A Generalized PWC Spiking Neuron Model and Its Neuron-Like Activities and Burst-Related Bifurcations

Yutaro YAMASHITA  Hiroyuki TORIKAI 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E95-A  No.7  pp.1125-1135
Publication Date: 2012/07/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
Keyword: 
spiking neuron model,  bifurcation,  piece-wise constant vector field,  VLSI neuron, 

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Summary: 
A generalized version of a piece-wise constant (ab. PWC) spiking neuron model is presented. It is shown that the generalization enables the model to reproduce 20 activities in the Izhikevich model. Among the activities, we analyze tonic bursting. Using an analytical one-dimensional iterative map, it is shown that the model can reproduce a burst-related bifurcation scenario, which is qualitatively similar to that of the Izhikevich model. The bifurcation scenario can be observed in an actual hardware.