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An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator subjected to weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise., Comment: 16 pages, 6 figures

Recently there has been a surge of new interest in three-dimensional wake patterns. In the present work, we have devised a method to control the spanwise end conditions and wake patterns using “end suction”, which is both continuously-variable and admits transient control. Classical steady-state patterns, such as parallel or oblique shedding or the “chevron” patterns are simply induced. The wake, at a given Reynolds number, is receptive to a continuous range of oblique shedding angles (θ), rather than to discrete angles, and there is excellent agreement with the “cos θ” formula for oblique-shedding frequencies. We show that the laminar shedding regime exists up to Reynolds numbers (Re) of 205, and that the immense disparity among reported critical Re for wake transition (Re = 140–190) can be explained in terms of spanwise end contamination. Our transient experiments have resulted in the discovery of new phenomena such as “phase shocks” and “phase expansions”, which can be explained in terms of a simple model assuming constant normal wavelength of the wake pattern. Peter Monkewitz (Lausanne) also predicts such transient phenomena from a Guinzburg-Landau model for the wake.

We have studied both theoretically and experimentally how an LC series circuit connected in parallel to a Josephson junction influences the Josephson dynamics. The presence of the shell circuit introduces two energy scales, which in specific cases, can strongly differ from the plasma frequency of the isolated junction. Josephson junctions were manufactured using the Nb/Al-AlOx/Nb fabrication technology with various on-chip LC shunt circuits. Spectroscopic measurements in the quantum limit show excellent agreement with theory taking into account the shunt inductance and capacitance in the resistively and capacitively shunted junction model. The results clearly show that the dynamics of the system are two-dimensional, resulting in two resonant modes of the system. These findings have important implications for the design and operation of Josephson junction based quantum bits. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3581139]

We study the collective dynamics of a driven two mode Bose-Hubbard model in the Josephson interaction regime. The classical phase-space is mixed, with chaotic and regular components, that determine the dynamical nature of the fringe-visibility. For weak off-resonant drive, where the chaotic component is small, the many-body dynamics corresponds to that of a Kapitza pendulum, with the relative-phase $\varphi$ between the condensates playing the role of the pendulum angle. Using a master equation approach we show that the modulation of the inter-site potential barrier stabilizes the $\varphi=\pi$ 'inverted pendulum' coherent state, and protects the fringe visibility., Comment: 5 pages, 4 figures

We report a systematic study of the transport properties of high critical temperature superconductor (HTS) biepitaxial Josephson junctions in the submicron range. Junction performances point to more uniform and reproducible devices and to better control of d-wave intrinsic properties. Outcomes promote novel insights into the transport mechanisms across grain boundaries and encourage further developments in the control of dissipation in HTS devices. The application of nanotechnology to HTS could be an additional tool to properly engineer the junction properties to match specific circuit design also in view of the integration into hybrid quantum circuits. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3388035]

The phase dynamics of a semiconductor laser with optical feedback is studied by construction of the Hilbert phase from its experimentally measured intensity time series. The Hurst exponent is evaluated for the phase fluctuations and grows from 0.5 to approximately 0.7 (indicating fractional Brownian motion) as the feedback strength is increased. A comparison with numerical computations based on a delay-differential equation model shows excellent agreement and reveals the relative roles of spontaneous emission noise and deterministic dynamics for different feedback strengths.

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and non-vanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization., Comment: 22 pages, 7 figures, the paper is to be published in Chaos, 2005, vol.15, issue 2, see http://chaos.aip.org/

Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.

The evolution of the carrier-envelope offset phase ϕCEO of a 10-fs Ti:Sapphire laser has been traced on time scales from microseconds to seconds using various techniques. Precise locking of this phase has been achieved down to an rms deviation of 1/40 of an optical cycle. Stability measurements have been performed independently of the feedback loop, focusing on the phase jitter introduced by the feedback loop itself, the pump laser, and a prism compressor. It is shown that a multi-mode pump laser introduces more phase noise on ϕCEO than a single-mode pump laser.

Scanning tunneling microscope measurements on single crystals of Bi 2 Sr 2 CaCu 2 O 8 + x materials have shown that the d-wave superconductivity in cuprates has nanoscale inhomogeneities and is still robust in spite of theirpresence. We study the dynamics of Josephson coupling between such granular d-wave superconductors, focusing on the effect of nodal Cooper pairs and disorder. We find that the nodal Cooper pairs give rise to a power-law Josephson coupling which leads to the stabilization of the superconducting phase. Our findings suggest that the d-wave superconductivity in an array of grains is unexpectedly robust against a disordering transition, as observed in the experiments. Furthermore, we predict the existence of a planar Josephson-plasmon mode with characteristic frequency that decreases with temperature.

We analyze Fiske resonances of one-dimensional parallel arrays of underdamped Josephson tunnel junctions. They appear in the current voltage (I–V) characteristics as resonant current singularities (steps) at finite voltages Vm when a magnetic field H is applied perpendicular to the array cells. We present measurements of current step amplitudes Icm, and of the maximum Josephson current Ic0 as a function of H, for arrays made of four, six, and ten small Josephson junctions. The I–V characteristics of the arrays exhibit three, five, and eight resonant current steps, respectively, at increasing voltages. In all devices we find that the current amplitude of the highest order step has just one maximum occurring at H≈1/2H*, being H* the first field value where Ic0(H*)≈Ic0(0). Numerical simulations of the phase dynamics in small parallel arrays as a function of the applied magnetic flux are performed. The results of the simulation reproduce the experimentally observed features.

We study the spatial stability of systems at onset of the temporal intermittent transition to chaos. We show that the phase dynamics during laminar episodes, described as orbits near a saddle-node bifurcation of limit cycles, is second order in time and can lead to propagative behaviour.

The phase dynamic equation of motion for a propagating periodic structure is derived in a euclidean invariant manner. The formulation is applied to the generalized Swift-Hohenberg model where the coefficients are complex numbers.

In many chemical reactions, an activation barrier must be overcome before a chemical transformation can occur. As such, understanding the behaviour of molecules in energetically excited states is critical to understanding the chemical changes that these molecules undergo. Among the most prominent reactions for mankind to understand are chemical changes that occur in our own biological molecules. A notable example is the focus towards understanding the interaction of DNA with ultraviolet radiation and the subsequent chemical changes. However, the interaction of radiation with large biological structures is highly complex, and thus the photochemistry of these systems as a whole is poorly understood. Studying the gas-phase spectroscopy and ultrafast dynamics of the building blocks of these more complex biomolecules offers the tantalizing prospect of providing a scientifically intuitive bottom-up approach, beginning with the study of the subunits of large polymeric biomolecules and monitoring the evolution in photochemistry as the complexity of the molecules is increased. While highly attractive, one of the main challenges of this approach is in transferring large, and in many cases, thermally labile molecules into vacuum. This review discusses the recent advances in cutting-edge experimental methodologies, emerging as excellent candidates for progressing this bottom-up approach.

This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in terms of average frequency, frequency detuning and parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insight into the dynamics inside amplitude death regions, eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions., Comment: 25 pages, 13 figures

A single-layer graphene has been uniformly grown on a Cu surface at elevated temperatures by thermal processing of a poly(methyl methacrylate) (PMMA) film in a rapid thermal annealing (RTA) system under vacuum. The detailed chemistry of the transition from solid-state carbon to graphene on the catalytic Cu surface was investigated by performing in situ residual gas analysis while PMMA/Cu-foil samples were being heated, in conjunction with interrupted growth studies to reconstruct ex situ the heating process. The data clearly show that the formation of graphene occurs by vaporizing hydrocarbon molecules from PMMA, such as methane and/or methyl radicals, which act as precursors, rather than by the direct graphitization of solid-state carbon. We also found that the temperature for vaporizing hydrocarbon molecules from PMMA and the length of time the gaseous hydrocarbon atmosphere is maintained, which are dependent on both the heating temperature profile and the amount of a solid carbon feedstock, are the dominant factors that determine the crystalline quality of the resulting graphene film. Under optimal growth conditions, the PMMA-derived graphene was found to have a carrier (hole) mobility as high as ∼2700 cm(2) V(-1) s(-1) at room temperature, which is superior to common graphene converted from solid carbon.

The phase dynamics of wavy vortex flow is studied by applying a forced modulation to the upper boundary of a large-aspect-ratio concentric cylinders system. The experimental results are consistent with a model based on coupled phase equations. We find that the perturbations propagate as traveling waves parallel with the axis of the system when there is a strong coupling between the axial and azimuthal phase variables, and diffusively for weak coupling. The propagating wave speed is measured for a range of Reynolds numbers.

Using molecular dynamics simulations, the melting points and liquid phase dynamic properties were studied for four alkyl-imidazolium-based ionic liquids, 1-n-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]), 1-n-butyl-2,3-dimethylimidazolium hexafluorophosphate ([BMMIM][PF6]), 1-ethyl-3-methylimidazolium hexafluorophosphate ([EMIM][PF6]), and 1-ethyl-2,3-dimethylimidazolium hexafluorophosphate ([EMMIM][PF6]), respectively. Experimentally it has been observed that the substitution of a methyl group for a hydrogen at the C2 position of the cation ring leads to an increase in both the melting point and liquid phase viscosity, contrary to arguments that had been made regarding associations between the ions. The melting points of the four ionic liquids were accurately predicted using simulations, as were the trends in viscosity. The simulation results show that the origin of the effect is mainly entropic, although enthalpy also plays an important role.

Synaptically coupled neurons show in-phase or antiphase synchrony depending on the chemical and dynamical nature of the synapse. Deterministic theory helps predict the phase differences between two phase-locked oscillators when the coupling is weak. In the presence of noise, however, deterministic theory faces difficulty when the coexistence of multiple stable oscillatory solutions occurs. We analyze the solution structure of two coupled neuronal oscillators for parameter values between a subcritical Hopf bifurcation point and a saddle node point of the periodic branch that bifurcates from the Hopf point, where a rich variety of coexisting solutions including asymmetric localized oscillations occurs. We construct these solutions via a multiscale analysis and explore the general bifurcation scenario using the lambda-omega model. We show for both excitatory and inhibitory synapses that noise causes important changes in the phase and amplitude dynamics of such coupled neuronal oscillators when multiple oscillatory solutions coexist. Mixed-mode oscillations occur when distinct bistable solutions are randomly visited. The phase difference between the coupled oscillators in the localized solution, coexisting with in-phase or antiphase solutions, is clearly represented in the stochastic phase dynamics.

We propose a device based on a Q-switched self-sustained oscillator with two nonlinear delayed feedback loops. Due to the appropriate phase transformation of the signal that influences the generation of each successive pulse, the phase difference between the two neighboring pulses evolves according to the Bernoulli doubling map. It corresponds to a hyperbolic chaotic attractor yielding a robust, structurally stable chaos. We discuss possible experimental implementations of the scheme.

The temperature-dependent helicity modulus Γ(T) of site-diluted triangular arrays of proximity-effect coupled Pb/Cu/Pb Josephson junctions has been extracted from measurements of the complex ac sheet conductance performed in the frequency range 0.1 Hz to 20 kHz in zero magnetic field. At low frequencies Γ(T) exhibits the characteristic superfluid drop predicted by the Kosterlitz-Thouless theory, demonstrating that a disordered array behaves like a homogeneous two-dimensional system at length scales-larger than the percolation correlation length.

We present the nonlinear phase equations describing the stability of a one-dimensional periodic pattern, with mean flow effect due to Galilean invariance. We show that the phase dynamics is second order in time, and could lead to an oscillatory instability of the pattern.

A fundamental equation of the phase dynamics is derived for a class of periodic structures by a systematic application of the multiple-scale expansion method, in which the instantaneous rate of change of the phase is shown to be determined only by the local values of spatial derivatives of the phase itself. The analys is shows that the phase equation is inapplicable to conservative systems. The expansion method is also applied to a class of forced periodic structures, and the same type of equation is derived although the dependent variable then does not correspond to the phase of the periodic structure.

Recently two groups1–3 have described the observation of confined states in an annulus near the onset of convection in binary fluid mixtures. These confined states are characterized by the fact that for part of the annulus a convective pattern is visible — that is the envelope of the convective pattern assumes a finite value — whereas the rest of the container is in the heat conduction state. These observations are now under intense investigation theoretically4–6 and experimentally2,3.

The asymptotic dynamics of the spin autocorrelation function is studied in the Griffiths phase of bond-dilute Ising and Heisenberg ferromagnets by Monte Carlo simulation, for simple relaxational dynamics (model A). Systems above, at and below the percolation threshold are studied. Relaxation is non-exponential in all cases. Agreement with theoretical predictions based on clustering arguments is excellent for the Heisenberg systems, less so for the Ising systems.

We show that the spontaneous formation of transverse spatial patterns due to diffraction in lasers can be described by a phase diffusion equation of the Kuramoto-Sivashinsky kind. Hence the origin of the pattern formation lies in spatial instabilities of the phase of the complex slowly varying laser field amplitude.

The application of the transient grating method to the understanding of gas-phase velocity distributions and collisional effects is presented. Theoretical models are discussed in view of the experimental data obtained from iodine vapor. Applications of the transient grating method to other gas-phase problems are also mentioned.

Hysteretic spiral turbulence is a remarkable phenomenon of coexistence of turbulent and laminar domains in Taylor-Couette flow. We observe and measure for the first time a nonuniform pitch in long geometries and its dependence on boundary conditions at the cylinder ends, and we explain these results within the framework of phase dynamics. We also discuss the influence of secondary flow on the azimuthal width of the spiral.

Spontaneous contractions of cardiomyocytes are driven by calcium oscillations due to the activity of ionic calcium channels and pumps. The beating phase is related to the time-dependent deviation of the oscillations from their average frequency, due to noise and the resulting cellular response. Here, we demonstrate experimentally that, in addition to the short-time (1--2 Hz), beat-to-beat variability, there are long-time correlations (tens of minutes) in the beating phase dynamics of isolated cardiomyocytes. Our theoretical model relates these long-time correlations to cellular regulation that restores the frequency to its average, homeostatic value in response to stochastic perturbations.

Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. We demonstrate experimentally the appearance of giant fractional Shapiro steps in anisotropic Josephson junction arrays as unambiguous evidence of a skewed current phase relationship. Introducing anisotropy in the array results in a giant collective high frequency response that reflects the properties of a single junction, as evidenced by the observation of a Fraunhofer like magnetic field dependence of the total critical current of the system. The observed phase dynamics can be perfectly captured within an extended resistively shunted Josephson junction model. These results directly indicate the potential of Josephson junction arrays to explore the current phase relation in a very broad frequency range (down to 50 MHz) and in a wide variety of novel link materials exhibiting non-conventional current phase relationships. Giant fractional Shapiro steps have been observed in Josephson junction arrays as resulting from magnetic flux quantization in the two-dimensional array. Here, the authors demonstrate the observation of giant fractional Shapiro steps in an anisotropic Josephson junction array, as unambiguous evidence of a skewed current phase relationship.

Adaptive dynamical networks appear in various real-word systems. One of the simplest phenomenological models for investigating basic properties of adaptive networks is the system of coupled phase oscillators with adaptive couplings. In this paper, we investigate the dynamics of this system. We extend recent results on the appearance of hierarchical frequency-multi-clusters by investigating the effect of the time-scale separation. We show that the slow adaptation in comparison with the fast phase dynamics is necessary for the emergence of the multi-clusters and their stability. Additionally, we study the role of double antipodal clusters, which appear to be unstable for all considered parameter values. We show that such states can be observed for a relatively long time, i.e., they are metastable. A geometrical explanation for such an effect is based on the emergence of a heteroclinic orbit., 16 pages, 8 figures

We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on chimera states involving amplitude as well as phase dynamics, complex topologies like small-world or hierarchical (fractal), noise, and delay. We show that a plethora of novel chimera patterns arise if one goes beyond the Kuramoto phase oscillator model. For the FitzHugh-Nagumo system, the Van der Pol oscillator, and the Stuart-Landau oscillator with symmetry-breaking coupling various multi-chimera patterns including amplitude chimeras and chimera death occur. To test the robustness of chimera patterns with respect to changes in the structure of the network, regular rings with coupling range R, small-world, and fractal topologies are studied. We also address the robustness of amplitude chimera states in the presence of noise. If delay is added, the lifetime of transient chimeras can be drastically increased.

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking., Comment: 10 pages, 8 figures

In this work, we consider a ring of coupled electronic (Wien-bridge) oscillators from a perspective combining modeling, simulation, and experimental observation. Following up on earlier work characterizing the pairwise interaction of Wien-bridge oscillators by Kuramoto-Sakaguchi phase dynamics, we develop a lattice model for a chain thereof, featuring an exponentially decaying spatial kernel. We find that for certain values of the Sakaguchi parameter α, states of traveling phase-domain fronts involving the coexistence of two clearly separated regions of distinct dynamical behavior, can establish themselves in the ring lattice. Experiments and simulations show that stationary coexistence domains of synchronization only manifest themselves with the introduction of a local impurity; here an incoherent cluster of oscillators can arise reminiscent of the chimera states in a range of systems with homogeneous oscillators and suitable nonlocal interactions between them.

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states. Here we explore systems in which both synchronization and swarming occur together. Specifically, we consider oscillators whose phase dynamics and spatial dynamics are coupled. We call them swarmalators, to highlight their dual character. A case study of a generalized Kuramoto model predicts five collective states as possible long-term modes of organization. These states may be observable in groups of sperm, Japanese tree frogs, colloidal suspensions of magnetic particles, and other biological and physical systems in which self-assembly and synchronization interact., Collective self-organized behavior can be observed in a variety of systems such as colloids and microswimmers. Here O’Keeffe et al. propose a model of oscillators which move in space and tend to synchronize with neighboring oscillators and outline five types of collective self-organized states.

We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and non-isochronocity of the interactions on the pattern formation. A few additional links facilitate the emergence of the fully synchronized state. With larger non-isochronicity, complex rotating waves or persistent irregular phase dynamics can derail the convergence to global synchronization. The observed long transients of irregular phase dynamics exemplify the possibility of a sudden onset of hyper synchronous behavior without any external stimulus or network reorganization., Comment: 4 pages main text and 4 pages supplemental material

Phase plays a crucial role in many quantum effects including interference. Here we lay the foundations for the study of phase in probabilistic theories more generally. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalized probabilistic theories or the convex framework. The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference in several example theories: classical probability theory, a version of Spekkens' toy model, quantum theory and box-world. We find that phase is ubiquitous; any non-classical theory can be said to have non-trivial phase dynamics. © IOP Publishing and Deutsche Physikalische Gesellschaft.

Synchronization phenomena in a fluid dynamical analogue of atmospheric circulation is studied experimentally by investigating the dynamics of a pair of thermally coupled, rotating baroclinic annulus systems. The coupling between the systems is in the well-known master-slave configuration in both periodic and chaotic regimes. Synchronization tools such as phase dynamics analysis are used to study the dynamics of the coupled system and demonstrate phase synchronization and imperfect phase synchronization, depending upon the coupling strength and parameter mismatch.

A study of Hodgkin–Huxley (HH) neuron under external sinusoidal excited stimulus is presented in this paper. As is well known, the stimulus frequency is to be considered as a bifurcate parameter and numerous phenomena, such as synchronization, period and chaos appear alternatively with the changing of the stimulus frequency. For the stimulus frequency less than 2fB (fB being the base frequency in this paper), the simulation results demonstrate that the single HH neuron could completely convey the sinusoidal signal in anti-phase into interspike interval (ISI) sequences. We also report, perhaps for the first time, another kind of phenomenon, the beat phenomenon, which exists in the phase dynamics of the ISI sequences of the HH neuron stimulated by a sinusoidal current. It is shown furthermore that intermittent transition results in the general route to chaos.

Synchrony and antiphase phase locking in synaptically coupled neurons have been studied by employing numerical simulations. By using a Morris–Lecar (ML) model of two coupled stochastic neural oscillators, the effect of noise on the phase dynamics is extensively investigated in two different synaptic-coupling schemes; reciprocal excitatory and excitatory–inhibitory synapses. All possible dynamical features are presented in the parameter space of two important branching parameters, the coupling strength gsyn and the synaptic time delay τd. In this work, antiphase states are observed and analyzed as the breaking dynamics of synchrony. As a transition state from synchrony to antiphase phase locking in the stochastic system, intermittent antiphase states are also reported.

We demonstrate that E×B shear, V_{E×B}^{'}, governs the dynamics of the cross phase of the peeling-ballooning-(PB-)mode-driven heat flux, and so determines the evolution from the edge-localized (ELMy) H mode to the quiescent (Q) H mode. A physics-based scaling of the critical E×B shearing rate (V_{E×B,cr}^{'}) for accessing the QH mode is predicted. The ELMy H mode to the QH-mode evolution is shown to follow from the conversion from a phase locked state to a phase slip state. In the phase locked state, PB modes are pumped continuously, so bursts occur. In the slip state, the PB activity is a coherent oscillation. Stronger E×B shearing implies a higher phase slip frequency. This finding predicts a new state of cross phase dynamics and shows a new way to understand the physics mechanism for ELMy to the QH-mode evolution.

New types of stable discrete solitons are discovered. They represent the first example of asymmetric dark solitons and shock waves with a nonzero background. Both types of solutions exhibit a strong intrinsic phase dynamics. Their domains of existence and criteria of stability are identified. Numerical experiments support the analytical findings.

We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.

We investigate the phase dynamics of moderately damped NbN/AlN/NbN Josephson junctions and we present experimental results on detailed aspects of phase diffusion processes. We measure both single escape and multiple escape and retrapping events obtaining a crossover temperature T* from Kramers to phase diffusion switching. We observe a clear dependence of the crossover temperature T* by the bias current ramp rate, while the damping factor Q remains the same. The measured effect is in strong agreement with theoretical predictions reported by Fenton and Warburton. © 2014 AIP Publishing LLC.

We consider a $\ensuremath{\varphi}$ Josephson junction, which has a bistable zero-voltage state with the stationary phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. In the nonzero voltage state the phase ``moves'' viscously along a tilted periodic double-well potential. When the tilting is reduced quasistatically, the phase is retrapped in one of the potential wells. We study the viscous phase dynamics to determine in which well ($\ensuremath{-}\ensuremath{\varphi}$ or $+\ensuremath{\varphi}$) the phase is retrapped for a given damping, when the junction returns from the finite-voltage state back to the zero-voltage state. In the limit of low damping, the $\ensuremath{\varphi}$ Josephson junction exhibits a butterfly effect---extreme sensitivity of the destination well on damping. This leads to an impossibility to predict the destination well.

We experimentally investigate the phase dynamics of laser networks with homogenous time-delayed mutual coupling and establish the fundamental rules that govern their state of synchronization. We identified a specific substructure that imposes its synchronization state on the entire network and show that for any coupling configuration the network forms at most two synchronized clusters. Our results indicate that the synchronization state of the network is a nonlocal phenomenon and cannot be deduced by decomposing the network into smaller substructures, each with its individual synchronization state.

We study the relationship between synchronization and the rate with which information is exchanged between nodes in a spatio-temporal network that describes the dynamics of classical particles under a substrate Remoissenet-Peyrard potential. We also show how phase and complete synchronization can be detected in this network. The difficulty in detecting phase synchronization in such a network appears due to the highly non-coherent character of the particle dynamics which unables a proper definition of the phase dynamics. The difficulty in detecting complete synchronization appears due to the spatio character of the potential which results in an asymptotic state highly dependent on the initial state., to appear in PRAMANA

Synchronization phenomena in coupled circadian oscillators of plant leaves were investigated experimentally using bioluminescence technology for a clock gene. Analyzing the phase of circadian oscillation, the phase-wave propagations and the phase delay caused by the vein network were observed. We describe these phase dynamics using a two-layer model with coupled Stuart-Landau equations. Global synchronization of circadian oscillators in the leaf is also investigated.

We demonstrate that a multiple delayed feedback is a powerful tool to control coherence properties of autonomous self-sustained oscillators. We derive the equation for the phase dynamics in presence of noise and delay, and analyze it analytically. In Gaussian approximation a closed set of equations for the frequency and the diffusion constant is obtained. Solutions of these equations are in good agreement with direct numerical simulations.