Synchronization invariance under network structural transformations

Physical Review. E
Lluís Arola-FernándezAlex Arenas

Abstract

Synchronization processes are ubiquitous despite the many connectivity patterns that complex systems can show. Usually, the emergence of synchrony is a macroscopic observable; however, the microscopic details of the system, as, e.g., the underlying network of interactions, is many times partially or totally unknown. We already know that different interaction structures can give rise to a common functionality, understood as a common macroscopic observable. Building upon this fact, here we propose network transformations that keep the collective behavior of a large system of Kuramoto oscillators invariant. We derive a method based on information theory principles, that allows us to adjust the weights of the structural interactions to map random homogeneous in-degree networks into random heterogeneous networks and vice versa, keeping synchronization values invariant. The results of the proposed transformations reveal an interesting principle; heterogeneous networks can be mapped to homogeneous ones with local information, but the reverse process needs to exploit higher-order information. The formalism provides analytical insight to tackle real complex scenarios when dealing with uncertainty in the measurements of the underlying co...Continue Reading

References

Mar 22, 2001·Nature·S H Strogatz
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juyong Park, M E J Newman
Feb 9, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adilson E MotterJürgen Kurths
May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Juan G RestrepoBrian R Hunt
Feb 21, 2006·Physical Review Letters·Changsong ZhouJürgen Kurths
Apr 12, 2006·Physical Review Letters·Alex ArenasConrad J Pérez-Vicente
Jun 29, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jesús Gómez-Gardeñes, Yamir Moreno
Dec 13, 2006·Physical Review Letters·Dongchuan YuLjupco Kocarev
Mar 16, 2007·Physical Review Letters·Jesús Gómez-GardeñesAlex Arenas
Apr 25, 2007·Proceedings of the National Academy of Sciences of the United States of America·Martin Rosvall, Carl T Bergstrom
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G Korniss
Aug 7, 2007·Physical Review Letters·Marc Timme
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Domenico Napoletani, Timothy D Sauer
Sep 4, 2008·Physical Review Letters·Igor Belykh, Andrey Shilnikov
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kartik Anand, Ginestra Bianconi
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Baruch Barzel, Ofer Biham
May 22, 2010·Proceedings of the National Academy of Sciences of the United States of America·Takashi Nishikawa, Adilson E Motter
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andrea Baronchelli, Romualdo Pastor-Satorras
Mar 17, 2011·Physical Review Letters·Daniel B LarremoreJuan G Restrepo
Apr 27, 2011·Physical Review Letters·Jesús Gómez-GardeñesYamir Moreno
Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kartik AnandSimone Severini
Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Víctor M EguíluzAlex Arenas
May 17, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Luce Prignano, Albert Díaz-Guilera
Oct 18, 2014·Physical Review Letters·Per Sebastian SkardalJie Sun

❮ Previous
Next ❯

Citations

Nov 6, 2018·Scientific Reports·Giulia CencettiDuccio Fanelli
May 22, 2019·Physical Review. E·Huawei FanXingang Wang
Jul 10, 2021·Chaos·Lluís Arola-FernándezAlex Arenas

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.