# Dresden 2006 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 51: Non-Linear Stochastic Systems

### DY 51.1: Vortrag

### Freitag, 31. März 2006, 11:30–11:45, H\"UL 186

**The power spectrum of a driven nonlinear stochastic system** — •Benjamin Lindner — MPI fuer Physik komplexer Systeme, Noethnitzer Str.38, 01187 Dresden

We study the effect of an external broad band driving on the power spectrum of a nonlinear stochastic system. A heuristic formula used frequently in the literature is shown to be valid at large internal noise of the system, i.e. when the system is effectively close to a linear dynamics. In the opposite limit of small internal noise, however, this formula may fail. We show that an external broadband perturbation can have effects not described by a purely linear theory: (1) power is reduced or added at frequencies which are outside the frequency band of the driving; (2) sharp peaks of the unperturbed system become much broader under the influence of random noise; (3) side bands appear in certain cases. We present two simple systems for which the power spectrum can be analytically calculated or at least approximated and discuss the implications of our findings for more general situations.

Ref. Lindner, Chacron, Longtin Phys. Rev. E 72, 021911 (2005)