Article Contents

2012, Volume 32, Issue 8: 2997-3007. Doi: 10.3934/dcds.2012.32.2997

This issue Previous Article Stochastic phase dynamics of noise driven synchronization of two conditional coherent oscillators Next Article

The Hopf bifurcation with bounded noise

1.
Department of Mathematical, Information & Computer Sciences, Point Loma Nazarene University, 3900 Lomaland Drive, San Diego, CA 92106
2.
KdV Institute for Mathematics, University of Amsterdam, Science Park 904, 1098 XH, Amsterdam
3.
Department of Mathematics, Ohio University, 321 Morton Hall, OH 45701 Athens

Received: May 2011

Revised: July 2011

Published: August 2012

Abstract / Introduction Related Papers Cited by

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.

Keywords:

Mathematics Subject Classification: Primary: 37H20; Secondary: 37G10, 34F20.

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