Strongly asymmetric clustering in systems of phase oscillators

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 71, Issue 1, 2005, Pages

  Banaji, Murad ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMMETRIC CLUSTERS (AC); EUCLIDIAN SPACE; PERMUTATION; PHASE OSCILLATORS;

BIFURCATION (MATHEMATICS); FOURIER TRANSFORMS; PERTURBATION TECHNIQUES; POLYNOMIALS; SYNCHRONIZATION; SYSTEM STABILITY;

OSCILLATORS (ELECTRONIC);

EID: 41349093087     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.71.016212     Document Type: Article

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20. Throughout the text, we bear in mind that roots can have multiplicity of greater than 1, but avoid repeating this fact everywhere that it is relevant.
21. Strictly speaking, what we have proved is that AC states are present at parameter values arbitrarily close to the bifurcation point, not actually at the bifurcation point.
22. Obviously the full system must be simulated with small added noise to avoid the possibility of spurious clustering behavior as mentioned in [15].
23. More precisely, it is these states which have larger basins of attraction, and to which random initial conditions converge.