Stochastic resonance between limit cycles. Spring pendulum in a thermostat

The effect of white noise on phase synchronization is studied numerically for a classical model of a spring pendulum with a multiple ratio of the frequencies of small oscillations (Vitt-Gorelik model). It is shown that in the model investigated a Fermi resonance regime occurs for a system in a thermostat. A new type of nonlinear dynamics is found — stochastic resonance between limit cycles. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 8, 585–589 (25 April 1999)     

Stochastic resonance in chaotic dynamics

It is suggested that chaotic dynamical systems characterized by intermittent jumps between two preferred regions of phase space display an enhanced sensitivity to weak periodic forcings through a stochastic resonance-like mechanism. This possibility is illustrated by the study of the residence time distribution in two examples of bimodal chaos: the periodically forced Duffing oscillator and a 1-dimensional map showing intermittent behavior.     

Stochastic resonance mechanism in aerosol index dynamics

We consider satellite time series concerning the atmospheric aerosol content. We prove that these time series are well described by a stochastic dynamical model. The principal peak in the power spectrum of these signals can be explained by stochastic resonance, linking variable external factors, such as Sun-Earth radiation budget and local insolation, to fluctuations on smaller spatial and temporal scale due to internal weather and antrophic components.     

Stochastic resonance between counterpropagating Bloch walls

The nonequilibrium Ising-Bloch front bifurcation of the FitzHugh-Nagumo model with nondiffusing inhibitor provides a beautiful instance of an extended bistable system made up of propagating (Bloch) fronts. Moreover, these fronts are chiral and parity-related, and the barrier between them is nonetheless but a stationary Ising front. By means of numerical simulation in the neighborhood of this bifurcation, we demonstrate the existence of stochastic resonance in the transition between Bloch fronts of opposite chiralities, when an additive noise is included. The signal-to-noise ratio is numerically observed to scale with the distance to the critical point. This scaling law is theoretically characterized in terms of an effective nonequilibrium potential.     

Stochastic resonance and charge density wave dynamics in quasi-one-dimensional conductors

Stochastic resonance (SR) in nonlinear systems is a counterintuitive concept in which a weak periodic signal and noise cooperate and give rise to a maximum in the signal-to-noise ratio at the output of the system when the noise is tuned to a certain value. The spatial coupling of a large number of oscillators showing SR may have a constructive effect and leads to the so-called array enhanced stochastic resonance (AESR). We discuss the possible application of SR and AESR concepts to charge density wave (CDW) dynamics in quasi-one-dimensional conductors. We show in a preliminary experiment that the addition of noise can modify the behavior of the CDW in the quasi-one-dimensional conductor K_0.30MoO₃.     

Nonlinear effects of magnetization precession near ferromagnetic resonance

The features of precession of the magnetic moment of a film near ferromagnetic resonance are investigated which are due to the magnetic-moment nutation in the effective field and to the frequency-doubling effect. The contribution to this precession from harmonics with frequencies which are multiples of the basic resonance frequency is analyzed for a garnet ferrite film of the (111) type in a perpendicular bias magnetic field.     

Stochastic resonance in paramagnetic resonance systems

Experimental evidence of the stochastic resonance phenomenon in an electron paramagnetic resonance (EPR) system is reported. The amplitude and phase response of the EPR system operating in bistable conditions are measured for increasing values of the noise intensity. Theoretical predictions based on a simple dynamical model for the relevant system observables are shown to be in good agreement with experimental results.     

Stochastic high-frequency precession of magnetization in layered structures with antiferromagnetic ordering

The conditions for the appearance of self-oscillating and stochastic regimes in an exchange-coupled multilayer structure in the presence of a longitudinal high-frequency magnetic field are studied. Bifurcational diagrams are constructed that reveal various types of dynamic states of magnetic moments in the multilayer structure and transitions between these states with varying the frequency of the ac field. Attractors of stochastic oscillations are studied, and Lyapunov exponents determining the divergence of their phase trajectories are numerically calculated.     

Stochastic dynamics of the magneto-optical trap

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed stochastic dynamics is described extensively. It is shown that it exists a variety of dynamical behaviors, which differ by the frequency components appearing in the dynamics. Indeed, some instabilities exhibit only low frequency components, while in other cases, a second time scale, corresponding to a higher frequency, appears in the motion of the center of mass of the cloud. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the existence of instabilities to folded stationary solutions where noise response is enhanced. The different types of regimes are explained by the existence of a relaxation frequency, which in some conditions is excited by noise.Received: 18 June 2003, Published online: 28 October 2003PACS: 32.80.Pj Optical cooling of atoms; trapping - 05.40.Ca Noise - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Stochastic resonance as dithering

A direct correspondence is demonstrated between the phenomenon of "stochastic resonance" in static nonlinear systems and the dithering effect well known in the theory of digital waveform coding. It is argued that many static systems displaying stochastic resonance are forms of dithered quantizers, and that the existence or absence of stochastic resonance in such systems can be predicted from the effects of "dither averaging" upon their transfer characteristics. Also, results are introduced regarding stochastic resonance in certain nonlinear systems with memory (e.g., hysteretic systems).     

Stochastic resonance in perspective

Summary We outline the historical development of stochastic resonance (SR), a phenomenon in which the signal and/or the signal-to-noise ratio in a nonlinear system increase with increasing intensity of noise. We discuss basic theoretical ideas explaining and describing SR, and we review some revealing experimental data that place SR within the wider context of statistical physics. We emphasize the close relationship of SR to some effects that are well known in condensed-matter physics. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

基于振动共振的随机共振控制

分析了非线性双稳系统在高、低两种不同频率信号作用下的动力学特性，给出了高频信号参数与双稳系统输出信号的信噪比和功率谱放大率关系的解析表达式，提出了基于振动共振的随机共振控制方法.理论分析和数值仿真结果表明，通过调节高频信号的幅值或频率大小，能有效地控制双稳系统输出信号的信噪比和功率谱放大率.     

Stochastic dynamics of Faddeev-Popov ghosts

The Langevin equations which determine the stochastic quantization for the complete quartet of tields of the Yang-Mills theory are constructed. The BRS symmetry is enforced at each value of the stochastic time. This defines the non-perturbative dynamics of the Faddeev-Popov ghosts.     

Stochastic resonance in neuron models

We study Axiom A flows and introduce a new definition of Gibbs states which is modeled after a current one for diffeomorphisms and by which Gibbs states are locally characterized by their transformation when pulled back by conjugating homeomorphisms. We show that Gibbs states are equilibrium states and vice versa. We also show that for subshifts this equivalence can be strengthened.     

Stochastic resonance in extended systems

Here, three highly nontrivial instances are briefly discussed, showing both the degree of maturity achieved by the field of stochastic resonance (SR) and the wealth of potential realizations of SR in extended systems: (1) a “bound” KPZ system, for which the knowledge of its nonequilibrium potential (NEP) makes simple the solution of a very complex problem; (2) the Ising-Bloch front bifurcation in an activator-inhibitor system, a case of SR between moving fronts of opposite chirality; (3) a spatiotemporally chaotic “toy model”, useful for climate research, exhibiting internal SR due to chaos suppression.     

Stochastic resonance in chaotic systems

The phenomenon of stochastic resonance (SR) is investigated for chaotic systems perturbed by white noise and a harmonic force. The bistable discrete map and the Lorenz system are considered as models. It is shown that SR in chaotic systems can be realized via both parameter variation (in the absence of noise) and by variation of the noise intensity with fixed values of the other parameters.