PMID: 15244537Jul 13, 2004Paper

Analytical results for fundamental time-delayed feedback systems subjected to multiplicative noise

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
T D Frank

Abstract

We study the stochastic behavior of fundamental time-delayed feedback systems subjected to multiplicative noise. We derive exact results for the first and second moments and the autocorrelation function. For a particular class of systems we show how the variance depends on the amplitude of the multiplicative noise. Furthermore, we identify parameter regions of stationary solutions with finite and infinite variances. Finally, we suggest that delay-induced Lévy flights may occur in time-delayed feedback systems involving multiplicative noise.

References

Jul 15, 1977·Science·M C Mackey, L Glass
Dec 7, 1993·Journal of Theoretical Biology·K Vasilakos, A Beuter
Sep 2, 1998·Nature·C M Harris, D M Wolpert
Jun 15, 1990·Physical Review. a·A LongtinM C Mackey
Jun 15, 1991·Physical Review. a·H SompolinskyD Kleinfeld
Oct 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M C Mackey, I G Nechaeva
Sep 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·P TassH Hefter
Dec 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C W Eurich, J G Milton
Oct 17, 1994·Physical Review Letters·I FischerE Göbel
Nov 6, 1995·Physical Review Letters·N KhrustovaR Imbihl
Dec 18, 1995·Physical Review Letters·E Villermaux
Jan 22, 1996·Physical Review Letters·J FossJ Milton
Mar 4, 2000·Mathematical Biosciences·P W NelsonA S Perelson
May 10, 2000·Biological cybernetics·R J Peterka
Oct 14, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S GuillouzicA Longtin
Jan 4, 2001·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·V K Jirsa, J A Kelso
Aug 11, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T D Frank, P J Beek
Jan 22, 2002·Physical Review Letters·C Masoller
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C SimmendingerA Pelster
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T D Frank
Oct 9, 2002·Physical Review Letters·Juan L Cabrera, John G Milton
Jun 6, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Michael Schanz, Axel Pelster
Jun 7, 2003·Network : Computation in Neural Systems·Axel HuttThomas Wennekers
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T D FrankR Friedrich
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D GoldobinA Pikovsky

❮ Previous
Next ❯

Citations

May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T D Frank
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T D Frank
Apr 12, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·K PatanarapeelertI M Tang
Feb 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T D FrankP J Beek
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ihor LubashevskyAndreas Heuer
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Thomas JünglingWolfgang Kinzel
Jan 20, 2018·Physical Review. E·Sarah A M Loos, Sabine H L Klapp
Mar 5, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Denis S Goldobin
Nov 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ihor LubashevskyAndreas Heuer

❮ 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

Physical Review Letters
Aleksander Weron, Marcin Magdziarz
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Aleksei V ChechkinRalf Metzler
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Tomasz Srokowski
© 2022 Meta ULC. All rights reserved