Please use this identifier to cite or link to this item:
Scopus Web of Science® Altmetric
Full metadata record
DC FieldValueLanguage
dc.contributor.authorRitchie, L.-
dc.contributor.authorLohe, M.-
dc.contributor.authorWilliams, A.-
dc.identifier.citationChaos: an interdisciplinary journal of nonlinear science, 2018; 28(5):053116-1-053116-11-
dc.description.abstractWe formulate a noncompact version of the Kuramoto model by replacing the invariance group SO(2) of the plane rotations by the noncompact group SO(1, 1). The N equations of the system are expressed in terms of hyperbolic angles αi and are similar to those of the Kuramoto model, except that the trigonometric functions are replaced by hyperbolic functions. Trajectories are generally unbounded, nevertheless synchronization occurs for any positive couplings κi, arbitrary positive multiplicative parameters λi and arbitrary exponents ωi. There are no critical values for the coupling constants. We measure the onset of synchronization by means of several order and disorder parameters. We show numerically and by means of exact solutions for N = 2 that solutions can develop singularities if the coupling constants are negative, or if the initial values are not suitably restricted. We describe a physical interpretation of the system as a cluster of interacting relativistic particles in 1 + 1 dimensions, subject to linear repulsive forces with space-time trajectories parametrized by the rapidity αi. The trajectories synchronize provided that the particle separations remain predominantly time-like, and the synchronized cluster can be viewed as a bound state of N relativistic particle constituents. We extend the defining equations of the system to higher dimensions by means of vector equations which are covariant with respect to SO(p, q).-
dc.description.statementofresponsibilityLouis M. Ritchie, M.A. Lohe and Anthony G. Williams-
dc.publisherAmerican Institute of Physics-
dc.rightsPublished by AIP Publishing-
dc.titleSynchronization of relativistic particles in the hyperbolic Kuramoto model-
dc.typeJournal article-
dc.identifier.orcidLohe, M. [0000-0002-5214-2225]-
dc.identifier.orcidWilliams, A. [0000-0002-1472-1592]-
Appears in Collections:Aurora harvest 8
Physics publications

Files in This Item:
There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.