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The variance of phase-resetting curves

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Abstract

Phase resetting curves (PRCs) provide a measure of the sensitivity of oscillators to perturbations. In a noisy environment, these curves are themselves very noisy. Using perturbation theory, we compute the mean and the variance for PRCs for arbitrary limit cycle oscillators when the noise is small. Phase resetting curves and phase dependent variance are fit to experimental data and the variance is computed using an ad-hoc method. The theoretical curves of this phase dependent method match both simulations and experimental data significantly better than an ad-hoc method. A dual cell network simulation is compared to predictions using the analytical phase dependent variance estimation presented in this paper. We also discuss how entrainment of a neuron to a periodic pulse depends on the noise amplitude.

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Acknowledgements

We would like to acknowledge NSF, NSF CAREER Award, and University of Minnesota Grant-in-Aid.

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Authors and Affiliations

  1. Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvannia, USA

    G. Bard Ermentrout

  2. Department of Physics, University of Minnesota, Minneapolis, USA

    Bryce Beverlin II

  3. Department of Biology, University of Texas at San Antonio, San Antonio, Texas, USA

    Todd Troyer

  4. Department of Biomedical Engineering, University of Minnesota, Minneapolis, USA

    Theoden I. Netoff

Authors
  1. G. Bard Ermentrout
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  2. Bryce Beverlin II
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  3. Todd Troyer
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  4. Theoden I. Netoff
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Correspondence to Theoden I. Netoff.

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Action Editor: Charles Wilson

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Ermentrout, G.B., Beverlin, B., Troyer, T. et al. The variance of phase-resetting curves. J Comput Neurosci 31, 185–197 (2011). https://doi.org/10.1007/s10827-010-0305-9

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  • DOI: https://doi.org/10.1007/s10827-010-0305-9

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