An approach to chaotic synchronization

Chaos
Alexander E Hramov, Alexey A Koronovskii

Abstract

This paper deals with the chaotic oscillator synchronization. An approach to the synchronization of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization, and generalized synchronization are the particular cases of the synchronized behavior called "time-scale synchronization." The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled Rössler systems and two coupled Chua's circuits.

References

Aug 15, 1991·Physical Review. a·L M Pecora, T L Carroll
Sep 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·K Murali, M Lakshmanan
Jun 1, 1994·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·K Murali, M Lakshmanan
Feb 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·N F RulkovH D Abarbanel
Oct 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·L M PecoraJ F Heagy
May 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·H D AbarbanelM M Sushchik
Aug 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·U ParlitzLjupco Kocarev
Nov 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Kestutis Pyragas
Feb 19, 1990·Physical Review Letters·L M Pecora, T L Carroll
Mar 11, 1996·Physical Review Letters·M G RosenblumJ Kurths
Sep 27, 2000·Physical Review Letters·C M TicosM Monti
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Stefano BoccalettiH Mancini
Dec 2, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Stefano Boccaletti, D L Valladares
Jan 4, 2001·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·Z Zheng, G Hu
Feb 15, 2001·Physical Review Letters·E AllariaR Meucci
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Stefano BoccalettiA Pelaez
Jul 20, 2001·Physical Review Letters·D J DeShazerR Roy
Oct 12, 2001·Journal of Neuroscience Methods·Michel Le Van QuyenFrancisco Varela
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Taherion, Y C Lai
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Quian QuirogaP Grassberger
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N F Rulkov
Aug 7, 2002·Neurophysiologie clinique = Clinical neurophysiology·Jean-Philippe LachauxFrancisco Varela
Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·O V SosnovtsevaN-H Holstein-Rathlou
Jun 5, 2003·Chaos·Reggie Brown, Ljupco Kocarev
Dec 20, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·M D ProkhorovA B Bespyatov

Citations

Dec 3, 2008·Chaos·He Huang, Gang Feng
Apr 20, 2005·Chaos·Alexander E HramovIrene S Rempen
Jul 8, 2008·Chaos·Anastasiya E FilatovaStefano Boccaletti
Oct 5, 2013·Chaos·Alexander E HramovM D Prokhorov
May 12, 2012·Computational and Mathematical Methods in Medicine·Junfeng SunShanbao Tong
Jun 6, 2012·IEEE Transactions on Bio-medical Engineering· Junfeng Sun Shanbao Tong
Jan 20, 2018·Physical Review. E·Alexey A KoronovskiiStefano Boccaletti
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander E HramovPavel V Popov
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander E HramovM D Prokhorov
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Weihua Deng
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander E HramovM D Prokhorov
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D V Senthilkumar, M Lakshmanan
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yao-Chen HungChin-Kun Hu
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander E HramovPavel V Popov
Jun 4, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Junfeng SunMichael Small
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander E HramovMaria K Kurovskaya
Aug 8, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ioan GrosuSyamal K Dana
Aug 17, 2020·Physical Review. E·Alexey A KoronovskiiAlexander N Pisarchik
Jan 4, 2017·Chaos·Wady A Rios HerreraMarkus F Müller
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Maxim O ZhuravlevAlexander E Hramov
Aug 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Olga I MoskalenkoAlexander E Hramov
Jan 1, 2021·Chaos·Tommaso AlbertiVirgilio Quattrociocchi

Related Concepts

Oscillometry
Physics
Systems Theory
Two-Parameter Models
Chaos Theory

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.

Neural Activity: Imaging

Imaging of neural activity in vivo has developed rapidly recently with the advancement of fluorescence microscopy, including new applications using miniaturized microscopes (miniscopes). This feed follows the progress in this growing field.

The Tendon Seed Network

Tendons are rich in the extracellular matrix and are abundant throughout the body providing essential roles including structure and mobility. The transcriptome of tendons is being compiled to understand the micro-anatomical functioning of tendons. Discover the latest research pertaining to the Tendon Seed Network here.

Myocardial Stunning

Myocardial stunning is a mechanical dysfunction that persists after reperfusion of previously ischemic tissue in the absence of irreversible damage including myocardial necrosis. Here is the latest research.

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.

Incretins

Incretins are metabolic hormones that stimulate a decrease in glucose levels in the blood and they have been implicated in glycemic regulation in the remission phase of type 1 diabetes. Here is the latest research.

Chromatin Regulation and Circadian Clocks

The circadian clock plays an important role in regulating transcriptional dynamics through changes in chromatin folding and remodelling. Discover the latest research on Chromatin Regulation and Circadian Clocks here.

Long COVID-19

“Long Covid-19” describes illness in patients who are reporting long-lasting effects of the SARS-CoV-19 infection, often long after they have recovered from acute Covid-19. Ongoing health issues often reported include low exercise tolerance and breathing difficulties, chronic tiredness, and mental health problems such as post-traumatic stress disorder and depression. This feed follows the latest research into Long Covid.

Spatio-Temporal Regulation of DNA Repair

DNA repair is a complex process regulated by several different classes of enzymes, including ligases, endonucleases, and polymerases. This feed focuses on the spatial and temporal regulation that accompanies DNA damage signaling and repair enzymes and processes.

Related Papers

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Stefano Boccaletti, D L Valladares
Physical Review Letters
M G RosenblumJ Kurths
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
N F RulkovH D Abarbanel
Physical Review Letters
L M Pecora, T L Carroll
© 2021 Meta ULC. All rights reserved