Steady-versus-Transient Plot for Analysis of Digital Maps

Hiroki YAMAOKA; Toshimichi SAITO

doi:10.1587/transfun.E99.A.1806

Steady-versus-Transient Plot for Analysis of Digital Maps

Hiroki YAMAOKA, Toshimichi SAITO

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A digital map is a simple dynamical system that is related to various digital dynamical systems including cellular automata, dynamic binary neural networks, and digital spiking neurons. Depending on parameters and initial condition, the map can exhibit various periodic orbits and transient phenomena to them. In order to analyze the dynamics, we present two simple feature quantities. The first and second quantities characterize the plentifulness of the periodic phenomena and the deviation of the transient phenomena, respectively. Using the two feature quantities, we construct the steady-versus-transient plot that is useful in the visualization and consideration of various digital dynamical systems. As a first step, we demonstrate analysis results for an example of the digital maps based on analog bifurcating neuron models.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.10 pp.1806-1812

Publication Date: 2016/10/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E99.A.1806

Type of Manuscript: PAPER

Category: Nonlinear Problems

Authors

Hiroki YAMAOKA
Hosei University
Toshimichi SAITO
Hosei University

Keyword

digital dynamical systems, digital spiking neurons, cellular automata, binary neural networks, chaos

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Hiroki YAMAOKA, Toshimichi SAITO, "Steady-versus-Transient Plot for Analysis of Digital Maps" in IEICE TRANSACTIONS on Fundamentals, vol. E99-A, no. 10, pp. 1806-1812, October 2016, doi: 10.1587/transfun.E99.A.1806.
Abstract: A digital map is a simple dynamical system that is related to various digital dynamical systems including cellular automata, dynamic binary neural networks, and digital spiking neurons. Depending on parameters and initial condition, the map can exhibit various periodic orbits and transient phenomena to them. In order to analyze the dynamics, we present two simple feature quantities. The first and second quantities characterize the plentifulness of the periodic phenomena and the deviation of the transient phenomena, respectively. Using the two feature quantities, we construct the steady-versus-transient plot that is useful in the visualization and consideration of various digital dynamical systems. As a first step, we demonstrate analysis results for an example of the digital maps based on analog bifurcating neuron models.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1806/_p

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@ARTICLE{e99-a_10_1806,
author={Hiroki YAMAOKA, Toshimichi SAITO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Steady-versus-Transient Plot for Analysis of Digital Maps},
year={2016},
volume={E99-A},
number={10},
pages={1806-1812},
abstract={A digital map is a simple dynamical system that is related to various digital dynamical systems including cellular automata, dynamic binary neural networks, and digital spiking neurons. Depending on parameters and initial condition, the map can exhibit various periodic orbits and transient phenomena to them. In order to analyze the dynamics, we present two simple feature quantities. The first and second quantities characterize the plentifulness of the periodic phenomena and the deviation of the transient phenomena, respectively. Using the two feature quantities, we construct the steady-versus-transient plot that is useful in the visualization and consideration of various digital dynamical systems. As a first step, we demonstrate analysis results for an example of the digital maps based on analog bifurcating neuron models.},
keywords={},
doi={10.1587/transfun.E99.A.1806},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - Steady-versus-Transient Plot for Analysis of Digital Maps
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1806
EP - 1812
AU - Hiroki YAMAOKA
AU - Toshimichi SAITO
PY - 2016
DO - 10.1587/transfun.E99.A.1806
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2016
AB - A digital map is a simple dynamical system that is related to various digital dynamical systems including cellular automata, dynamic binary neural networks, and digital spiking neurons. Depending on parameters and initial condition, the map can exhibit various periodic orbits and transient phenomena to them. In order to analyze the dynamics, we present two simple feature quantities. The first and second quantities characterize the plentifulness of the periodic phenomena and the deviation of the transient phenomena, respectively. Using the two feature quantities, we construct the steady-versus-transient plot that is useful in the visualization and consideration of various digital dynamical systems. As a first step, we demonstrate analysis results for an example of the digital maps based on analog bifurcating neuron models.
ER -