Return Map Quantization from an Integrate-and-Fire Model with Two Periodic Inputs

Hiroyuki TORIKAI  Toshimichi SAITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.7   pp.1336-1343
Publication Date: 1999/07/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
Integrate-and-Fire Model,  return map,  chaos,  quantization,  computer aided analysis,  

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In this paper, we consider the Integrate-and-Fire Model (ab. IFM) with two periodic inputs. The IFM outputs a pulse-train which is governed by a one dimensional return map. Using the return map, the relationship between the inputs and the output is clarified: the first input determines the global shape of the return map and the IFM outputs various periodic and chaotic pulse-trains; the second input quantizes the state of the return map and the IFM outputs various periodic pulse-trains. Using a computer aided analysis method, the quantized return map can be analyzed rigorously. Also, some typical phenomena are confirmed in the laboratory.