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The Role of Axonal Delay in the Synchronization of Networks of Coupled Cortical Oscillators

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Abstract

Coupled oscillator models use a single phase variable to approximate the voltage oscillation of each neuron during repetitivefiring where the behavior of the model depends on the connectivityand the interaction function chosen to describe the coupling. Weintroduce a network model consisting of a continuum of theseoscillators that includes the effects of spatially decaying coupling and axonal delay. We derive equations for determining the stability of solutions and analyze the network behavior for two different interaction functions. The first is a sine function, and the second is derived from a compartmental model of a pyramidal cell.In both cases, the system of coupled neural oscillators can undergo a bifurcation from synchronous oscillations to waves.The change in qualitative behavior is due to the axonal delay,which causes distant connections to encourage a phase shift between cells. We suggest that this mechanism could contribute to the behavior observed in several neurobiological systems.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    S.M. Crook

  2. Mathematical Research Branch, NIDDK, National Institutes of Health, Bethesda, MD, 20814, USA

    S.M. Crook

  3. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA, 15260, USA

    G.B. Ermentrout

  4. Division of Biology, Computation and Neural Systems Program, California Institute of Technology, Pasadena, CA, 91125, USA

    M.C. Vanier

  5. Division of Biology, California Institute of Technology, Pasadena, CA, 91125, USA

    J.M. Bower

Authors
  1. S.M. Crook
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  2. G.B. Ermentrout
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  3. M.C. Vanier
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  4. J.M. Bower
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Crook, S., Ermentrout, G., Vanier, M. et al. The Role of Axonal Delay in the Synchronization of Networks of Coupled Cortical Oscillators. J Comput Neurosci 4, 161–172 (1997). https://doi.org/10.1023/A:1008843412952

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  • DOI: https://doi.org/10.1023/A:1008843412952

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