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

Hiroyuki TORIKAI; Toshimichi SAITO

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

Hiroyuki TORIKAI, Toshimichi SAITO

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E82-A No.7 pp.1336-1343

Publication Date: 1999/07/25

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Type of Manuscript: PAPER

Category: Nonlinear Problems

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Hiroyuki TORIKAI, Toshimichi SAITO, "Return Map Quantization from an Integrate-and-Fire Model with Two Periodic Inputs" in IEICE TRANSACTIONS on Fundamentals, vol. E82-A, no. 7, pp. 1336-1343, July 1999, doi: .
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_7_1336/_p

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@ARTICLE{e82-a_7_1336,
author={Hiroyuki TORIKAI, Toshimichi SAITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Return Map Quantization from an Integrate-and-Fire Model with Two Periodic Inputs},
year={1999},
volume={E82-A},
number={7},
pages={1336-1343},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={July},}

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TY - JOUR
TI - Return Map Quantization from an Integrate-and-Fire Model with Two Periodic Inputs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1336
EP - 1343
AU - Hiroyuki TORIKAI
AU - Toshimichi SAITO
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 1999
AB - 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.
ER -