THE HOPF BIFURCATION WITH BOUNDED NOISE

We study Hopf-Andronov bifurcations in a class of random differential equations (RDEs) with bounded noise. We observe that when an ordinary differential equation that undergoes a Hopf bifurcation is subjected to bounded noise then the bifurcation that occurs involves a discontinuous change in the Mi...

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Bibliographic Details
Published inDiscrete and continuous dynamical systems. Series A Vol. 32; no. 8; p. 2997
Main Authors Botts, Ryan T, Homburg, Ale Jan, Young, Todd R
Format Journal Article
LanguageEnglish
Published United States 01.08.2012
Subjects
Random dynamical system
minimal forward invariant set
stationary measure
random differential equation
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Summary:We study Hopf-Andronov bifurcations in a class of random differential equations (RDEs) with bounded noise. We observe that when an ordinary differential equation that undergoes a Hopf bifurcation is subjected to bounded noise then the bifurcation that occurs involves a discontinuous change in the Minimal Forward Invariant set.
ISSN:1078-0947
DOI:10.3934/dcds.2012.32.2997