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Liu Z, Lai YC, Hoppensteadt FC. Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators. Phys Rev E Stat Nonlin Soft Matter Phys. 2001;63(5):055201doi: 10.1103/PhysRevE.63.055201.
Liu, Z., Lai, Y. C., & Hoppensteadt, F. C. (2001). Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators. Physical review. E, Statistical, nonlinear, and soft matter physics, 63(5), 055201. https://doi.org/10.1103/PhysRevE.63.055201
Liu, Z, et al. "Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 63,5 (2001): 055201. doi: https://doi.org/10.1103/PhysRevE.63.055201
Liu Z, Lai YC, Hoppensteadt FC. Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators. Phys Rev E Stat Nonlin Soft Matter Phys. 2001 May;63(5):055201. doi: 10.1103/PhysRevE.63.055201. Epub 2001 Apr 09. PMID: 11414950.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2001 May;63(5):055201. doi: 10.1103/PhysRevE.63.055201. Epub 2001 Apr 09.

Phase clustering and transition to phase synchronization in a large number of coupled nonlinear oscillators.

Physical review. E, Statistical, nonlinear, and soft matter physics

Z Liu, Y C Lai, F C Hoppensteadt

Affiliations

  1. Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA.

PMID: 11414950 DOI: 10.1103/PhysRevE.63.055201

Abstract

The transition to phase synchronization in systems consisting of a large number (N) of coupled nonlinear oscillators via the route of phase clustering (phase synchronization among subsets of oscillators) is investigated. We elucidate the mechanism for the merger of phase clusters and find an algebraic scaling between the critical coupling parameter required for phase synchronization and N. Our result implies that, in realistic situations, phase clustering may be more prevalent than full phase synchronization.

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