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Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics
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Golubitsky, Martin and Stewart, Ian (2016) Rigid patterns of synchrony for equilibria and periodic cycles in network dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26 (9). pp. 1-13. 094803. doi:10.1063/1.4953664 ISSN 1054-1500.
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Official URL: http://dx.doi.org/10.1063/1.4953664
Abstract
We survey general results relating patterns of synchrony to network topology, applying the formalism of coupled cell systems. We also discuss patterns of phase-locking for periodic states, where cells have identical waveforms but regularly spaced phases. We focus on rigid patterns, which are not changed by small perturbations of the differential equation. Symmetry is one mechanism that creates patterns of synchrony and phase-locking. In general networks, there is another: balanced colorings of the cells. A symmetric network may have anomalous patterns of synchrony and phase-locking that are not consequences of symmetry. We introduce basic notions on coupled cell networks and their associated systems of admissible differential equations. Periodic states also possess spatio-temporal symmetries, leading to phase relations; these are classified by the H/K theorem and its analog for general networks. Systematic general methods for computing the stability of synchronous states exist for symmetric networks, but stability in general networks requires methods adapted to special classes of model equations.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Differentiable dynamical systems | ||||||||
Journal or Publication Title: | Chaos: An Interdisciplinary Journal of Nonlinear Science | ||||||||
Publisher: | American Institute of Physics | ||||||||
ISSN: | 1054-1500 | ||||||||
Official Date: | 23 June 2016 | ||||||||
Dates: |
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Volume: | 26 | ||||||||
Number: | 9 | ||||||||
Number of Pages: | 13 | ||||||||
Page Range: | pp. 1-13 | ||||||||
Article Number: | 094803 | ||||||||
DOI: | 10.1063/1.4953664 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 15 September 2016 | ||||||||
Date of first compliant Open Access: | 23 June 2017 |
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