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

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Khajeh Alijani, Azadeh. (2009) Mode locking in a periodically forced resonate-and-fire neuron model. Physical Review E, Vol.80 (No.5). ISSN 1539-3755

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Official URL: http://dx.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.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Mathematics

Library of Congress Subject Headings (LCSH):

Neurons -- Mathematical models

Journal or Publication Title:

Physical Review E

Publisher:

American Physical Society

ISSN:

1539-3755

Official Date:

25 November 2009

Dates:

Date	Event
25 November 2009	Published

Volume:

Vol.80

Number:

No.5

Number of Pages:

Identification Number:

10.1103/PhysRevE.80.051922

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Funder:

University of Warwick

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