Bifurcation analysis of a general class of non-linear integrate and fire neurons. - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Reports (Research Report) Year : 2008

Bifurcation analysis of a general class of non-linear integrate and fire neurons.

Jonathan Touboul
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Abstract

In this paper we define a class of formal neuron models being computationally efficient and biologically plausible, i.e. able to reproduce a wide gamut of behaviors observed in in-vivo or in-vitro recordings of cortical neurons. This class includes for instance two models widely used in computational neuroscience, the Izhikevich and the Brette--Gerstner models. These models consist in a 4-parameters dynamical system. We provide the full local bifurcations diagram of the members of this class, and show that they all present the same bifurcations: an Andronov-Hopf bifurcation manifold, a saddle-node bifurcation manifold, a Bogdanov-Takens bifurcation, and possibly a Bautin bifurcation. Among other global bifurcations, this system shows a saddle homoclinic bifurcation curve. We show how this bifurcation diagram generates the most prominent cortical neuron behaviors. This study leads us to introduce a new neuron model, the \emph{quartic model}, able to reproduce among all the behaviors of the Izhikevich and Brette--Gerstner models, self-sustained subthreshold oscillations, which are of great interest in neuroscience.
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Dates and versions

inria-00142987 , version 1 (23-04-2007)
inria-00142987 , version 2 (24-04-2007)
inria-00142987 , version 3 (21-02-2008)
inria-00142987 , version 4 (04-03-2008)
inria-00142987 , version 5 (12-03-2008)

Identifiers

  • HAL Id : inria-00142987 , version 5

Cite

Jonathan Touboul. Bifurcation analysis of a general class of non-linear integrate and fire neurons.. [Research Report] RR-6161, INRIA. 2008, pp.47. ⟨inria-00142987v5⟩
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