Abstract
We consider families of random dynamical systems induced by parametrized one-dimensional stochastic differential equations. We give necessary and sufficient conditions on the invariant measures of the associated Markov semigroups which ensure a stochastic bifurcation. This leads to sufficient conditions on drift and diffusion coefficients for a stochastic pitchfork and transcritical bifurcation of the family of random dynamical systems.
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Crauel, H., Imkeller, P., Steinkamp, M. (1999). Bifurcations of One-Dimensional Stochastic Differential Equations. In: Stochastic Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-22655-9_2
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DOI: https://doi.org/10.1007/0-387-22655-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98512-1
Online ISBN: 978-0-387-22655-2
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