-consistent equations for group angular velocity and order parameter for the model in the thermodynamic limit. Using the self-consistent equations we investigate transition to synchronization in SK model on uncorrelated scale-free (SF) and Erdos-Rényi (ER) networks in detail. Depending on the degree distribution exponent (γ) of SF networks and phase-frustration parameter, the population undergoes from first-order transition [explosive synchronization (ES)] to second-order transition and vice versa. In ER networks transition is always second order irrespective of the values of the phase-lag parameter. We observe that the critical coupling strength for the onset of synchronization is decreased by phase-frustration parameter in case of SF network where as in ER network, the phase-frustration delays the onset of synchronization. Extensive numerical simulations using SF and ER networks are performed to validate the analytical results. An analytical expression of critical coupling strength for the onset of synchronization is also derived from the self-consistent equations considering the vanishing order parameter limit.

Original languageEnglish
Article number052216
JournalPhysical Review E
Volume96
Issue number5
DOIs
StatePublished - 21 Nov 2017

Bibliographical note

Publisher Copyright:
© 2017 American Physical Society.

Funding

The authors would like to thank Syamal Dana for interesting comments and suggestions. P.K. acknowledges support from DST, India under the DST-INSPIRE scheme (Code: IF140880). C.H. is supported by the CHE/PBC, Israel.

FundersFunder number
DST-INSPIREIF140880
Division of Chemistry
Department of Science and Technology, Ministry of Science and Technology, India
Planning and Budgeting Committee of the Council for Higher Education of Israel

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