Open AccessThe Hopf bifurcation with bounded noise
Author(s) -
Ryan T. Botts,
Ale Jan Homburg,
Todd Young
Publication year - 2012
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2012.32.2997
Subject(s) - bounded function , hopf bifurcation , mathematics , bifurcation , pitchfork bifurcation , saddle node bifurcation , transcritical bifurcation , mathematical analysis , physics , nonlinear system , quantum mechanics
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.
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