Sharp changes in fractal basin of attraction in passive dynamic walking

Okamoto, Kota; Akashi, Nozomi; Obayashi, Ippei et al.

Nonlinear Dynamics, 2023, 111(23), 21941-21955

Number of Access:783（2025-08-29 05:24 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/93366

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Title
Sharp changes in fractal basin of attraction in passive dynamic walking
Creator
CreatorName
Okamoto, Kota
CreatorName
Akashi, Nozomi
NRID
1000030583455 1000030583455
CreatorName
Obayashi, Ippei
NRID
1000010740251 1000010740251
CreatorName
Nakajima, Kohei
NRID
1000050202057 1000050202057
CreatorName
Kokubu, Hiroshi
NRID
1000060206662 1000060206662
CreatorName
Senda, Kei
NRID
1000070227429 1000070227429
CreatorName
Tsuchiya, Kazuo
NRID
1000060432366 1000060432366
researchmap permalink
shinya_aoi shinya_aoi
ORCID
0000-0001-9243-2641 0000-0001-9243-2641
Scopus Author ID
6604066318 6604066318
CreatorName
Aoi, Shinya
Subject
Basin of attraction
Disappearance
Fractality
Passive dynamic walking
Size
Description
The version of record of this article, first published in Nonlinear Dynamics, is available online at Publisher’s website: https://doi.org/10.1007/s11071-023-08913-w
Abstract
A passive dynamic walker is a mechanical system that walks down a slope without any control, and gives useful insights into the dynamic mechanism of stable walking. This system shows specific attractor characteristics depending on the slope angle due to nonlinear dynamics, such as period-doubling to chaos and its disappearance by a boundary crisis. However, it remains unclear what happens to the basin of attraction. In our previous studies, we showed that a fractal basin of attraction is generated using a simple model over a critical slope angle by iteratively applying the inverse image of the Poincaré map, which has stretching and bending effects. In the present study, we show that the size and fractality of the basin of attraction sharply change many times by changing the slope angle. Furthermore, we improved our previous analysis to clarify the mechanisms for these changes and the disappearance of the basin of attraction based on the stretching and bending deformation in the basin formation process. These findings will improve our understanding of the governing dynamics to generate the basin of attraction in walking.
Publisher
Springer Science and Business Media B.V.
Source Title
Nonlinear Dynamics
Volume (Issue)
111(23)
Page
21941-21955
Date of Issued
2023-11-22
Language
English
Handle URL
https://hdl.handle.net/11094/93366
PISSN
0924090X
eISSN
1573269X
Relation.isIdenticalTo
DOI (Publisher Version)
https://doi.org/10.1007/s11071-023-08913-w
Access Rights
open access
CopyRight
This article is licensed under a Creative Commons Attribution 4.0 International License.
oaire:version
Version of Record
Category
学術雑誌論文 Journal Article