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Synchrony in Networks of Neuronal Oscillators

  • Conference paper
Multiple-Time-Scale Dynamical Systems

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 122))

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Abstract

We review numerous recent results in which geometric singular perturbation methods have been used to analyze the population rhythms of neuronal networks. The neurons are modeled as relaxation oscillators and the coupling between neurons is modeled in a way that is motivated by properties of chemical synapses. The results give conditions for when excitatory or inhibitory synaptic coupling leads to either synchronized or desynchronized rhythms. Applications to models for sleep rhythms, image segmentation and wave propagation in inhibitory networks are also discussed.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, Ohio, 43210, USA

    D. Terman

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  1. D. Terman
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Editor information

Editors and Affiliations

  1. Division of Applied Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, RI, 02912, USA

    Christopher K. R. T. Jones

  2. United Technologies Research Center, East Hartford, CT, 06108, USA

    Alexander I. Khibnik

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© 2001 Springer Science+Business Media New York

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Terman, D. (2001). Synchrony in Networks of Neuronal Oscillators. In: Jones, C.K.R.T., Khibnik, A.I. (eds) Multiple-Time-Scale Dynamical Systems. The IMA Volumes in Mathematics and its Applications, vol 122. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0117-2_8

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  • DOI: https://doi.org/10.1007/978-1-4613-0117-2_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6529-0

  • Online ISBN: 978-1-4613-0117-2

  • eBook Packages: Springer Book Archive

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