Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators

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Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators

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Title: Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators
Author: Ashwin, Peter
Borresen, Jon
Citation: 70, p. 026203
Publisher: American Physical Society
Journal: Physical Review E
Date Issued: 2004
URI: http://hdl.handle.net/10036/20155
DOI: 10.1103/PhysRevE.70.026203
Links: http://link.aps.org/abstract/PRE/v70/e026203
Abstract: We study properties of the dynamics underlying slow cluster oscillations in two systems of five globally coupled oscillators. These slow oscillations are due to the appearance of structurally stable heteroclinic connections between cluster states in the noise-free dynamics. In the presence of low levels of noise they give rise to long periods of residence near cluster states interspersed with sudden transitions between them. Moreover, these transitions may occur between cluster states of the same symmetry, or between cluster states with conjugate symmetries given by some rearrangement of the oscillators. We consider the system of coupled phase oscillators studied by Hansel et al. [Phys. Rev. E 48, 3470 (1993)] in which one can observe slow, noise-driven oscillations that occur between two families of two cluster periodic states; in the noise-free case there is a robust attracting heteroclinic cycle connecting these families. The two families consist of symmetric images of two inequivalent periodic orbits that have the same symmetry. For N=5 oscillators, one of the periodic orbits has one unstable direction and the other has two unstable directions. Examining the behavior on the unstable manifold for the two unstable directions, we observe that the dimensionality of the manifold can give rise to switching between conjugate symmetry orbits. By applying small perturbations to the system we can easily steer it between a number of different marginally stable attractors. Finally, we show that similar behavior occurs in a system of phase-energy oscillators that are a natural extension of the phase model to two dimensional oscillators. We suggest that switching between conjugate symmetries is a very efficient method of encoding information into a globally coupled system of oscillators and may therefore be a good and simple model for the neural encoding of information.
Type: Article
Description: Peter Ashwin and Jon Borresen, Physical Review E, Vol. 70, p. 026203 (2004). "Copyright © 2004 by the American Physical Society."
Keywords: synchronizationdynamicsmaps
ISSN: 1539-37551550-2376


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