title: THE HOPF BIFURCATION WITH BOUNDED NOISE.
abstract: 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.
authors.affiliation: Department of Mathematical, Information & Computer Sciences, Point Loma Nazarene University, 3900 Lomaland Drive, San Diego, CA 92106, USA.
authors.forename: Ryan T
authors.initials: RT
authors.lastname: Botts
authors.affiliation: KdV Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, Netherlands, and Department of Mathematics, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands.
authors.forename: Ale Jan
authors.initials: AJ
authors.lastname: Homburg
authors.affiliation: Department of Mathematics, Ohio University, 321 Morton Hall, OH 45701 Athens, USA.
authors.forename: Todd R
authors.initials: TR
authors.lastname: Young
keywords: Random dynamical system; minimal forward invariant set; random differential equation; stationary measure
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Mar;79(3 Pt 2):036209
references.pmid: 19392037
references.citation: Topol Methods Nonlinear Anal. 2010 Mar;35(1):77-98
references.pmid: 22211081