PMID: 11308877Apr 20, 2001Paper

Periodically forced leaky integrate-and-fire model

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
K Pakdaman

Abstract

The discharge pattern of periodically forced leaky integrate-and-fire models is studied. While previous analyses have been mainly concerned with the response of this model to sinusoidal stimulation, our results hold for arbitrary periodic inputs. It is shown that, for any periodic input, the map representing the relation between input phases at consecutive discharge times can be restricted to a piecewise continuous, orientation preserving circle map. This implies that (i) the rotation number is well defined and independent of the initial condition, and (ii) in the same way as for sinusoidal forcing, other forms of periodic stimuli can evoke only one of four types of response, namely, phase locking, quasiperiodic discharges, nonchaotic aperiodic firing, and termination of the discharge after a finite number of firings.

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Citations

Nov 27, 2004·Journal of Mathematical Biology·Tomás Gedeon, Matt Holzer
Dec 15, 2004·Biological cybernetics·Bernhard JilgeMilan R Dimitrijevic
Oct 23, 2001·Neural Networks : the Official Journal of the International Neural Network Society·K PakdamaT Shimokawa
Jul 23, 2005·Chaos·V B KazantsevJ M Bilbault
May 13, 2005·IEEE Transactions on Bio-medical Engineering·Michael DenkerAllen I Selverston
Sep 27, 2005·Neural Networks : the Official Journal of the International Neural Network Society·Stéphane BinczakVladimir I Nekorkin
Feb 20, 2003·Neural Computation·Romain Brette, Emmanuel Guigon
Nov 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S CoombesG D Smith
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P H E Tiesinga
Mar 14, 2003·Journal of Neurophysiology·John D Hunter, John G Milton
Apr 28, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jan R Engelbrecht, Renato Mirollo

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