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This article is cited in 11 scientific papers (total in 11 papers)
On the 70th birthday of L.P. Shilnikov
Hard bifurcations in dynamical systems with bounded random perturbations
A. J. Homburga, T. Youngb a KdV Institute for Mathematics,
University of Amsterdam,
Plantage Muidergracht 24,
1018 TV Amsterdam, The Netherlands
b Department of Mathematics,
Ohio University,
Athens, OH 45701
Abstract:
We study bifurcations in dynamical systems with bounded random perturbations. Such systems, which arise quite naturally, have been nearly ignored in the literature, despite a rich body of work on systems with unbounded, usually normally distributed, noise. In systems with bounded random perturbations, new kinds of bifurcations that we call 'hard' may happen and in fact do occur in many situations when the unperturbed deterministic systems experience elementary, codimension-one bifurcations such as saddle-node and homoclinic bifurcations. A hard bifurcation is defined as discontinuous change in the density function or support of a stationary measure of the system.
Keywords:
bifurcations, random perturbations.
Received: 03.10.2005 Accepted: 11.12.2005
Citation:
A. J. Homburg, T. Young, “Hard bifurcations in dynamical systems with bounded random perturbations”, Regul. Chaotic Dyn., 11:2 (2006), 247–258
Linking options:
https://www.mathnet.ru/eng/rcd671 https://www.mathnet.ru/eng/rcd/v11/i2/p247
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