Filter-Induced Bifurcation of Simple Spike-Train Dynamics
Summary :
This paper studies spike-train dynamics of the bifurcating neuron and its pulse-coupled system. The neuron has periodic base signal that is given by applying a periodic square wave to a basic low-pass filter. As key parameters of the filter vary, the systems can exhibit various bifurcation phenomena. For example, the neuron exhibits period-doubling bifurcation through which the period of spike-train is doubling. The coupled system exhibits two kinds of (smooth and non-smooth) tangent bifurcations that can induce “chaos + chaos = order”: chaotic spike-trains of two neurons are changed into periodic spike-train by the pulse-coupling. Using the mapping procedure, the bifurcation phenomena can be analyzed precisely. Presenting simple test circuits, typical phenomena are confirmed experimentally.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.7 pp.1508-1515
- Publication Date
- 2014/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.1508
- Type of Manuscript
- PAPER
- Category
- Nonlinear Problems
Authors
Shota KIRIKAWA
Hosei University
Toshimichi SAITO
Hosei University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Shota KIRIKAWA, Toshimichi SAITO, "Filter-Induced Bifurcation of Simple Spike-Train Dynamics" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 7, pp. 1508-1515, July 2014, doi: 10.1587/transfun.E97.A.1508.
Abstract: This paper studies spike-train dynamics of the bifurcating neuron and its pulse-coupled system. The neuron has periodic base signal that is given by applying a periodic square wave to a basic low-pass filter. As key parameters of the filter vary, the systems can exhibit various bifurcation phenomena. For example, the neuron exhibits period-doubling bifurcation through which the period of spike-train is doubling. The coupled system exhibits two kinds of (smooth and non-smooth) tangent bifurcations that can induce “chaos + chaos = order”: chaotic spike-trains of two neurons are changed into periodic spike-train by the pulse-coupling. Using the mapping procedure, the bifurcation phenomena can be analyzed precisely. Presenting simple test circuits, typical phenomena are confirmed experimentally.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.1508/_p
Copy
@ARTICLE{e97-a_7_1508,
author={Shota KIRIKAWA, Toshimichi SAITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Filter-Induced Bifurcation of Simple Spike-Train Dynamics},
year={2014},
volume={E97-A},
number={7},
pages={1508-1515},
abstract={This paper studies spike-train dynamics of the bifurcating neuron and its pulse-coupled system. The neuron has periodic base signal that is given by applying a periodic square wave to a basic low-pass filter. As key parameters of the filter vary, the systems can exhibit various bifurcation phenomena. For example, the neuron exhibits period-doubling bifurcation through which the period of spike-train is doubling. The coupled system exhibits two kinds of (smooth and non-smooth) tangent bifurcations that can induce “chaos + chaos = order”: chaotic spike-trains of two neurons are changed into periodic spike-train by the pulse-coupling. Using the mapping procedure, the bifurcation phenomena can be analyzed precisely. Presenting simple test circuits, typical phenomena are confirmed experimentally.},
keywords={},
doi={10.1587/transfun.E97.A.1508},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - Filter-Induced Bifurcation of Simple Spike-Train Dynamics
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1508
EP - 1515
AU - Shota KIRIKAWA
AU - Toshimichi SAITO
PY - 2014
DO - 10.1587/transfun.E97.A.1508
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2014
AB - This paper studies spike-train dynamics of the bifurcating neuron and its pulse-coupled system. The neuron has periodic base signal that is given by applying a periodic square wave to a basic low-pass filter. As key parameters of the filter vary, the systems can exhibit various bifurcation phenomena. For example, the neuron exhibits period-doubling bifurcation through which the period of spike-train is doubling. The coupled system exhibits two kinds of (smooth and non-smooth) tangent bifurcations that can induce “chaos + chaos = order”: chaotic spike-trains of two neurons are changed into periodic spike-train by the pulse-coupling. Using the mapping procedure, the bifurcation phenomena can be analyzed precisely. Presenting simple test circuits, typical phenomena are confirmed experimentally.
ER -
English
