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Title: Partially coherent twisted states in arrays of coupled phase oscillators

We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly “twisted” in space. To analyze these, we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies, and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.
Authors:
;  [1] ;  [2]
  1. Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin (Germany)
  2. INMS, Massey University, Private Bag 102-904 NSMC, Auckland (New Zealand)
Publication Date:
OSTI Identifier:
22250982
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; COUPLING; EIGENSTATES; ONE-DIMENSIONAL CALCULATIONS; SIMULATION; SPACE; STABILITY