论文研究 - 双稳态螺旋波：阶梯式螺旋波
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Open Access Library Journal
2017, Volume 4, e3982
ISSN Online: 2333-9721
ISSN Print: 2333-9705
DOI:
10.4236/oalib.1103982 Nov. 22, 2017 1 Open Access Library Journal
Bi-Stable Spiral Waves: Stepped Spiral Waves
Jian Gao
*
, Qun Wang, Huaping Lv
School of Physics and Electronic Engineering, Jiangsu Normal University, Xuzhou, China
Abstract
A new type of bi-stable spiral waves called “stepped spiral waves”, is invest
i-
gated in this study in an oscillatory medium exhibiting period-doubling b
i-
furcations. Prior to the period-
doubling bifurcation of this system, the stepped
spiral waves are produced by an unwanted phase trajectory event; the loss of
symmetry takes the form of synchronization defect lines, where the trajectory
in the local oscillation phase space changes into two different ways. The fo
r-
mation principle of this type of bi-
stable spiral wave and the internal structure
and geometry of these synchronization defects are studied, and several pote
n-
tial categories of stepped spiral waves are discussed.
Subject Areas
Internal Medicine, Molecular Biology
Keywords
Renin, Aldosterone, Metabolic Syndrome, Ischaemic Stroke
1. Introduction
Spatiotemporal pattern formation in reaction-diffusion (RD) systems is an un-
derlying mechanism responsible for complex biological patterns [1] [2] [3] [4]
[5]. Spiral waves are typical patterns in RD systems [6]-[11] which have been
observed throughout such diverse systems as chemical reactions [12] [13] [14]
[15], fluid convection [16] [17], microorganism populations [18],
Xenopus laevis
oocytes [19], cardiac muscle [20] [21], chicken retinae [22], and model RD sys-
tems [23] [24] [25] [26] [27]. They have been extensively studied both experi-
mentally and theoretically.
A spatially distributed oscillatory medium may undergo bifurcations when the
period of the orbit doubles at every point in the system. Prior to the occurrences
of these period-doubling bifurcations, the system may support stable rotationally
How to cite this paper:
Gao, J., Wang, Q
.
and
Lv, H.P. (2017) Bi-
Stable Spiral Waves:
Stepped Spiral Waves
.
Open Access Library
Journal
,
4
: e3982.
https:
//doi.org/10.4236/oalib.1103982
Received:
September 17, 2017
Accepted:
November 19, 2017
Published:
November 22, 2017
Copyright © 201
7 by authors and Open
Access Library Inc
.
This work is licensed under the Creative
Commons Attribution International
License (CC BY
4.0).
http://creativecommons.org/licenses/by/4.0/
Open Access
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