We report observation of an inverse energy cascade in second sound acoustic turbulence He II. Its onset occurs above a critical driving and it is accompanied by giant waves that constitute analogue the rogue occasionally appear on surface ocean. The theory phenomenon developed shown to be good agreement with experiments.

Abstract Noise is commonly regarded as having a destructive but relatively innocuous effect, blurring our view of system no effect on the underlying processes involved. In this paper we show, using examples from stochastic nonlinear dynamics, that these intuitive ideas about noise can be very misleading. For example, an known resonance means addition extra to actually improve signal-to-noise ratio.

The application of methods drawn from nonlinear and stochastic dynamics to the analysis cardiovascular time series is reviewed, with particular reference identification changes associated ageing. natural variability heart rate (HRV) considered in detail, including respiratory sinus arrhythmia (RSA) corresponding modulation instantaneous cardiac frequency by rhythm respiration. HRV has been intensively studied using traditional spectral analyses, e.g. Fourier transform or autoregressive...

The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. coupling functions that connect them contain detailed information about the functional mechanisms underlying interactions prescribe physical rule specifying how an interaction occurs. Here, we aim to present a coherent comprehensive review encompassing rapid progress made recently analysis, understanding applications of functions. basic concepts characteristics presented through...

Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review these TFRs, summarizing all practically relevant aspects use, reconsidering some conventions introducing new concepts procedures to advance applicability value. Furthermore, detailed numerical theoretical study three specific questions is provided, application methods,...

In signal processing applications, it is often necessary to extract oscillatory components and their properties from time–frequency representations, e.g. the windowed Fourier transform or wavelet transform. The first step in this procedure find an appropriate ridge curve: a sequence of amplitude peak positions (ridge points), corresponding component interest providing measure its instantaneous frequency. This not trivial issue, optimal method for extraction still settled agreed. We discuss...

The effect of a high-frequency force on the response bistable system to low-frequency signal is considered for both overdamped and weakly damped cases. It shown that can be optimized by an appropriate choice vibration amplitude. This vibrational resonance displays many analogies well known phenomenon stochastic resonance, but with filling role usually played noise.

A nonequilibrium, bistable flow driven by exponentially correlated Gaussian noise is considered. An approximate, nonlinear Fokker-Planck--type equation, modeling effectively the long-time dynamics of bistable, non-Markovian constructed, and mean sojourn time evaluated in limit weak noise. Keeping strength constant, predicted to undergo an exponential increase with increasing correlation time. Representing colored electronic circuit, sojourn-time distribution have been measured...

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables evolution coupling functions other parameters to be followed. dynamics, with Bayesian inference time-evolving achieved by shaping prior densities incorporate knowledge previous samples. The tested numerically applied reveal quantify time-varying nature cardiorespiratory interactions.

Complex systems are all around us including, for example, biological cells, bee colonies, the brain, climate, telecommunication infrastructures, stock market, and economy. Typically, they consist of many distinct but interacting elements, may be characterised by states elements. But change as a result interactions, interactions themselves corresponding to system. It is this chicken-and-egg situation that gives rise complex behaviour well-known difficulties in understanding it, let alone...

We describe an analysis of cardiac and respiratory time series recorded from 189 subjects both genders aged 16–90. By application the synchrosqueezed wavelet transform, we extract frequencies phases with better resolution than is possible marked events procedure. treating heart respiration as coupled oscillators, then apply a method based on Bayesian inference to find underlying coupling parameters their dependence, deriving them measures such synchronization, directionality relative...

The signals emanating from complex systems are usually composed of a mixture different oscillations which, for reliable analysis, should be separated each other and the inevitable background noise. Here we introduce an adaptive decomposition tool-nonlinear mode (NMD)-which decomposes given signal into set physically meaningful any wave form, simultaneously removing NMD is based on powerful combination time-frequency analysis techniques-which, together with choice their parameters, make it...

The design of analogue electronic experiments to investigate phenomena in nonlinear dynamics, especially stochastic phenomena, is described practical terms. advantages and disadvantages this approach, comparison more conventional digital methods, are discussed. It pointed out that simulation provides a simple, inexpensive, technique easily applied any laboratory facilitate the implementation complicated expensive experimental projects; there some important problems for which methods have so...

Phase synchronization between cardiac and respiratory oscillations is investigated during anesthesia in rats. Synchrograms time evolution of indices are used to show that the system passes reversibly through a sequence different phase-synchronized states as level changes, indicating it can undergo phase transitionlike phenomena. It appears state may be characterize depth anesthesia.

The first observations of noise-induced enhancements and phase shifts a weak periodic signal-characteristics signatures stochastic resonance (SR)-are reported for monostable system. results are shown to be in good agreement with theoretical description based on linear-response theory the fluctuation dissipation theorem. It is argued that SR general phenomenon can principle occur any underdamped nonlinear oscillator.

A comment on the Letter by L. Gammaitoni et al., Phys. Rev. Lett. 62, 349 (1989).Received 16 October 1989DOI:https://doi.org/10.1103/PhysRevLett.65.2606©1990 American Physical Society

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 making it possible to visualize investigate them. The probability distribution measured a white-noise-driven system, taken as an example, shown be agreement with theory.

A new experiment has been performed to study the formation of topological defects (quantized vortices) during rapid quenches liquid 4He through superfluid transition, with particular care taken minimise vortex creation via conventional hydrodynamic flow processes. It is found that generated vortices, if any, are being produced at densities least two orders magnitude less than might be expected on basis Kibble-Zurek mechanism.

We introduce a directionality index for time series based on comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well reveal and quantify asymmetry in coupling. is tested numerical model coupled van der Pol oscillators, applied to cardiorespiratory data healthy subjects. There no need preprocessing fine-tuning the parameters, which makes method very simple, computationally fast robust.