NDLI: Feigenbaum Graphs: A Complex Network Perspective of Chaos

Content Provider	PubMed Central
Author	Luque, Bartolo Lacasa, Lucas Ballesteros, Fernando J. Robledo, Alberto
Editor	Moreno, Yamir
Copyright Year	2011
Abstract	The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.
Related Links	http://dx.doi.org/10.1371/journal.pone.0022411
Starting Page	22411
File Format	PDF
ISSN	19326203
e-ISSN	19326203
Journal	PLoS ONE
Issue Number	9
Volume Number	6
Language	English
Publisher	Public Library of Science
Publisher Date	2011-09-01
Access Restriction	Open
Rights Holder	Public Library of Science
Subject Keyword	Biochemistry, Genetics and Molecular Biology(all) Agricultural and Biological Sciences(all) Medicine(all) Research in Higher Education
Content Type	Text
Resource Type	Article
Subject	Multidisciplinary

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Does Human Migration Affect International Trade? A Complex-Network Perspective

A Complex Network Approach to Stylometry

Link Prediction in Complex Networks: A Mutual Information Perspective

Nonlinear Dynamics Analysis of a Self-Organizing Recurrent Neural Network: Chaos Waning

Feigenbaum graphs: a complex network perspective of chaos

A Complex Network Approach to Distributional Semantic Models

The Oral Tolerance as a Complex Network Phenomenon

Thermostability of In Vitro Evolved Bacillus subtilis Lipase A: A Network and Dynamics Perspective

Trade Integration and Trade Imbalances in the European Union: A Network Perspective

Feigenbaum Graphs: A Complex Network Perspective of Chaos

Similar Documents

Does Human Migration Affect International Trade? A Complex-Network Perspective

A Complex Network Approach to Stylometry

Link Prediction in Complex Networks: A Mutual Information Perspective

Nonlinear Dynamics Analysis of a Self-Organizing Recurrent Neural Network: Chaos Waning

Feigenbaum graphs: a complex network perspective of chaos

A Complex Network Approach to Distributional Semantic Models

The Oral Tolerance as a Complex Network Phenomenon

Thermostability of In Vitro Evolved Bacillus subtilis Lipase A: A Network and Dynamics Perspective

Trade Integration and Trade Imbalances in the European Union: A Network Perspective

Feigenbaum Graphs: A Complex Network Perspective of Chaos