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Reports (Research Report) Year : 2008

Spiking dynamics of bidimensional integrate-and-fire neurons

Romain Brette
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The class of non-linear integrate and fire neuron models introduced in the previous chapter, containing such models as the Izhikevich and the Brette-Gerstner ones, are hybrid dynamical systems defined both by a continuous dynamics, the subthreshold behavior, and a discrete dynamics, the spike and reset process. The dynamical properties of the subthreshold system has studied in \cite{touboul:08b}. This previous study does not account for the spiking properties of the model. We study in this chapter the spike patterns produced by these models. These patterns of activity are the result of an interplay between the continuous subthreshold dynamics and the reset process. Interestingly, the reset induces in bidimensional models behaviors only observed in higher dimensional continuous systems such as bursting and chaos. This is why in the first section we study in depth the subthreshold dynamical system, and characterize its main dynamical properties, and a suitable framework in order to study the spike dynamics through the use of a discrete map, called the adaptation map. We then present how the spiking behavior of the model is linked with dynamical properties of the map, and show in particular that the system can exhibit a transition to chaos via period doubling, which was previously observed in Hodgkin-Huxley models and in Purkinje cells.
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Dates and versions

inria-00276924 , version 1 (03-05-2008)
inria-00276924 , version 2 (29-08-2008)
inria-00276924 , version 3 (08-09-2008)
inria-00276924 , version 4 (06-01-2009)
inria-00276924 , version 5 (11-06-2018)


  • HAL Id : inria-00276924 , version 3


Jonathan Touboul, Romain Brette. Spiking dynamics of bidimensional integrate-and-fire neurons. [Research Report] RR-6531, 2008. ⟨inria-00276924v3⟩


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