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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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Borresen, Jon en_GB
dc.contributor.department University of Exeter en_GB
dc.date.accessioned 2008-03-07T16:15:38Z en_GB
dc.date.accessioned 2011-01-25T10:33:49Z en_US
dc.date.accessioned 2013-03-20T12:26:41Z
dc.date.issued 2004 en_GB
dc.description.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. en_GB
dc.identifier.citation 70, p. 026203 en_GB
dc.identifier.doi 10.1103/PhysRevE.70.026203 en_GB
dc.identifier.uri http://hdl.handle.net/10036/20155 en_GB
dc.language.iso en en_GB
dc.publisher American Physical Society en_GB
dc.relation.url http://link.aps.org/abstract/PRE/v70/e026203 en_GB
dc.subject synchronization en_GB
dc.subject dynamics en_GB
dc.subject maps en_GB
dc.title Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators en_GB
dc.type Article en_GB
dc.date.available 2008-03-07T16:15:38Z en_GB
dc.date.available 2011-01-25T10:33:49Z en_US
dc.date.available 2013-03-20T12:26:41Z
dc.identifier.issn 1539-3755 en_GB
dc.identifier.issn 1550-2376 en_GB
dc.description Peter Ashwin and Jon Borresen, Physical Review E, Vol. 70, p. 026203 (2004). "Copyright © 2004 by the American Physical Society." en_GB
dc.identifier.journal Physical Review E en_GB


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