On-off Intermittency Research Articles

Water as the main regulator of intracellular processes

This paper addresses the investigation of water as the main regulator of intracellular processes. The research is based on assessing the impact associated water phase electromagnetic activity has on biological processes as well as determining its relationship to quantum states of delocalized electron system. The study demonstrates that the characteristics of electromagnetic emissions of water in SHF- and low-frequency (Hz–kHz) ranges are determined by dynamic states of superconductivity of associated water phase and are described within the framework of self-organization of hightemperature granulated superconductor with on-off intermittency. The paper describes the importance of obtained quantum laws in order to substantiate a regulatory role of associated water phase related to high organism sensitivity to electromagnetic emissions, and the detection of reasons for human diseases of metabolic etiology.

Multistate intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity.

We observe experimentally two regimes of intermittency on the route to chaos of a semiconductor laser subjected to optical feedback from a long external cavity as the feedback level is increased. The first regime encountered corresponds to multistate intermittency involving two or three states composed of several combinations of periodic, quasiperiodic, and subharmonic dynamics. The second regime is observed for larger feedback levels and involves intermittency between period-doubled and chaotic regimes. This latter type of intermittency displays statistical properties similar to those of on-off intermittency.

Influence sampling of trailing variables of dynamical systems

AbstractFor dealing with dynamical instability in predictions, numerical models should be provided with accurate initial values on the attractor of the dynamical system they generate. A discrete control scheme is presented to this end for trailing variables of an evolutive system of ordinary differential equations. The Influence Sampling (IS) scheme adapts sample values of the trailing variables to input values of the determining variables in the attractor. The optimal IS scheme has affordable cost for large systems. In discrete data assimilation runs conducted with the Lorenz 1963 equations and a nonautonomous perturbation of the Lorenz equations whose dynamics shows on-off intermittency the optimal IS was compared to the straightforward insertion method and the Ensemble Kalman Filter (EnKF). With these unstable systems the optimal IS increases by one order of magnitude the maximum spacing between insertion times that the insertion method can handle and performs comparably to the EnKF when the EnKF converges. While the EnKF converges for sample sizes greater than or equal to 10, the optimal IS scheme does so fromsample size 1. This occurs because the optimal IS scheme stabilizes the individual paths of the Lorenz 1963 equations within data assimilation processes.

How is overland flow produced under intermittent rain? An analysis using plot-scale rainfall simulation on dryland soils

The characteristic intermittency of rainfall includes temporary cessations (hiatuses), as well as periods of very low intensity within more intense events. To understand how these characteristics of rainfall affect overland flow production, rainfall simulations involving repeated cycles of on-off intermittency were carried out on dryland soils in arid western New South Wales, Australia. Periods of rain (10 mm/h) and no-rain were applied in alternation with cycle times from 3 min to 25 min, in experiments lasting 1–1.5 h. Results showed that intermittency could delay the onset of runoff by more than 30 min, reduce the runoff ratio, reduce the peak runoff rate, and reduce the apparent event infiltration rate by 30–45%. When hiatuses in rainfall were longer than 15–20 min, runoff that had resulted from prior rain ceased completely before the recommencement of rain. Results demonstrate that if rainfall intermittency is not accounted for, estimates of infiltrability based on runoff plot data can be systematically in error. Despite the use of intermittent rain, the episodic occurrence of runoff could be predicted successfully by fitting multiple affine Horton infiltration equations, whose changing f0 and Kf coefficients, but uniform values of fc, reflected the redistribution of soil moisture and the change in the infiltrability f during hiatuses in rainfall. The value of fc varied little among the fitted equations, so constituting an affine set of relationships. This new approach provides an alternative to the use of steady-state methods that are common in rainfall simulation experiments and which typically yield only an estimate of fc. The new field results confirm that intermittency affects infiltration and runoff depths and timing at plot scale and on intra-event timescales. Additional work on other soil types, and at other spatial and temporal scales, is needed to test the generality of these findings.

On-off intermittency in coupled chaotic thermoacoustic oscillations.

This paper documents on-off intermittency observed in coupled thermoacoustic chaotic oscillations. Mode competition between two or three oscillation modes engenders chaotic oscillations through quasiperiodic oscillations introduced by a local cross-sectional change in a gas-filled tube. Complete synchronization is then obtained by connecting two thermoacoustic chaotic oscillators via a rigid plate with an orifice. From the analysis of pressure fluctuations, theoretical statistical scaling laws related to the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, when the thermoacoustic complete synchronization breaks down through an on-off intermittency route with the decreased orifice size.

Random interval diffeomorphisms

We consider a class of step skew product systems of interval diffeo-morphisms over shift operators, as a means to study random compositions of interval diffeomorphisms. The class is chosen to present in a simplified setting intriguing phenomena of intermingled basins, master-slave synchronization and on-off intermittency. We provide a self-contained discussion of these phenomena.

On-off intermittency in coupled chaotic thermoacoustic systems

We present chaos-chaos synchronization in coupled thermally induced acoustic gas oscillation systems. By introducing a local cross-sectional change in a gas-filled tube subjected to a temperature gradient, chaotic oscillations are found to be achieved through the mode competition. The chaos-chaos synchronization is then obtained by connecting the two thermoacoustic oscillators via a rigid plate with an orifice. Theoretical statistical scaling laws regarding the laminar phases, spectral density, and amplitude probability distribution are found to be satisfied in the coupled thermoacoustic oscillators, as presented from the analysis of pressure fluctuations when the thermoacoustic chaos-chaos synchronization breaks down with the decreased orifice size.

Multistability and complex basins in a nonlinear duopoly with price competition and relative profit delegation.

In this article, we investigate the local and global dynamics of a nonlinear duopoly model with price-setting firms and managerial delegation contracts (relative profits). Our study aims at clarifying the effects of the interaction between the degree of product differentiation and the weight of manager's bonus on long-term outcomes in two different states: managers behave more aggressively with the rival (competition) under product complementarity and less aggressively with the rival (cooperation) under product substitutability. We combine analytical tools and numerical techniques to reach interesting results such as synchronisation and on-off intermittency of the state variables (in the case of homogeneous attitude of managers) and the existence of chaotic attractors, complex basins of attraction, and multistability (in the case of heterogeneous attitudes of managers). We also give policy insights.

Fluctuation scaling in the visual cortex at threshold.

Fluctuation scaling relates trial-to-trial variability to the average response by a power function in many physical processes. Here we address whether fluctuation scaling holds in sensory psychophysics and its functional role in visual processing. We report experimental evidence of fluctuation scaling in human color vision and form perception at threshold. Subjects detected thresholds in a psychophysical masking experiment that is considered a standard reference for studying suppression between neurons in the visual cortex. For all subjects, the analysis of threshold variability that results from the masking task indicates that fluctuation scaling is a global property that modulates detection thresholds with a scaling exponent that departs from 2, β=2.48±0.07. We also examine a generalized version of fluctuation scaling between the sample kurtosis K and the sample skewness S of threshold distributions. We find that K and S are related and follow a unique quadratic form K=(1.19±0.04)S^{2}+(2.68±0.06) that departs from the expected 4/3 power function regime. A random multiplicative process with weak additive noise is proposed based on a Langevin-type equation. The multiplicative process provides a unifying description of fluctuation scaling and the quadratic S-K relation and is related to on-off intermittency in sensory perception. Our findings provide an insight into how the human visual system interacts with the external environment. The theoretical methods open perspectives for investigating fluctuation scaling and intermittency effects in a wide variety of natural, economic, and cognitive phenomena.

Time-frequency analysis of characteristic patterns of the activity of neuron ensembles in the brain by means of continuous wavelet transform

The time-frequency characteristics of sleep spindles on EEG are studied by means of continuous wavelet transforms. Age dependence and dependence on epileptic status of animals of these characteristics was studied, the on-off intermittency in behavior of sleep spindles was found.

Multiplicative-cascade dynamics in pole balancing.

Pole balancing is a key task for probing the prospective control that organisms must engage in for purposeful action. The temporal structure of pole-balancing behaviors will reflect the on-line operation of control mechanisms needed to maintain an upright posture. In this study, signatures of multifractality are sought and found in time series of the vertical angle of a pole balanced on the fingertip. Comparisons to surrogate time series reveal multiplicative-cascade dynamics and interactivity across scales. In addition, simulations of a pole-balancing model generating on-off intermittency [J. L. Cabrera and J. G. Milton, Phys. Rev. Lett. 89, 158702 (2002)] were analyzed. Evidence of multifractality is also evident in simulations, though comparing simulated and participant series reveals a significantly greater contribution of cross-scale interactivity for the latter. These findings suggest that multiplicative-cascade dynamics are an extension of on-off intermittency and play a role in prospective coordination.

Blinking Statistics and Excitation-Dependent Luminescence Yield in Si and CdSe Nanocrystals

ON–OFF intermittency or blinking is a phenomenon observed in single quantum emitters, which reduces their overall light emission. Even though it seems to be a fundamental property of quantum dots (QDs), substantial differences can be found in the blinking statistics of different nanocrystals. This work compares the blinking of numerous single, oxide-capped Si nanocrystals with that of CdSe/ZnS core–shell nanocrystals, measured under the same conditions in the same experimental system and over a broad range of excitation power densities. We find that ON- and OFF-times can be described by exponential statistics in Si QDs, as opposed to power-law statistics for the CdSe nanocrystals. The type of blinking (power-law or monoexponential) does not depend on excitation but seems to be an intrinsic property of the material system. Upon increasing excitation power, the duty cycle of Si quantum dots remains constant, whereas it decreases for CdSe nanocrystals, which is readily explained by blinking statistics. Both ON–OFF and OFF–ON transitions can be regarded as light-induced in Si/SiO2 QDs, while the OFF–ON transition in CdSe/ZnS nanocrystals is not stimulated by photons. The differences in blinking behavior in these systems will be discussed.

Experimental noise-induced on-off intermittency in two bidirectionally-coupled diode lasers

Intermittent switches between chaotic and steady-state regimes are observed in experiments with two mutually-coupled diode lasers subject to common white gaussian noise. Both time series and power spectrum analyses yield typical scaling laws for on-off intermittency.

Intermittency in relation with 1/f noise and stochastic differential equations

One of the models of intermittency is on-off intermittency, arising due to time-dependent forcing of a bifurcation parameter through a bifurcation point. For on-off intermittency, the power spectral density (PSD) of the time-dependent deviation from the invariant subspace in a low frequency region exhibits 1/f power-law noise. Here, we investigate a mechanism of intermittency, similar to the on-off intermittency, occurring in nonlinear dynamical systems with invariant subspace. In contrast to the on-off intermittency, we consider the case where the transverse Lyapunov exponent is zero. We show that for such nonlinear dynamical systems, the power spectral density of the deviation from the invariant subspace can have 1/fβ form in a wide range of frequencies. That is, such nonlinear systems exhibit 1/f noise. The connection with the stochastic differential equations generating 1/fβ noise is established and analyzed, as well.

Intermittency in spherical Couette dynamos

We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.

Wavelet-based multifractal analysis of nonlinear time series: The earthquake-driven tsunami of 27 February 2010 in Chile

We study general multifractal properties of tidal gauge and long-wave time series which show a well defined transition between two states, as is the case of sea level when a tsunami arrives. We adopt a method based on discrete wavelets, called wavelet leaders, which has been successfully used in a wide range of applications from image analysis to biomedical signals. First, we analyze an empirical time series of tidal gauge from the tsunami event of 27 February 2010 in Chile. Then, we study a numerical solution of the driven-damped regularized long-wave equation (RLWE) which displays on-off intermittency. Both time series are characterized by a sudden change between two sharply distinct dynamical states. Our analysis suggests a correspondence between the pre- and post-tsunami states (ocean background) and the on state in the RLWE, and also between the tsunami state (disturbed ocean) and the off state in the RLWE. A qualitative similarity in their singularity spectra is observed, and since the RLWE is used to model shallow water dynamics, this result could imply an underlying dynamical similarity.

Automatic extraction and analysis of oscillatory patterns on nonstationary EEG signals by means of wavelet transform and the empirical modes method

The time-frequency structure and dynamics of oscillatory patterns in electroencephalograms of rats is studied by means of continuous wavelet transform and the decomposition of the signal by empirical modes. A method for the automatic selection of patterns using the empirical modes is developed. The method is applied to the study of sleep spindles, and it is shown that their dynamics depends on the regularities of on-off intermittency.

Adaptive Fractal Analysis Reveals Limits to Fractal Scaling in Center of Pressure Trajectories

Fractal time series analysis methods are commonly used for analyzing center of pressure (COP) signals with the goal of revealing the underlying neuromuscular processes for upright stance control. The use of fractal methods is often coupled with the assumption that the COP is an instance of fractional Gaussian noise (fGn) or fractional Brownian motion (fBm). Our purpose was to evaluate the applicability of the fGn-fBm framework to the COP in light of several characteristics of COP signals revealed by a new method, adaptive fractal analysis (AFA). AFA quantifies how the variance of the residuals to fits of a globally smooth trend signal scales with the time scale at which the fits are performed. Application of AFA to COP signals revealed that there are potentially three fractal scaling regions in the COP as opposed to one as expected from a pure fGn or fBm process. The scaling region at the fastest scale was anti-persistent and spanned ~30-90 ms, the intermediate was persistent and spanned ~200 ms-1.9 s, and the slowest was anti-persistent and spanned ~5-40 s. The intermediate fractal scaling region was the most clearly defined, but it only contributed around 11% of the total spectral energy of the COP signal, indicating that other features of the COP signal contribute more importantly to the overall dynamics. Also, more than half of the Hurst exponents estimated for the intermediate region were greater than the theoretically expected range [0,1] for fGn-fBm processes. These results suggest the fGn-fBm framework is not appropriate for modeling COP signals. ON-OFF intermittency might provide a better modeling framework for the COP, and multiscale approaches may be more appropriate for analyzing COP data.

On-off intermittency in an optically injected semiconductor laser

We report on the observation of on-off intermittency in an optically injected dual-mode semiconductor laser. It is shown that quasi-single-mode chaotic dynamics of the injected mode are accompanied by intermittent and irregular bursts of the intensity of the uninjected mode. We define a threshold intensity of the uninjected mode to distinguish laminar and bursting states of the system. For small values of the threshold parameter we observe excellent agreement with the predictions of theory for the distribution of the laminar phase durations. For larger values of the threshold parameter, a gap appears in the distribution of laminar phase durations. Numerical simulations demonstrate that this gap is a consequence of the fact that in this case the on states of the system define large intensity spikes, which can belong either to the same or to distinct bursts away from the single-mode manifold.

On-off intermittency over an extended range of control parameter

We propose a simple phenomenological model exhibiting on-off intermittency over an extended range of control parameter. We find that the distribution of the "off" periods has a power-law tail with an exponent varying continuously between -1 and -2, at odds with standard on-off intermittency which occurs at a specific value of the control parameter and leads to the exponent -3/2. This nontrivial behavior results from the competition between a strong slowing down of the dynamics at small values of the observable and a systematic drift toward large values.