Synchronous slowing down in coupled logistic maps via random network topology

The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down o...

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Main Authors:	Wang, Sheng-Jun, Du, Ru-Hai, Jin, Tao, Wu, Xing-Sen, Qu, Shi-Xian
Format:	Online
Language:	English
Published:	Nature Publishing Group 2016
Online Access:	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4810433/

id	pubmed-4810433
recordtype	oai_dc
spelling	pubmed-48104332016-04-04 Synchronous slowing down in coupled logistic maps via random network topology Wang, Sheng-Jun Du, Ru-Hai Jin, Tao Wu, Xing-Sen Qu, Shi-Xian Article The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down of synchronization process is observed, which is a novel phenomenon. The result shows that there are two typical kinds of transient process before the system reaches complete synchronization, which is demonstrated by both the coupled multiple-period maps and the coupled multiple-band chaotic maps. When the coupling is weak, the evolution of the system is governed mainly by the local dynamic, i.e., the node states are attracted by the stable orbits or chaotic attractors of the single map and evolve toward the synchronized orbit in a less coherent way. When the coupling is strong, the node states evolve in a high coherent way toward the stable orbit on the synchronized manifold, where the collective dynamics dominates the evolution. In a mediate coupling strength, the interplay between the two paths is responsible for the slowing down. The existence of different synchronization paths is also proven by the finite-time Lyapunov exponent and its distribution. Nature Publishing Group 2016-03-29 /pmc/articles/PMC4810433/ /pubmed/27021897 http://dx.doi.org/10.1038/srep23448 Text en Copyright © 2016, Macmillan Publishers Limited http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
repository_type	Open Access Journal
institution_category	Foreign Institution
institution	US National Center for Biotechnology Information
building	NCBI PubMed
collection	Online Access
language	English
format	Online
author	Wang, Sheng-Jun Du, Ru-Hai Jin, Tao Wu, Xing-Sen Qu, Shi-Xian
spellingShingle	Wang, Sheng-Jun Du, Ru-Hai Jin, Tao Wu, Xing-Sen Qu, Shi-Xian Synchronous slowing down in coupled logistic maps via random network topology
author_facet	Wang, Sheng-Jun Du, Ru-Hai Jin, Tao Wu, Xing-Sen Qu, Shi-Xian
author_sort	Wang, Sheng-Jun
title	Synchronous slowing down in coupled logistic maps via random network topology
title_short	Synchronous slowing down in coupled logistic maps via random network topology
title_full	Synchronous slowing down in coupled logistic maps via random network topology
title_fullStr	Synchronous slowing down in coupled logistic maps via random network topology
title_full_unstemmed	Synchronous slowing down in coupled logistic maps via random network topology
title_sort	synchronous slowing down in coupled logistic maps via random network topology
description	The speed and paths of synchronization play a key role in the function of a system, which has not received enough attention up to now. In this work, we study the synchronization process of coupled logistic maps that reveals the common features of low-dimensional dissipative systems. A slowing down of synchronization process is observed, which is a novel phenomenon. The result shows that there are two typical kinds of transient process before the system reaches complete synchronization, which is demonstrated by both the coupled multiple-period maps and the coupled multiple-band chaotic maps. When the coupling is weak, the evolution of the system is governed mainly by the local dynamic, i.e., the node states are attracted by the stable orbits or chaotic attractors of the single map and evolve toward the synchronized orbit in a less coherent way. When the coupling is strong, the node states evolve in a high coherent way toward the stable orbit on the synchronized manifold, where the collective dynamics dominates the evolution. In a mediate coupling strength, the interplay between the two paths is responsible for the slowing down. The existence of different synchronization paths is also proven by the finite-time Lyapunov exponent and its distribution.
publisher	Nature Publishing Group
publishDate	2016
url	https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4810433/
_version_	1613558710699819008

Synchronous slowing down in coupled logistic maps via random network topology

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