On-off Intermittency Research Articles

Intermittent behavior near the boundary of generalized synchronization in unidirectionally coupled time-delayed systems

The aim of the work is an analysis of characteristics of intermittent behavior taking place near the boundary of generalized synchronization in unidirectionally coupled time-delayed generators. The case of interaction of systems characterized by different numbers of positive Lyapunov exponents is considered. To determine the lengths of characteristic phases of the system behavior the auxiliary system method has been used. The result of the work is the determination of the type of intermittency taking place near the boundary of generalized synchronization. In this case by calculation the statistical characteristics of the laminar phase lengths (distributions of the laminar phase lengths and the dependencies of the mean lengths of the laminar phases on the criticality parameters) it has been found that near the boundary of the synchronous regime the on-off intermittency is observed. It has been shown that the intermittent generalized synchronization in time-delayed systems is characterized by multistability. For these purposes a time-averaged measure of multistability depending on the value of the coupling parameter between systems has been calculated and compared with the behavior of the spectrum of Lyapunov exponents. It has been found that the multistability measure can be used to detect the generalized synchronization in time-delayed systems.

Dynamics and Global Bifurcations in Two Symmetrically Coupled Non-Invertible Maps

The theory of critical curves determines the main characteristics of a discrete dynamical system in two dimensions. One important property that has garnered recent attention is the problem of chaos synchronization, along with the location of its chaotic attractors, basin boundaries, and bifurcation mechanisms. Varying the parameters of the maps reveals the instrumental role that these curves play, where the bifurcation leads to complex topological structures of the basins occurs by contact with the basin boundaries, resulting in the appearance or disappearance of some components of the basin. This study focuses on the properties of a discrete dynamical system consisting of two symmetrically coupled non-invertible maps, specifically those with an invariant one-dimensional submanifold (or one-dimensional maps). These maps exhibit a complex structure of basins with the coexistence of symmetric chaotic attractors, riddled basins, blow-out, on-off intermittency, and, most significantly, the appearance of chaotic synchronization with a correlation between all the characteristics. The numerical method of critical curves can be used to demonstrate a wide range of dynamic scenarios and explain the bifurcations that lead to their occurrence. These curves play a crucial role in a system of two symmetrically coupled maps, and their significance will be discussed.

Pseudolaminar chaos from on-off intermittency.

In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)0031-900710.1103/PhysRevLett.128.074101] known from delay systems with lag-time modulation. Applying, however, to such systems a test for laminar chaos, as proposed in [Phys. Rev. E 101, 032213 (2020)2470-004510.1103/PhysRevE.101.032213], these signals fail such a test, thus leading to the notion of pseudolaminar chaos. The latter can be interpreted as integrated periodically driven on-off intermittency. We demonstrate that, on a signal level, true laminar and pseudolaminar chaos are hardly distinguishable in systems with and without dynamical noise. However, very pronounced differences become apparent when correlations of signals and increments are considered. We compare and contrast these properties of pseudolaminar chaos with true laminar chaos.

Subcritical jump probability and anomalous order parameter autocorrelations

We study the magnetization dynamics in finite 2D and 3D Ising lattices of size N for temperatures T just below the pseudo-critical temperature T pc (N) when the free energy, as a function of the mean magnetization M, possesses doubly degenerate minima at . We calculate the jump probability P LR between the microstate-subspaces with M < 0 (L) and M > 0 (R). We find a universal law for the decay of P LR as a function of . We show that for a given simulation time there is a temperature below which the mean number of jumps becomes less than . Below the two microstate-subspaces become practically disconnected. We observe an anomalous enhancement of the magnetization autocorrelations for T approaching which can be explained as a transition from type I (at ) to on-off (at ) intermittency in the magnetization effective dynamics. Possible phenomenological implications of this behaviour are briefly discussed.

Noise-induced synchronization of spin-torque oscillators

Noise-induced synchronization is a phenomenon where several oscillators with different initial conditions show synchronized motion, even in the absence of a coupling between them, when common stochastic input signals are injected. The phenomenon has attracted attention from nonlinear science, as well as applied physics, because it enables environmental noise to be used to synchronize many oscillators and is a necessary condition for brain-inspired computing. Here we develop a theoretical analysis of noise-induced synchronization in spin-torque oscillators (STOs). The analytical form for the Lyapunov exponent for the present model we derive indicates that there are two contributions from input signal to noise-induced synchronization in STOs. The first is that the input signal directly aligns the phases of the magnetizations, and the second is that the input signal changes the oscillating amplitude, and the amplitude-phase coupling results in synchronization. The validity of the analytical results was qualitatively confirmed by numerical simulation. We also show the existence of on-off intermittency at finite temperature, whose statistical properties are similar to those of other oscillator systems.

On-off intermittency and irruptions in host-parasitoid dynamics

Environmental stochasticity affects population dynamics in a variety of ways, including the possibility of drastic modifications in the stability properties of the ecosystem. In this work, we investigate a case of coupled host-parasitoid dynamics adopting Beddington’s conceptual two-dimensional map. We stochastically perturb some of the parameters controlling either the host dynamics or the host-parasitoid interaction, observing a dramatic change in the system dynamics with the emergence of on-off intermittency, a behavior characterized by the irregular alternation between quiescent phases and sudden population bursts. This phenomenon is herein offered as a qualitative, environmental-based description of population outbreaks.

The occurrence of locally riddled basins and on-off intermittency in a parametric nonlinear system

In this paper, a one parameter family (Fβ)β∈(0,1) of maps of the unit square I×I is studied. We observe that, for some values of parameter, our model exhibits one chaotic attractor Aβ,0, lying in the invariant subspace I×{0}, with a locally riddled basin of attraction. Rigorous analysis for the occurrence of locally riddled basin is given. Using the monotonicity and concavity of the fiber maps in our model, we give a classification, with respect to the number of attracting invariant graphs. We examine the bifurcation effects that appear in our model on varying parameter; in particular, a nonregular temporal bursting and the appearance of an on-off intermittency is investigated. Finally, we show that the model undergoes a nonhysteretic blowout bifurcation.

Extreme events in globally coupled chaotic maps

Understanding and predicting uncertain things are the central themes of scientific evolution. Human beings revolve around these fears of uncertainties concerning various aspects like a global pandemic, health, finances, to name but a few. Dealing with this unavoidable part of life is far tougher due to the chaotic nature of these unpredictable activities. In the present article, we consider a global network of identical chaotic maps, which splits into two different clusters, despite the interaction between all nodes are uniform. The stability analysis of the spatially homogeneous chaotic solutions provides a critical coupling strength, before which we anticipate such partial synchronization. The distance between these two chaotic synchronized populations often deviates more than eight times of standard deviation from its long-term average. The probability density function of these highly deviated values fits well with the generalized extreme value distribution. Meanwhile, the distribution of recurrence time intervals between extreme events resembles the Weibull distribution. The existing literature helps us to characterize such events as extreme events using the significant height. These extremely high fluctuations are less frequent in terms of their occurrence. We determine numerically a range of coupling strength for these extremely large but recurrent events. On-off intermittency is the responsible mechanism underlying the formation of such extreme events. Besides understanding the generation of such extreme events and their statistical signature, we furnish forecasting these events using the powerful deep learning algorithms of an artificial recurrent neural network. This long short-term memory (LSTM) can offer handy one-step forecasting of these chaotic intermittent bursts. We also ensure the robustness of this forecasting model with two hundred hidden cells in each LSTM layer.

A note on symmetry breaking in a non linear marketing model

In this paper, we consider the nonlinear discrete-time dynamic model proposed by Bischi and Baiardi (Chaos Solitons Fractals 79:145-156, 2015a). The model considers players with adaptive adjustment mechanisms towards the best reply and a form of inertia in adopting such mechanism. Moreover, we formulate an extension of the original model, where endogenous market size is considered. Through numerical simulations, we show that multiple attractors may exist in the presence of homogeneous agents and the emergence of non-synchronized trajectories both in the short (on-off intermittency) and long (global riddling) run. Therefore, the article highlights that strategic contexts exist in which the players’ knowledge of the market and the adoption of the best reply do not always allow the use of the representative agent’s rhetoric to describe the dynamics of the model.

On-Off Intermittency in a Three-Species Food Chain

The environment affects population dynamics through multiple drivers. Here we explore a simplified version of such influence in a three-species food chain, making use of the Hastings–Powell model. This represents an idealized resource–consumer–predator chain, or equivalently, a vegetation–host–parasitoid system. By stochastically perturbing the value of some parameters in this dynamical system, we observe dramatic modifications in the system behavior. In particular, we show the emergence of on–off intermittency, i.e., an irregular alternation between stable phases and sudden bursts in population size, which hints towards a possible conceptual description of population outbursts grounded into an environment-driven mechanism.

Lévy on-off intermittency.

We present an alternative form of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space (α,β) of the noise, with stability parameter α∈(0,2) and skewness parameter β∈[-1,1]. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case α=2. Three regimes are located at 1<α<2, where the noise has finite mean but infinite variance. They are differentiated by β and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterized by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at 0<α≤1. There, the mean of the noise diverges, and no critical transition occurs. In one case, the origin is always unstable, independently of the distance μ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of μ. We thus demonstrate that an instability subject to nonequilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.

Intermittency of three-dimensional perturbations in a point-vortex model.

Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a regularized 2D point-vortex flow coupled to localized 3D perturbations ("ergophages"), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the amplitude of the ergophages grows or decays exponentially on average, with an instantaneous growth rate that fluctuates randomly in time. The instantaneous growth rate has a small auto-correlation time, and a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cutoff) depending on the point-vortex base flow. Consequently, the logarithm of the ergophage amplitude performs a Lévy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Lévy on-off intermittency, which we define and study in a companion paper [van Kan et al., Phys. Rev. E 103, 052115 (2021)1063-651X10.1103/PhysRevE.103.052115]. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the condensate is disrupted and the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories, our model provides a new perspective on 3D instabilities growing on 2D flows, which will be useful in analyzing and understanding the much more complex results of DNS and potentially guide further theoretical developments.

Long-term persistence, invariant time scales and on-off intermittency of fog events

In this work we study different characteristics of fog long-term persistence, in events with different physical formation mechanisms. Specifically, we focus on the characterization of fog long-term persistence from observational data, by means of a Detrended Fluctuation Analysis (DFA) of its associated low-visibility time series. We analyze fog events with radiation and orographic underlying physical formation mechanisms, and identify a two-range pattern of long-term persistence. Our analysis leads to the emergence of a characteristic time, τ∗, at the crossover point between different scaling exponents in the DFA, independent of the time scale at which the fog event is studied. We also show that these scale-invariant characteristic times are related to the duration of fog/no-fog periods, what suggests that τ∗ is a good measure to study and compare fog events persistence, and also that fog events can be studied as on-off intermittent processes. We apply a binarizing process and confirm that the two-range shape structure in the DFA is maintained in the binary time series associated to fog events. We also show how τ∗ is related to the binary structure of the time series.

Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators.

The type of transition from asynchronous behavior to the generalized synchronization regime in mutually coupled chaotic oscillators has been studied. To separate the epochs of the synchronous and asynchronous motion in time series of mutually coupled chaotic oscillators, a method based on the local Lyapunov exponent calculation has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled dynamical systems for which the type of transition is well known. The transition to generalized synchronization regime in mutually coupled systems has been shown to be an on-off intermittency as well as in the case of the unidirectional coupling.

Jump intermittency as a second type of transition to and from generalized synchronization.

The transition from asynchronous dynamics to generalized chaotic synchronization and then to completely synchronous dynamics is known to be accompanied by on-off intermittency. We show that there is another (second) type of the transition called jump intermittency which occurs near the boundary of generalized synchronization in chaotic systems with complex two-sheeted attractors. Although this transient behavior also exhibits intermittent dynamics, it differs sufficiently from on-off intermittency supposed hitherto to be the only type of motion corresponding to the transition to generalized synchronization. This type of transition has been revealed and the underling mechanism has been explained in both unidirectionally and mutually coupled chaotic Lorenz and Chen oscillators. To detect the epochs of synchronous and asynchronous motion in mutually coupled oscillators with complex topology of an attractor a technique based on finding time intervals when the phase trajectories are located on equal or different sheets of chaotic attractors of coupled oscillators has been developed. We have also shown that in the unidirectionally coupled systems the proposed technique gives the same results that may obtained with the help of the traditional method using the auxiliary system approach.

Multifractal Intermittency in Granular Flow through Bottlenecks.

We experimentally analyze the intermittent nature of granular silo flow when the discharge is controlled by an extracting belt at the bottom. We discover the existence of four different scenarios. For low extraction rates, the system is characterized by an on-off intermittency. When the extraction rate is increased the structure functions of the grains velocity increments, calculated for different lag times, reveal the emergence of multifractal intermittency. Finally, for very high extraction rates that approach the purely gravitational discharge, we observe that the dynamics become dependent on the outlet size. For large orifices the behavior is monofractal, whereas for small ones, the fluctuations of the velocity increments deviate from Gaussianity even for very large time lags.

On-off intermittency and hard turbulence in the flow of fluid in the magnetic field.

This work provides an analysis of experiments in which various modes of mercury flow in a constant external magnetic field were observed; we examined the temperature oscillations in the mercury flow in a heated pipe at various Reynolds and Hartmann numbers. In some modes, the temperature oscillations have specific forms of strong aperiodic "bursts" over the weak irregular background, which are specific to the developed turbulent flow. To determine the nature of these temperature oscillations and the characteristics of the fluid flow, we examined them through the apparatus of nonlinear dynamics. The totality of all the results (autocorrelation function, correlation integral, maximum Lyapunov exponents, and Fourier transform) provide evidence of the chaotic nature of the observed flow modes despite the relative weakness of high-frequency harmonics in comparison to low-frequency ones. In the case of separate bursts of turbulence, the duration of the laminar phase τ follows the known distribution ∼τ-3/2, derived from the theory of on-off intermittency.

Phase diagram of coupled thermoacoustic chaotic oscillators

Linear analysis of thermoacoustic oscillations have been extensively made, but there is still a lack of knowledge on nonlinear phenomena such as synchronization and chaotic oscillations. Thermoacoustic chaotic oscillations have been reported in Taconis and combustion oscillators but these systems do not allow a well-controlled experiment because of the extreme temperature conditions. By making the system acoustically dissonant, we recently succeeded in generating thermoacoustic chaotic oscillations with modest temperatures. In this study, we present spatiotemporal evolution of thermoacoustic chaos from pressure measurements, and report an experimental bifurcation diagram when two thermoacoustic chaotic oscillators are dissipatively coupled to each other. The two-parameter bifurcation diagram is constructed by varying the frequency mismatch and the coupling strength. Complete chaos synchronization is observed in the region with a frequency mismatch of less than 1% of the uncoupled oscillator, with on-off intermittency phenomenon for low coupling strength. In other regions, synchronization between quasiperiodic oscillations and that between limit-cycle oscillations and oscillation death are observed as well as asynchronous states.

Kinematic and magnetic coherent structures in solar and stellar turbulence

AbstractWe show that on-off intermittency in solar and stellar cycles is a result of amplitude-phase synchronization in multiscale interactions in solar/stellar dynamos or magnetorotational instability which leads to the formation of kinematic and magnetic coherent structures, and the novel techniques of Lagrangian coherent structures can detect transport barriers and vortices such as magnetic flux tubes/ropes in solar and stellar turbulence with high accuracy.

Collective Sensing of β-Cells Generates the Metabolic Code.

Major part of a pancreatic islet is composed of β-cells that secrete insulin, a key hormone regulating influx of nutrients into all cells in a vertebrate organism to support nutrition, housekeeping or energy storage. β-cells constantly communicate with each other using both direct, short-range interactions through gap junctions, and paracrine long-range signaling. However, how these cell interactions shape collective sensing and cell behavior in islets that leads to insulin release is unknown. When stimulated by specific ligands, primarily glucose, β-cells collectively respond with expression of a series of transient Ca2+ changes on several temporal scales. Here we reanalyze a set of Ca2+ spike trains recorded in acute rodent pancreatic tissue slice under physiological conditions. We found strongly correlated states of co-spiking cells coexisting with mostly weak pairwise correlations widespread across the islet. Furthermore, the collective Ca2+ spiking activity in islet shows on-off intermittency with scaling of spiking amplitudes, and stimulus dependent autoassociative memory features. We use a simple spin glass-like model for the functional network of a β-cell collective to describe these findings and argue that Ca2+ spike trains produced by collective sensing of β-cells constitute part of the islet metabolic code that regulates insulin release and limits the islet size.