Stochastic Resonance and Stochastic Synchronization

L. Schimansky-Geier$^1$, A Neiman$^2$, F. Moss$^2$ and J. A. Freund$^1$

$^2$Center for Neurodynamics, University of Missouri at St. Louis

Abstract:

We show that stochastic resonance can be interpreted as stochastic phase synchronization. Introducing a phase desccription to stochastic bistable dynamics we investigate conditions where strong phase relations are obeyed between an inputting signal and the stochastic output of the bistable dynamics. By considering dichotomic input and output signals we are able to analytically prove the occurrence of noise-induced frequency and phase locking characterized by a plateau of the mean output switching rate and a minimum of the phase diffusion coefficient. Relevant parameters are the frequency and amplitude of the inputting signal and the noise intensity of the bistable dynamics. The later determines the eigen-times of the stochastic systems and replaces the eigen-frequency of a corresponding oscillator. Subsequently regions of stochastic synchronization form Arnold tongues in the amplitude/noise intensity space.

In the second part we apply concepts of stochastic synchronization to behavioural experiments on paddlefish. It was shown experimentally that juvenile paddlefish makes use of stochastic resonance during prey detection. We show an increase of the average phase locking period for subthreshold signals acting on the paddlefish rostrum in the neighbourhood of swarms yielding a source of external electrical noise.

Literature:
J. A. Freund, A. Neiman and L. Schimansky-Geier, Europhys. Lett. 50 8-14 (2000).
J. A. Freund, J. Kienert, L. Schimansky-Geier, B. Beisner, A. Neiman, D. Russel, T. Yakusheva and F. Moss, Phys. Rev. E 63, 031910 1-11 (2001); Journal of Theoret. Biology, accepted for publication.