Consistency properties of chaotic systems driven by time-delayed feedback

Physical Review. E
Thomas JünglingI Fischer

Abstract

Consistency refers to the property of an externally driven dynamical system to respond in similar ways to similar inputs. In a delay system, the delayed feedback can be considered as an external drive to the undelayed subsystem. We analyze the degree of consistency in a generic chaotic system with delayed feedback by means of the auxiliary system approach. In this scheme an identical copy of the nonlinear node is driven by exactly the same signal as the original, allowing us to verify complete consistency via complete synchronization. In the past, the phenomenon of synchronization in delay-coupled chaotic systems has been widely studied using correlation functions. Here, we analytically derive relationships between characteristic signatures of the correlation functions in such systems and unequivocally relate them to the degree of consistency. The analytical framework is illustrated and supported by numerical calculations of the logistic map with delayed feedback for different replica configurations. We further apply the formalism to time series from an experiment based on a semiconductor laser with a double fiber-optical feedback loop. The experiment constitutes a high-quality replica scheme for studying consistency of the del...Continue Reading

References

Apr 1, 1992·Physical Review. a·F T ArecchiR Meucci
Feb 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·N F RulkovH D Abarbanel
May 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·H D AbarbanelM M Sushchik
Feb 19, 1990·Physical Review Letters·L M Pecora, T L Carroll
Aug 22, 1994·Physical Review Letters·G GiacomelliF T Arecchi
Nov 13, 2003·Physical Review Letters·Atsushi UchidaRajarshi Roy
Apr 20, 2004·Physical Review Letters·Fatihcan M AtayAndreas Wende
Feb 9, 2005·Physical Review Letters·Atsushi UchidaRajarshi Roy
Jul 23, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Guy Van der SandeClaudio R Mirasso
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Atsushi UchidaRajarshi Roy
Sep 28, 2010·Physical Review Letters·Giovanni GiacomelliAntonio Politi
Dec 21, 2011·Physical Review Letters·Sven HeiligenthalWolfgang Kinzel
May 1, 2012·Physical Review Letters·Miguel C SorianoClaudio R Mirasso
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Johannes SchumacherGordon Pipa
Oct 4, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Olga I MoskalenkoStefano Boccaletti
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kazutaka Kanno, Atsushi Uchida
Jul 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Olga I MoskalenkoAlexander E Hramov
Aug 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sven HeiligenthalWolfgang Kinzel
Feb 4, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hideyuki KatoClaudio R Mirasso
Dec 11, 2014·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Xavier PorteIngo Fischer
Mar 25, 2015·Nature Communications·Michiel HermansPeter Bienstman
Apr 11, 2015·Physical Review Letters·Neus OliverIngo Fischer
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Thomas JünglingIngo Fischer
Nov 3, 2016·Chaos·Neus OliverIngo Fischer

❮ Previous
Next ❯

Citations

Mar 3, 2019·Chaos·Thomas LymburnThomas Jüngling
Oct 3, 2019·Chaos·Thomas LymburnThomas Jüngling
Feb 20, 2020·Physical Review. E·Thomas JünglingMichael Small
Apr 4, 2021·Chaos·Thomas LymburnThomas Jüngling

❮ 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.

Related Papers

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Kazutaka Kanno, Atsushi Uchida
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
J M González-Miranda
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
K HickeI Fischer
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Hideyuki KatoClaudio R Mirasso
© 2022 Meta ULC. All rights reserved