Patterns of Synchrony in Coupled Cell Networks with Multiple Arrows

动力系统理论 等价类(音乐) 等价关系 数学 多稳态 Lift(数据挖掘) 拓扑(电路) 计算机科学 纯数学 非线性系统 物理 组合数学 量子力学 数据挖掘
作者
Martin Golubitsky,Ian Stewart,Andrei Török
出处
期刊:Siam Journal on Applied Dynamical Systems [Society for Industrial and Applied Mathematics]
卷期号:4 (1): 78-100 被引量:264
标识
DOI:10.1137/040612634
摘要

A coupled cell system is a network of dynamical systems, or "cells," coupled together. The architecture of a coupled cell network is a graph that indicates how cells are coupled and which cells are equivalent. Stewart, Golubitsky, and Pivato presented a framework for coupled cell systems that permits a classification of robust synchrony in terms of network architecture. They also studied the existence of other robust dynamical patterns using a concept of quotient network. There are two difficulties with their approach. First, there are examples of networks with robust patterns of synchrony that are not included in their class of networks; and second, vector fields on the quotient do not in general lift to vector fields on the original network, thus complicating genericity arguments. We enlarge the class of coupled systems under consideration by allowing two cells to be coupled in more than one way, and we show that this approach resolves both difficulties. The theory that we develop, the "multiarrow formalism," parallels that of Stewart, Golubitsky, and Pivato. In addition, we prove that the pattern of synchrony generated by a hyperbolic equilibrium is rigid (the pattern does not change under small admissible perturbations) if and only if the pattern corresponds to a balanced equivalence relation. Finally, we use quotient networks to discuss Hopf bifurcation in homogeneous cell systems with two-color balanced equivalence relations.
最长约 10秒,即可获得该文献文件

科研通智能强力驱动
Strongly Powered by AbleSci AI
更新
PDF的下载单位、IP信息已删除 (2025-6-4)

科研通是完全免费的文献互助平台,具备全网最快的应助速度,最高的求助完成率。 对每一个文献求助,科研通都将尽心尽力,给求助人一个满意的交代。
实时播报
风中无血发布了新的文献求助10
3秒前
昏睡的绍辉完成签到,获得积分10
5秒前
6秒前
搜集达人应助daxiong采纳,获得10
9秒前
量子星尘发布了新的文献求助10
10秒前
10秒前
乐乐应助哼哼唧唧采纳,获得10
12秒前
风中无血完成签到,获得积分10
13秒前
zeng发布了新的文献求助10
20秒前
22秒前
苏航完成签到,获得积分20
22秒前
24秒前
FashionBoy应助伪装的鱼采纳,获得10
24秒前
24秒前
daxiong发布了新的文献求助10
26秒前
阿Q完成签到,获得积分10
26秒前
28秒前
28秒前
nczpf2010发布了新的文献求助10
29秒前
yufanhui应助包容剑鬼采纳,获得10
31秒前
肉肉发布了新的文献求助20
31秒前
Li完成签到 ,获得积分10
32秒前
33秒前
乔乔兔发布了新的文献求助10
33秒前
哼哼唧唧发布了新的文献求助10
34秒前
Hello应助田田采纳,获得10
35秒前
喜悦松完成签到,获得积分10
36秒前
完美世界应助伪装的鱼采纳,获得10
36秒前
调皮初蝶发布了新的文献求助10
37秒前
38秒前
beituo完成签到,获得积分10
38秒前
38秒前
bkagyin应助从容的戎采纳,获得10
39秒前
轻松的亦寒应助辻辰采纳,获得20
40秒前
41秒前
一颗大树完成签到,获得积分10
41秒前
万能图书馆应助Clr采纳,获得30
41秒前
ff发布了新的文献求助10
44秒前
45秒前
高大鸭子完成签到 ,获得积分10
45秒前
高分求助中
A new approach to the extrapolation of accelerated life test data 1000
Picture Books with Same-sex Parented Families: Unintentional Censorship 700
ACSM’s Guidelines for Exercise Testing and Prescription, 12th edition 500
Nucleophilic substitution in azasydnone-modified dinitroanisoles 500
不知道标题是什么 500
Indomethacinのヒトにおける経皮吸収 400
Phylogenetic study of the order Polydesmida (Myriapoda: Diplopoda) 370
热门求助领域 (近24小时)
化学 材料科学 医学 生物 工程类 有机化学 生物化学 物理 内科学 纳米技术 计算机科学 化学工程 复合材料 遗传学 基因 物理化学 催化作用 冶金 细胞生物学 免疫学
热门帖子
关注 科研通微信公众号,转发送积分 3975378
求助须知:如何正确求助?哪些是违规求助? 3519775
关于积分的说明 11199621
捐赠科研通 3256067
什么是DOI,文献DOI怎么找? 1798124
邀请新用户注册赠送积分活动 877386
科研通“疑难数据库(出版商)”最低求助积分说明 806305