Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 30: Nonlinear stochastic systems
DY 30.9: Vortrag
Freitag, 29. Februar 2008, 12:15–12:30, MA 001
Chaos induced oscillations by multiplicative noise in the Kapitza Pendulum — •Angelo Facchini1,2, Chiara Mocenni1,2, and Antonio Vicino1,2 — 1Center for the Study of Complex Systems, University of Siena, Italy — 2Department of Information Engineering, University of Siena, Italy
Also known as the Kapitza Pendulum, the parametrically forced pendulum has been widely investigated by many scientists as the paradigmatic toy model of a wide range of phenomena. Physically it consists of a physical pendulum whose pivot oscillates sinusoidally with amplitude A and frequency ω. Despite the simplicity, the KP depends strongly on its parameters. In particular the variation of the amplitude of the sinusoidal forcing, produces complex behaviors such the stabilization of the inverted position, parametrically forced oscillations, bifurcations and chaotic oscillations (for more details see [Am. J. of Physics, 60, 903-908, 1992;]). The influence of noise on the dynamical behavior of the KP has been also studied. In particular, the role of additive noise has been studied by Blackburn [Proc. of the Royal Soc. A, 462, 1043-1052, 2006], while the case of the randomly oscillating pivot has been investigated by Landa [Phys. Rev. E, 54, 3535, 1996]. Both found the arise of noise-mediated chaotic oscillations and noise-mediated transitions. We study the influence of the stochastic perturbation of the parameter A. This results in the study of the effect of multiplicative noise on the pendulum. We show that the adding of a very small amount of noise induces the anticipation of bifurcation points and sustains permanently chaotic oscillations, extending the results of Blackburn.