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Phase-locking and Arnold coding in prototypical network topologies


Martignoli, S; Stoop, R (2008). Phase-locking and Arnold coding in prototypical network topologies. Discrete and Continuous Dynamical Systems. Series B, 9(1):145-162.

Abstract

Phase- and frequency-locking phenomena among coupled biological oscillators are a topic of current interest, in particular to neuroscience. In the case of mono-directionally pulse-coupled oscillators, phase-locking is well understood, where the phenomenon is globally described by Arnold tongues.
Here, we develop the tools that allow corresponding investigations to be made for more general pulse-coupled networks. For two bi-directionally coupled oscillators, we prove the existence of three-dimensional Arnold tongues that mediate from the mono- to the bi-directional coupling topology. Under this transformation, the coupling strength at which the onset of chaos is observed is invariant. The developed framework also allows us to compare information transfer in feedforward versus recurrent networks.
We find that distinct laws govern the propagation of phase-locked spike-time information, indicating a qualitative difference between classical artificial vs. biological computation.

Abstract

Phase- and frequency-locking phenomena among coupled biological oscillators are a topic of current interest, in particular to neuroscience. In the case of mono-directionally pulse-coupled oscillators, phase-locking is well understood, where the phenomenon is globally described by Arnold tongues.
Here, we develop the tools that allow corresponding investigations to be made for more general pulse-coupled networks. For two bi-directionally coupled oscillators, we prove the existence of three-dimensional Arnold tongues that mediate from the mono- to the bi-directional coupling topology. Under this transformation, the coupling strength at which the onset of chaos is observed is invariant. The developed framework also allows us to compare information transfer in feedforward versus recurrent networks.
We find that distinct laws govern the propagation of phase-locked spike-time information, indicating a qualitative difference between classical artificial vs. biological computation.

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Citations

5 citations in Web of Science®
5 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Neuroinformatics
Dewey Decimal Classification:570 Life sciences; biology
Language:English
Date:2008
Deposited On:08 Mar 2009 19:45
Last Modified:05 Apr 2016 13:10
Publisher:American Institute of Mathematical Sciences
ISSN:1531-3492
Related URLs:http://www.aimsciences.org/journals/dcdsB/index.htm (Publisher)

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