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A two-variable model of somatic-dendritic interactions in a bursting neuron

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Abstract

We present a two-variable delay-differential-equation model of a pyramidal cell from the electrosensory lateral line lobe of a weakly electric fish that is capable of burst discharge. It is a simplification of a six-dimensional ordinary differential equation model for such a cell whose bifurcation structure has been analyzed (Doiron et al., J. Comput. Neurosci., 12, 2002). We have modeled the effects of back-propagating action potentials by a delay, and use an integrate-and-fire mechanism for action potential generation. The simplicity of the model presented here allows one to explicitly derive a two-dimensional map for successive interspike intervals, and to analytically investigate the effects of time-dependent forcing on such a model neuron. Some of the effects discussed include ‘burst excitability’, the creation of resonance tongues under periodic forcing, and stochastic resonance. We also investigate the effects of changing the parameters of the model.

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Authors and Affiliations

  1. Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, ON, Canada, K1N 6N5

    Carlo R. Laing & André Longtin

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  1. Carlo R. Laing
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  2. André Longtin
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Correspondence to Carlo R. Laing.

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Laing, C.R., Longtin, A. A two-variable model of somatic-dendritic interactions in a bursting neuron. Bull. Math. Biol. 64, 829–860 (2002). https://doi.org/10.1006/bulm.2002.0303

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  • DOI: https://doi.org/10.1006/bulm.2002.0303

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