%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 }