Investigating nonlinear dynamics from time series: The influence of symmetries and the choice of observables

Chaos
C Letellier, Luis A Aguirre

Abstract

When a dynamical system is investigated from a time series, one of the most challenging problems is to obtain a model that reproduces the underlying dynamics. Many papers have been devoted to this problem but very few have considered the influence of symmetries in the original system and the choice of the observable. Indeed, it is well known that there are usually some variables that provide a better representation of the underlying dynamics and, consequently, a global model can be obtained with less difficulties starting from such variables. This is connected to the problem of observing the dynamical system from a single time series. The roots of the nonequivalence between the dynamical variables will be investigated in a more systematic way using previously defined observability indices. It turns out that there are two important ingredients which are the complexity of the coupling between the dynamical variables and the symmetry properties of the original system. As will be mentioned, symmetries and the choice of observables also has important consequences in other problems such as synchronization of nonlinear oscillators. (c) 2002 American Institute of Physics.

References

May 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·H D Abarbanel, M B Kennel
Jun 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G Gouesbet, C Letellier
Mar 12, 1990·Physical Review Letters·E OttJ A Yorke
Feb 19, 1990·Physical Review Letters·L M Pecora, T L Carroll
Apr 17, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C Letellier, R Gilmore
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·L Le ScellerG Gouesbet

❮ Previous
Next ❯

Citations

Mar 7, 2007·Journal of Mathematical Biology·J MaquetLuis A Aguirre
Apr 25, 2012·Journal of the Association for Research in Otolaryngology : JARO·Stanley HuangElizabeth S Olson
Jan 22, 2013·Physica Medica : PM : an International Journal Devoted to the Applications of Physics to Medicine and Biology : Official Journal of the Italian Association of Biomedical Physics (AIFB)·Andrzej TukiendorfJacek Bojarski
Dec 17, 2002·Comptes rendus biologies·Christophe LetellierMichel Thellier
Apr 1, 2007·Journal of Biological Dynamics·W M Schaffer, T V Bronnikova
Jul 1, 2007·Journal of Biological Dynamics·W M Schaffer, T V Bronnikova
Dec 5, 2012·PLoS Computational Biology·Madineh Sedigh-SarvestaniBruce J Gluckman
Jul 2, 2009·Chaos·Christophe LetellierU S Freitas
Jun 11, 2004·Chaos·L M Hively, V A Protopopescu
Jan 16, 2013·Journal of Theoretical Biology·C LetellierL A Aguirre
May 29, 2015·Acta Biotheoretica·Jorge DuarteJosep Sardanyés
May 12, 2004·Journal of Theoretical Biology·Jean MaquetLuis A Aguirre
Jul 6, 2014·Journal of Theoretical Biology·Louise VigerChristophe Letellier
May 20, 2015·Chaos, Solitons, and Fractals·Claudia LainscsekChristophe Letellier
Mar 2, 2018·Scientific Reports·Christophe LetellierMurilo S Baptista
Oct 4, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Luis Antonio AguirreLeonardo Antônio B Tôrres
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christophe Letellier, Luis A Aguirre
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Everton G SouzaSérgio R Lopes
Aug 8, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christophe Letellier, Luis A Aguirre
Nov 1, 2018·PloS One·Luis A AguirreChristophe Letellier
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Arik Yochelis, Moshe Sheintuch
May 17, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christophe Letellier, Luis A Aguirre
Apr 15, 2016·Physical Review. E·Jiang Wang, Andrew L Ferguson
Nov 3, 2017·Chaos·Luis A AguirreChristophe Letellier
Sep 27, 2018·Physical Review. E·Christophe LetellierLuis A Aguirre
Jan 1, 2015·Physical Review. X·Andrew J WhalenSteven J Schiff
Jan 8, 2020·Communications Biology·Daniel TokerMark D'Esposito
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ezequiel Bianco-MartinezChristophe Letellier
Jan 3, 2019·Chaos·Sylvain MangiarottiChristophe Letellier
Apr 1, 2019·Chaos·Arthur N Montanari, Luis A Aguirre
Oct 3, 2019·Chaos·Anastasiya SalovaRaissa M D'Souza
Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Luis A Aguirre, Christophe Letellier
Jul 7, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dalila Amroun-AlianeChristophe Letellier
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christophe LetellierJean Maquet
Aug 16, 2006·Physical Review Letters·Christophe Letellier
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Luis Antonio Aguirre, Edgar Campos Furtado
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel J Cross, R Gilmore

❮ Previous
Next ❯

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.

Related Papers

Journal of Theoretical Biology
Jean MaquetLuis A Aguirre
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
C LetellierJean Maquet
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
C Letellier, Luis A Aguirre
© 2022 Meta ULC. All rights reserved