Stochastic self-sustained oscillations of non-autonomous systems
International Institute of Nonlinear Dynamics, Department of Physics, Saratov State University, Astrakhanskaya Street 83, Saratov 410012, Russia
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Revised: 9 August 2010
Published online: 1 October 2010
In the present minireview, we analyze autonomous and non-autonomous oscillations of dynamical and stochastic systems in the framework of common concepts. We introduce the definition of an attractor for a non-autonomous system. We also propose the definition of self-sustained oscillations, which can be applied for both autonomous and non-autonomous systems. We consider noise-induced oscillations and formulate the definition of stochastic self-sustained oscillations for this case. All the statements made in this work are illustrated by particular examples.
© EDP Sciences, Springer-Verlag, 2010