A Simple Spiking Neuron with Periodic Input: Basic Bifurcation and Encoding Function

Authors:
Shimon Teshima;Toshimichi Saito
Affiliations:
Hosei University, Tokyo, Japan 184-8584;Hosei University, Tokyo, Japan 184-8584
Venue:
ICONIP '09 Proceedings of the 16th International Conference on Neural Information Processing: Part II
Year:
2009

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Abstract

This paper studies dynamics of a simple bifurcating neuron to which spike-train input is applied a refractory threshold. The neuron can exhibit rich periodic orbits that is super-stable for initial state and has very fast transient. The periodic orbits are characterized by the rotation number that relates to rate coding of the spike-train. The dynamics can be simplified into the 1-D map of spiking phase. The phase map is piecewise linear and basic bifurcation phenomena can be clarified theoretically.