We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of stochastic resonance. We present an approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics, one finds upon contraction onto two states a non-Markovian renewal dynamics. A proper definition of an output discrete phase is given, and the time rate of change of its noise average determines the corresponding output frequency. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. In this case, for an appropriate choice of the parameter values, the system exhibits a noise-induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior ones.
%0 Journal Article
%1 CAS05
%A Casado-Pascual, Jesús
%A nez, José Gómez-Ordó\
%A Morillo, Manuel
%A Lehmann, Jorg
%A Goychuk, I.
%A Hänggi, Peter
%D 2005
%J Phys.~Rev.~E
%K Gaussian Markov analysis noise; numerical processes; stochastic synchronisation; systems; white
%N 1
%P 011101
%R 10.1103/physreve.71.011101
%T Theory of frequency and phase synchronization in a rocked bistable stochastic system
%V 71
%X We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of stochastic resonance. We present an approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics, one finds upon contraction onto two states a non-Markovian renewal dynamics. A proper definition of an output discrete phase is given, and the time rate of change of its noise average determines the corresponding output frequency. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. In this case, for an appropriate choice of the parameter values, the system exhibits a noise-induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior ones.
@article{CAS05,
abstract = {We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of stochastic resonance. We present an approach to the stochastic counting process of noise-induced switching events: starting from the Markovian dynamics of the nonstationary, continuous particle dynamics, one finds upon contraction onto two states a non-Markovian renewal dynamics. A proper definition of an output discrete phase is given, and the time rate of change of its noise average determines the corresponding output frequency. The phenomenon of noise-assisted phase synchronization is investigated in terms of an effective, instantaneous phase diffusion. The theory is applied to rectangular-shaped rocking signals versus increasing input-noise strengths. In this case, for an appropriate choice of the parameter values, the system exhibits a noise-induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal. Precise numerical simulations corroborate very favorably our analytical results. The novel theoretical findings are also compared with prior ones.},
added-at = {2009-03-03T17:19:04.000+0100},
author = {Casado-Pascual, Jes\'us and nez, Jos\'e G\'omez-Ord\'o\ and Morillo, Manuel and Lehmann, Jorg and Goychuk, I. and H{\"a}nggi, Peter},
biburl = {https://www.bibsonomy.org/bibtex/257ca66e33f92f4ca0abff9c8e6685c4c/bronckobuster},
doi = {10.1103/physreve.71.011101},
eid = {011101},
interhash = {c5d96ef701ed5208b23f47ae8b5d19d0},
intrahash = {57ca66e33f92f4ca0abff9c8e6685c4c},
journal = {Phys.~Rev.~E},
keywords = {Gaussian Markov analysis noise; numerical processes; stochastic synchronisation; systems; white},
number = 1,
numpages = {9},
pages = 011101,
timestamp = {2009-03-03T17:19:58.000+0100},
title = {Theory of frequency and phase synchronization in a rocked bistable stochastic system},
volume = 71,
year = 2005
}