Theory of frequency and phase synchronization in a rocked bistable stochastic system.
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.
Casado-Pascual
Jesús
J
Física Teórica, Universidad de Sevilla, Apartado de Correos 1065, Sevilla 41080, Spain. jcasado@us.es
Gómez-Ordóñez
José
J
Morillo
Manuel
M
Lehmann
Jörg
J
Goychuk
Igor
I
Hänggi
Peter
P
D000200:Action Potentials / Q000502:physiology; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D013269:Stochastic Processes; D009435:Synaptic Transmission / Q000502:physiology