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Approximations to the time evolution of an Izhikevich neuron

Author

Listed:
  • August Romeo

    (Department of Basic Psychology, Faculty of Psychology, University of Barcelona (UB), Pg. Vall d'Hebron 171, 08035 Barcelona, Spain)

  • Hans Supèr

    (Department of Basic Psychology, Faculty of Psychology, University of Barcelona (UB), Pg. Vall d'Hebron 171, 08035 Barcelona, Spain;
    Institute for Brain, Cognition and Behavior (IR3C), Barcelona, Spain;
    Catalan Institution for Research and Advanced Studies (ICREA), Barcelona, Spain)

Abstract

Possible ways of obtaining information about the solutions of Izhikevich's "simple model" for a spiking neuron are considered. The method of power series in time is reviewed. From a different viewpoint, in the case of constant input and weak recovery scale effects, advantage is taken of a small-parameter expansion. The obtained approximations can be expressed in terms of elementary functions.

Suggested Citation

  • August Romeo & Hans Supèr, 2014. "Approximations to the time evolution of an Izhikevich neuron," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(10), pages 1-16.
    • Handle: RePEc:wsi:ijmpcx:v:25:y:2014:i:10:n:s0129183114500521
    DOI: 10.1142/S0129183114500521
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