Heterogeneously coupled maps: hub dynamics and emergence across connectivity layers
File(s)
Accepted version
OA Location
Author(s)
van Strien, Sebastian
Pereira, Tiago
Tanzi, Matteo
Type
Journal Article
Abstract
The aim of this paper is to rigorously study the dynamics of Heterogeneously Coupled Maps (HCM). Such systems are determined by a network with heterogeneous degrees. Some nodes, called hubs, are very well connected while most nodes interact with few others. The local dynamics on each node is chaotic, coupled with other nodes according to the network structure. Such high-dimensional systems are hard to understand in full, nevertheless we are able to describe the system over exponentially large time scales. In particular, we show that the dynamics of hub nodes can be very well approximated by a low-dimensional system. This allows us to establish the emergence of macroscopic behaviour such as coherence of dynamics among hubs of the same connectivity layer (i.e. with the same number of connections), and chaotic behaviour of the poorly connected nodes. The HCM we study provide a paradigm to explain why and how the dynamics of the network can change across layers.
Date Issued
2020-04-02
Date Acceptance
2017-11-27
Citation
Journal of the European Mathematical Society, 2020, 22 (7), pp.2183-2252
ISSN
1435-9855
Publisher
European Mathematical Society
Start Page
2183
End Page
2252
Journal / Book Title
Journal of the European Mathematical Society
Volume
22
Issue
7
Copyright Statement
© 2020 EMS Publishing House. All rights reserved.
Sponsor
Commission of the European Communities
Identifier
https://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=22&iss=7&rank=3
Grant Number
339523
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
Coupled maps
ergodic theory
heterogeneous networks
SYNCHRONIZATION
NETWORKS
CHAOS
HYPERBOLICITY
EIGENVALUES
SPECTRUM
LATTICES
DENSITY
math.DS
math.DS
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2020-04-02