Experimental phase synchronization of a chaotic convective flow

Phase synchronization of baroclinic waves in a differentially heated rotating annulus experiment subject to periodic forcing with a variable duty cycle

A series of laboratory experiments in a thermally driven, rotating fluid annulus are presented that investigate the onset and characteristics of phase synchronization and frequency entrainment between the intrinsic, chaotic, oscillatory amplitude modulation of travelling baroclinic waves and a periodic modulation of the (axisymmetric) thermal boundary conditions, subject to time-dependent coupling. The time-dependence is in the form of a prescribed duty cycle in which the periodic forcing of the boundary conditions is applied for only a fraction δ of each oscillation. For the rest of the oscillation, the boundary conditions are held fixed. Two profiles of forcing were investigated that capture different parts of the sinusoidal variation and δ was varied over the range 0.1≤δ≤1. Reducing δ was found to act in a similar way to a reduction in a constant coupling coefficient in reducing the width of the interval in forcing frequency or period over which complete synchronization was observed (the "Arnol'd tongue") with respect to the detuning, although for the strongest pulse-like forcing profile some degree of synchronization was discernible even at δ=0.1. Complete phase synchronization was obtained within the Arnol'd tongue itself, although the strength of the amplitude modulation of the baroclinic wave was not significantly affected. These experiments demonstrate a possible mechanism for intraseasonal and/or interannual "teleconnections" within the climate system of the Earth and other planets that does not rely on Rossby wave propagation across the planet along great circles.

On the estimation of phase synchronization, spurious synchronization and filtering

Phase synchronization, viz., the adjustment of instantaneous frequencies of two interacting self-sustained nonlinear oscillators, is frequently used for the detection of a possible interrelationship between empirical data recordings. In this context, the proper estimation of the instantaneous phase from a time series is a crucial aspect. The probability that numerical estimates provide a physically relevant meaning depends sensitively on the shape of its power spectral density. For this purpose, the power spectrum should be narrow banded possessing only one prominent peak [M. Chavez et al., J. Neurosci. Methods 154, 149 (2006)]. If this condition is not fulfilled, band-pass filtering seems to be the adequate technique in order to pre-process data for a posterior synchronization analysis. However, it was reported that band-pass filtering might induce spurious synchronization [L. Xu et al., Phys. Rev. E 73, 065201(R), (2006); J. Sun et al., Phys. Rev. E 77, 046213 (2008); and J. Wang and Z. Liu, EPL 102, 10003 (2013)], a statement that without further specification causes uncertainty over all measures that aim to quantify phase synchronization of broadband field data. We show by using signals derived from different test frameworks that appropriate filtering does not induce spurious synchronization. Instead, filtering in the time domain tends to wash out existent phase interrelations between signals. Furthermore, we show that measures derived for the estimation of phase synchronization like the mean phase coherence are also useful for the detection of interrelations between time series, which are not necessarily derived from coupled self-sustained nonlinear oscillators.

Characterizing the phase synchronization transition of chaotic oscillators

The chaotic phase synchronization transition is studied in connection with the zero Lyapunov exponent. We propose a hypothesis that it is associated with a switching of the maximal finite-time zero Lyapunov exponent, which is introduced in the framework of a large deviation analysis. A noisy sine circle map is investigated to introduce this hypothesis and it is tested in an unidirectionally coupled Rössler system by using the covariant Lyapunov vector associated with the zero Lyapunov exponent.

Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits

We report the experimental demonstration of chaotic phase synchronization (CPS) in unidirectionally coupled time-delay systems using electronic circuits. We have also implemented experimentally an efficient methodology for characterizing CPS, namely, the localized sets. Snapshots of the evolution of coupled systems and the sets as observed from the oscilloscope confirming CPS are shown experimentally. Numerical results from different approaches, namely, phase differences, localized sets, changes in the largest Lyapunov exponents, and the correlation of probability of recurrence (C(CPR)) corroborate the experimental observations.

Experimental observation of chaotic phase synchronization of a periodically modulated frequency-doubled Nd:YAG laser

We present experimental observations of chaotic phase synchronization of a sinusoidally modulated frequency-doubled Nd:YAG laser. Periodic and chaotic phase synchronization is detected using recurrence analysis and pseudo ensemble averaging applied to the observed intensity fluctuations and the modulated pump current.

Transition from phase to generalized synchronization in time-delay systems

The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlation of probability of recurrence, joint probability of recurrence, and similarity of probability of recurrence. We have quantified the different synchronization regimes in terms of these indices. The existence of phase synchronization is also characterized by typical transitions in the Lyapunov exponents of the coupled time-delay systems.

Experimental synchronization of spatiotemporal chaos in nonlinear optics

We demonstrate that a unidirectional coupling between a pattern forming system and its replića induces complete synchronization of the slave to the master system onto a spatiotemporal chaotic state.

Detecting and characterizing phase synchronization in nonstationary dynamical systems

We propose a general framework for detecting and characterizing phase synchronization from noisy, nonstationary time series. For detection, we propose to use the average phase-synchronization time and show that it is extremely sensitive to parameter changes near the onset of phase synchronization. To characterize the degree of temporal phase synchronization, we suggest to monitor the evolution of phase diffusion from a moving time window and argue that this measure is practically useful as it can be enhanced by increasing the size of the window. While desynchronization events can be caused by either a lack of sufficient deterministic coupling or noise, we demonstrate that the time scales associated with the two mechanisms are quite different. In particular, noise-induced desynchronization events tend to occur on much shorter time scales. This allows for the effect of noise on phase synchronization to be corrected in a practically doable manner. We perform a control study to substantiate these findings by constructing and investigating a prototype model of nonstationary dynamical system that consists of coupled chaotic oscillators with time-varying coupling parameter.

Phase synchronization between two essentially different chaotic systems

In this paper, we numerically investigate phase synchronization between two coupled essentially different chaotic oscillators in drive-response configuration. It is shown that phase synchronization can be observed between two coupled systems despite the difference and the large frequency detuning between them. Moreover, the relation between phase synchronization and generalized synchronization is compared with that in coupled parametrically different systems. In the systems studied, it is found that phase synchronization occurs after generalized synchronization in coupled essentially different chaotic systems.

Synchronization of non-phase-coherent chaotic electrochemical oscillations

Experiments on phase and generalized synchronization of two coupled, nonidentical chaotic electrochemical oscillations are presented. We adapt measures of characterizing synchronization of a non-phase-coherent chaotic behavior and compare its properties and physicochemical mechanism to those of a phase-coherent behavior. Phase synchronization sets in along with the onset of generalized synchronization for the non-phase-coherent oscillations in contrast to phase-coherent oscillations in which the phase synchronization usually occurs at a weaker coupling strength.

Experimental control of coherence of a chaotic oscillator

We give experimental evidence that a delayed feedback control strategy is able to efficiently enhance the coherence of an experimental self-sustained chaotic oscillator obtained from a CO2 laser with electro-optical feedback. We demonstrate that coherence control is achieved for various choices of the delay time in the feedback control, including values that would lead to the stabilization of an unstable periodic orbit embedded within the chaotic attractor. The relationship between the two processes is discussed.

Irrational phase synchronization

We study the occurrence of physically observable phase locked states between chaotic oscillators and rotors in which the frequencies of the coupled systems are irrationally related. For two chaotic oscillators, the phenomenon occurs as a result of a coupling term which breaks the 2 pi invariance in the phase equations. In the case of rotors, a coupling term in the angular velocities results in very long times during which the coupled systems exhibit alternatively irrational phase synchronization and random phase diffusion. The range of parameters for which the phenomenon occurs contains an open set, and is thus physically observable.

Detecting local synchronization in coupled chaotic systems

We introduce a technique to detect and quantify local functional dependencies between coupled chaotic systems. The method estimates the fraction of locally synchronized configurations, in a pair of signals with an arbitrary state of global synchronization. Application to a pair of interacting Rössler oscillators shows that our method is able to quantify the number of dynamical configurations where a local prediction task is possible, as well as in the absence of global synchronization features.

Frequency entrainment of nonautonomous chaotic oscillators

We give evidence of frequency entrainment of dominant peaks in the chaotic spectra of two coupled chaotic nonautonomous oscillators. At variance with the autonomous case, the phenomenon is here characterized by the vanishing of a previously positive Lyapunov exponent in the spectrum, which takes place for a broad range of the coupling strength parameter. Such a state is studied also for the case of chaotic oscillators with ill-defined phases due to the absence of a unique center of rotation. Different phase synchronization indicators are used to circumvent this difficulty.

Competition of synchronization domains in arrays of chaotic homoclinic systems

We investigate the response of an open chain of bidirectionally coupled chaotic homoclinic systems to external periodic stimuli. When one end of the chain is driven by a periodic signal, the system propagates a phase synchronization state in a certain range of coupling strengths and external frequencies. When two simultaneous forcings are applied at different points of the array, a rich phenomenology of stable competitive states is observed, including temporal alternation and spatial coexistence of synchronization domains.

Phase synchronization of chaotic attractors with prescribed periodic signals

Given a chaotic attractor in a dynamical system with dense periodic windows (i.e., structurally unstable), is it possible to find a periodic driver that will phase synchronize the chaotic attractor? We conjecture that the answer is typically yes, and we give an example for a funneling chaotic attractor in the Roessler system.

Asymmetric coupling effects in the synchronization of spatially extended chaotic systems

We analyze the effects of asymmetric couplings in setting different synchronization states for a pair of unidimensional fields obeying complex Ginzburg-Landau equations. Novel features such as asymmetry enhanced complete synchronization, limits for the appearance of phase synchronized states, and selection of the final synchronized dynamics are reported and characterized.

Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers

Using mutually coupled nonidentical continuous-wave Nd:YAG lasers, we experimentally confirmed the recently proposed transition route from phase synchronization to complete synchronization. As evidence of this transition we obtained the probability distribution of the intermittent synchronization time near the threshold of the complete synchronization transition.

A secure communication scheme based on the phase synchronization of chaotic systems

Phase synchronization of chaotic systems with both weak and strong couplings has recently been investigated extensively. Similar to complete synchronization, this type of synchronization can also be applied in secure communications. We develop a digital secure communication scheme that utilizes the instantaneous phase as the signal transmitted from the drive to the response subsystems. Simulation results show that the scheme is difficult to be broken by some traditional attacks. Moreover, it operates with a weak positive conditional Lyapunov exponent in the response subsystem.

Constructive effects of noise in homoclinic chaotic systems

Many chaotic oscillators have coherent phase dynamics but strong fluctuations in the amplitudes. At variance with such a behavior, homoclinic chaos is characterized by quite regular spikes but strong fluctuation in their time intervals due to the chaotic recurrence to a saddle point. We study influences of noise on homoclinic chaos. We demonstrate both numerically and experimentally on a CO2 laser various constructive effects of noise, including coherence resonance, noise-induced synchronization in uncoupled systems and noise-enhanced phase synchronization, deterministic resonance with respect to signal frequency, and stochastic resonance versus noise intensity in response to weak signals. The peculiar sensitivity of the system along the weak unstable manifold of the saddle point underlines the unified mechanism of these nontrivial and constructive noise-induced phenomena.

Phase synchronization in the perturbed Chua circuit

We show experimental and numerical results of phase synchronization between the chaotic Chua circuit and a small sinusoidal perturbation. Experimental real-time phase synchronized states can be detected with oscilloscope visualization of the attractor, using specific sampling rates. Arnold tongues demonstrate robust phase synchronized states for perturbation frequencies close to the characteristic frequency of the unperturbed Chua.

Experimental characterization of the transition to phase synchronization of chaotic CO2 laser systems

We investigate the transition route to phase synchronization in a chaotic laser with external modulation. Such a transition is characterized by the presence of a regime of periodic phase synchronization, in which phase slips occur with maximal coherence in the phase difference between output signal and external modulation. We provide the first experimental evidence of such a regime and demonstrate that it occurs at the crossover point between two different scaling laws of the intermittent-type behavior of phase slips.

Phase synchronization of chaotic attractors in the presence of two competing periodic signals

We discuss the situation where two periodic signals compete to phase synchronize a chaotic attractor. Depending on the relative position of the periods with respect to the synchronization tongue for a single frequency signal, we distinguish several different cases. We find that, depending on parameters, it is possible that one or the other signal will entrain exclusively, or that they will entrain alternately, at their average frequency, or not at all.

Collective phase locked states in a chain of coupled chaotic oscillators

We discuss the emergence of a collective phase locked state in an open chain of N unidirectionally weakly coupled nonidentical chaotic oscillators. Such a regime is characterized by a Lyapunov spectrum where N-1 exponents that were zero in the uncoupled regime assume negative values as the coupling strength increases. The dynamics of such collective state is studied, and a comparison is drawn with the case of phase synchronization of a pair of coupled chaotic oscillators. In particular, it is shown that a full phase synchronized state cannot be constructed without at least partial correlation in the chaotic amplitudes.

Phase synchronization in coupled Nd:YAG lasers

We investigate experimentally the transition to phase synchronization in coupled Nd:YAG lasers. As the coupling strength increases, the phase difference of two chaotic laser outputs develops from nonsynchronous to a phase-synchronous state via +/-2pi phase jumps. We analyze this transition.

Detecting phase synchronization in a chaotic laser array

Detection of phase synchronization of coupled chaotic oscillators is examined experimentally for the case of a linear laser array. Phase variables are computed by applying a Gaussian filter, peaked at a positive frequency, to the signal obtained from the intensity time series of the individual lasers. Relationships between different frequency components of the oscillator dynamics that are not otherwise apparent are unambiguously detected.