Analytical determination of the bifurcation thresholds in stochastic differential equations with delayed feedback

Mathieu Gaudreault, François Drolet, Jorge Viñals

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average x (t)

Original languageEnglish (US)
Article number051124
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume82
Issue number5
DOIs
StatePublished - Nov 17 2010
Externally publishedYes

Fingerprint

Pitchfork Bifurcation
Delayed Feedback
Stochastic Equations
differential equations
time lag
Bifurcation
Stochastic Differential Delay Equations
Differential equation
thresholds
Line
Delay Time
Hopf Bifurcation
Time Scales

Cite this

Analytical determination of the bifurcation thresholds in stochastic differential equations with delayed feedback. / Gaudreault, Mathieu; Drolet, François; Viñals, Jorge.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 82, No. 5, 051124, 17.11.2010.

Research output: Contribution to journalArticle

@article{996c2630dfdd413297aa3668ca09e74d,
title = "Analytical determination of the bifurcation thresholds in stochastic differential equations with delayed feedback",
abstract = "Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average x (t)",
author = "Mathieu Gaudreault and Fran{\cc}ois Drolet and Jorge Vi{\~n}als",
year = "2010",
month = "11",
day = "17",
doi = "10.1103/PhysRevE.82.051124",
language = "English (US)",
volume = "82",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Analytical determination of the bifurcation thresholds in stochastic differential equations with delayed feedback

AU - Gaudreault, Mathieu

AU - Drolet, François

AU - Viñals, Jorge

PY - 2010/11/17

Y1 - 2010/11/17

N2 - Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average x (t)

AB - Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time τ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average x (t)

UR - http://www.scopus.com/inward/record.url?scp=78651348648&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651348648&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.82.051124

DO - 10.1103/PhysRevE.82.051124

M3 - Article

AN - SCOPUS:78651348648

VL - 82

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 5

M1 - 051124

ER -