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Approximate Synchronization by a Single Inhibitory Pulse

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An Introduction to Modeling Neuronal Dynamics

Part of the book series: Texts in Applied Mathematics ((TAM,volume 66))

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Abstract

A simple way of synchronizing a population of neurons is to subject all neurons to the same inhibitory synaptic input pulse.

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Notes

  1. 1.

    The stable river is a well-defined trajectory of the system (29.12),(29.13): It is the only solution of (29.12), (29.13) with θ(t) ∈ (−π, π) for all t, θ(t) → −π∕2 as t → −∞. By contrast, the “unstable river” is not a well-defined trajectory here.

  2. 2.

    I certainly hope it doesn’t, since we omitted this term in [11]. We did include it in the later paper [12].

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Authors and Affiliations

  1. Department of Mathematics, Tufts University, Medford, MA, USA

    Christoph Börgers

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  1. Christoph Börgers
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Börgers, C. (2017). Approximate Synchronization by a Single Inhibitory Pulse. In: An Introduction to Modeling Neuronal Dynamics. Texts in Applied Mathematics, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-319-51171-9_29

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