A prehistory problem is formulated for large occasional fluctuations in noise-driven systems. It has been studied theoretically and experimentally, thereby illuminating the concept of optimal paths and making it possible to visualize and investigate them. The prehistory probability distribution measured for a white-noise-driven system, taken as an example, is shown to be in agreement with the theory. PACS numbers: 05.40.+J, 02.50,+s, 05.20.-y Fluctuations in physical systems can often be viewed [1] as arising because of external noise. Under stationary conditions, a weak-noise-driven system fluctuates mostly about its attractor (or attractors, if several of them coexist). However, there is also a small probability that the system will be found at a position in phase space far from an attractor. It is just these large deviations from the average that are responsible for a number of interesting physical phenomena, e.g., for switching in a variety of multistable systems (including multimode lasers, passive optically bistable systems, and Josephson junctions) and large-angle scattering (in particular, that of light) in nearly homogeneous media.A convenient and powerful approach to the analysis of the tails of the probability density distribution p(x) (where the components of the vector x enumerate the dynamical variables of a system) for systems driven by Gaussian noise is based [2-8] on the method of optimal fluctuation [9]. This approach exploits the idea that the tails of p(x) must be formed by large occasional outbursts of noise fit) that push the system far from the attractor. The probabilities of such large outbursts are small, and the value of pixf) for a given remote Xf will actually be determined by the probability of the most probable outburst among those bringing the system to x/. This particular realization is just the optimal fluctuation for the given Xf. Because a realization (a path) of noise fit) results in a corresponding realization of the dynamical variable xO), there also exists an optimal path x op{ (t;Xf) along which the system arrives at x/, with an overwhelming probability. Although eminently reasonable and highly successful, such approaches have lacked a direct basis in experiment-the existence of optimal paths never having been demonstrated-and, to this extent, the use of the method of optimal fluctuation has amounted to an act of faith.In this Letter, we propose a new approach to the investigation of rare events in noise-driven systems, addressing ourselves directly to the question of how one of these events (i.e., the arrival of the system at Xf) comes to

We describe an analysis of cardiac and respiratory time series recorded from 189 subjects of both genders aged 16–90. By application of the synchrosqueezed wavelet transform, we extract the respiratory and cardiac frequencies and phases with better time resolution than is possible with the marked events procedure. By treating the heart and respiration as coupled oscillators, we then apply a method based on Bayesian inference to find the underlying coupling parameters and their time dependence, deriving from them measures such as synchronization, coupling directionality and the relative contributions of different mechanisms. We report a detailed analysis of the reconstructed cardiorespiratory coupling function, its time evolution and age dependence. We show that the direct and indirect respiratory modulations of the heart rate both decrease with age, and that the cardiorespiratory coupling becomes less stable and more time-variable.

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the activation energy of escape depends linearly on the force amplitude. This dependence is described by the logarithmic susceptibility, which is analyzed theoretically and through analog and digital simulations. A closed-form explicit expression for the escape rate of an overdamped Brownian particle is presented and shown to be in quantitative agreement with the simulations. We also describe experiments on a Brownian particle optically trapped in a double-well potential. A suitable periodic modulation of the optical intensity breaks the spatio-temporal symmetry of an otherwise spatially symmetric system. This has allowed us to localize a particle in one of the symmetric wells. (c) 2001 American Institute of Physics.

The kinetics of a periodically driven nonlinear oscillator, bistable in a nearly resonant field, has been investigated theoretically and through analogue experiments. An activation dependence of the probabilities of fluctuational transitions between the coexisting attractors has been observed, and the activation energies of the transitions have been calculated and measured for a wide range of parameters. The position of the kinetic phase transition (KPT), at which the populations of the attractors are equal, has been established. A range of critical phenomena is shown to arise in the vicinity of the KPT including, in particular, the appearance of a supernarrow peak in the spectral density of the fluctuations, and the occurrence of high-frequency stochastic resonance (HFSR). The experimental measurements of the transition probabilities, the KPT line, the multipeaked spectral densities, the strength of the supernarrow spectral peak, and of the HFSR effect are shown to be in good agreement with the theoretical predictions.