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Mode locking in a periodically forced resonate-and-fire neuron model

Azadeh Khajeh Alijani*

  • Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

  • *azadeh.khajeh-alijani@warwick.ac.uk
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Phys. Rev. E 80, 051922 – Published 25 November, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.051922

Abstract

The resonate-and-fire (RF) model is a spiking neuron model which from a dynamical systems perspective is a piecewise smooth system (impact oscillator). We analyze the response of the RF neuron oscillator to periodic stimuli by expressing the firing events in terms of an implicit one-dimensional time map. Based on such a firing map, we describe mode-locked solutions and their stability, leading to the so-called Arnol’d tongues. The boundaries of these tongues correspond to either local bifurcations of the firing time map or grazing bifurcations of the discontinuity of the flow. Despite the fact that the periodically driven RF system shows periodic firing, its behavior may become chaotic when the forcing frequency is near the resonant frequency. We compare these results to numerical simulations of the model undergoing sinusoidal forcing. Furthermore, upon varying a system parameter, the RF system can be reduced to the integrate-and-fire system and in this case we show the consistency of the results on mode-locked solutions.

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Phys. Rev. E 80, 051922– Published 25 November, 2009
  • Received 21 May 2009

© 2009 American Physical Society

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