Travelling chimeras in oscillator lattices with advective-diffusive coupling.

We consider a one-dimensional array of phase oscillators coupled via an auxiliary complex field. While in the seminal chimera studies by Kumamoto and Battogtokh only diffusion of the field was considered, we include advection which makes the coupling left-right asymmetric. Chimera starts to move and we demonstrate that a weakly turbulent moving pattern appears. It possesses a relatively large synchronous domain where the phases are nearly equal, and a more disordered domain where the local driving field is small. For a dense system with a large number of oscillators, there are strong local correlations in the disordered domain, which at most places looks like a smooth phase profile. We find also exact regular travelling wave chimera-like solutions of different complexity, but only some of them are stable. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia.

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. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Levels of sirolimus in saliva and blood following mouthwash application.

OBJECTIVES: Sirolimus (rapamycin) is a mammalian target of rapamycin (mTOR) inhibitor with antiproliferative activity. Its systemic administration is currently evaluated for the management of squamous cell carcinoma and various oral disorders. Topical oral application can enhance availability, efficacy and improve safety and compliance. Our objective was to evaluate the release profile and the safety of a sirolimus mouthwash. SUBJECTS AND METHODS: A sirolimus mouthwash (0.05 mg ml(-1) ) was applied to ten healthy male volunteers. Saliva and blood samples were taken after rinsing. Mass spectrometry and chemiluminescent microparticle immunoassay were used to determine saliva and blood levels of sirolimus. A topical oral release profile measurement and safety evaluation were performed. RESULTS: After rinsing with the mouthwash, a classic immediate release profile was noted in the oral cavity. Extremely high initial sirolimus levels rapidly declined over a 4-hour period. Systemic exposure was limited, with a maximum level significantly lower than therapeutic doses, and safety was confirmed. CONCLUSIONS: A single rinse with sirolimus mouthwash leads to high transient levels of the drug in the saliva. Although levels were variable, a therapeutic concentration was achieved topically along with minimal systemic absorption. These results broaden the potential clinical use of oral topical rapalogs.

[Update and review of oral lichen planus].

Lichen planus is a chronic mucucutaneous disease affecting the oral cavity in up to 2% of the population. It has variable oral manifestations, may be asymptomatic or accompanied by severe pain. It has features which are similar to autoimmune diseases although its pathogenesis is not fully understood. Stress is associated with exacerbations and dental materials and/or medications can cause lichenoid reactions. Some reports link hepatitis C with the condition. The chronic nature of the disease, its occasional severity, the fact it is considered a pre-malignant condition, together with its prevalence, make it essential for the general dentist to be aware and informed about it. The dentist's role is important at all stages includes a thorough clinical examination, identification pathological lesions, and following diagnosis, regular dental treatment and minimization of exacerbations. A specialist should be consulted regarding diagnosis and ongoing dental treatments. The specialist will add local or systemic treatments as needed and provide long-term follow-up in order to diagnose malignant changes as quickly as possible.

Spreading of energy in the Ding-Dong model.

We study the properties of energy spreading in a lattice of elastically colliding harmonic oscillators (Ding-Dong model). We demonstrate that in the regular lattice the spreading from a localized initial state is mediated by compactons and chaotic breathers. In a disordered lattice, the compactons do not exist, and the spreading eventually stops, resulting in a finite configuration with a few chaotic spots.

Disorder fosters chimera in an array of motile particles.

We consider an array of nonlocally coupled oscillators on a ring, which for equally spaced units possesses a Kuramoto-Battogtokh chimera regime and a synchronous state. We demonstrate that disorder in oscillators positions leads to a transition from the synchronous to the chimera state. For a static (quenched) disorder we find that the probability of synchrony survival depends on the number of particles, from nearly zero at small populations to one in the thermodynamic limit. Furthermore, we demonstrate how the synchrony gets destroyed for randomly (ballistically or diffusively) moving oscillators. We show that, depending on the number of oscillators, there are different scalings of the transition time with this number and the velocity of the units.

Abnormal mixing of passive scalars in chaotic flows.

We study the relaxation of a passive scalar towards the uniform equilibrium distribution in an advection-diffusion problem where the phase space for the pure advection problem is a mixture of chaotic domains and elliptic islands. Since the advection-diffusion problem is linear, the relaxation can be characterized by the eigenvalues and eigenmodes of the evolution operator. Almost degenerate eigenvalues then give rise to deviations from simple exponential decay behavior. We show by example that the corresponding eigenmodes can be supported by islands or weakly connected chaotic domains. These theoretical considerations are related to some experimental observations in two-dimensional flows.

Reconstruction of a neural network from a time series of firing rates.

Randomly coupled neural fields demonstrate irregular variation of firing rates, if the coupling is strong enough, as has been shown by Sompolinsky et al. [Phys. Rev. Lett. 61, 259 (1988)]PRLTAO0031-900710.1103/PhysRevLett.61.259. We present a method for reconstruction of the coupling matrix from a time series of irregular firing rates. The approach is based on the particular property of the nonlinearity in the coupling, as the latter is determined by a sigmoidal gain function. We demonstrate that for a large enough data set and a small measurement noise, the method gives an accurate estimation of the coupling matrix and of other parameters of the system, including the gain function.

Marginal chimera state at cross-frequency locking of pulse-coupled neural networks.

We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies or become frequency locked. In the observed 2:1 locking state of the mean fields, individual neurons in one population are asynchronous with the mean fields, while in another population they have the same frequency as the mean field. These synchronous neurons form a chimera state, where part of them build a fully synchronized cluster, while other remain scattered. We explain this chimera as a marginal one, caused by a self-organized neutral dynamics of the effective circle map.

Continuous approach for the random-field Ising chain.

We study the random-field Ising chain in the limit of strong exchange coupling. In order to calculate the free energy we apply a continuous Langevin-type approach. This continuous model can be solved exactly, whereupon we are able to locate the crossover between an exponential and a power-law decay of the free energy with increasing coupling strength. In terms of magnetization, this crossover restricts the validity of the linear scaling. The known analytical results for the free energy are recovered in the corresponding limits. The outcomes of numerical computations for the free energy are presented, which confirm the results of the continuous approach. We also discuss the validity of the replica method which we then utilize to investigate the sample-to-sample fluctuations of the finite size free energy.

Multiscaling of noise-induced parametric instability.

We describe the statistical properties of growth rates of a linear oscillator driven by a parametric noise. We show that in general the fluctuations of local Lyapunov exponents are non-Gaussian and demonstrate multiscaling. Analytical calculations of the generalized Lyapunov exponents are complemented with approximative and numerical results; this allows us to identify the parameter range where the deviations from the Gaussian statistics become important.

Comment on "Simple approach to the creation of a strange nonchaotic attractor in any chaotic system".

We address the problem of existence of strange nonchaotic attractors (SNAs) in quasiperiodically forced dynamical systems. Recently, Shuai and Wong [Phys. Rev. E 59, 5338 (1999)] suggested a universal method for constructing a SNA in an arbitrary system possessing chaos. We demonstrate here that, in general, this method fails. For arbitrary systems, it gives a SNA only in a vicinity of transition to chaos. We discuss also a special example, where the method by Shuai and Wong indeed produces a SNA.

Comment on "Intermittency in chaotic rotations".

Lai et al. [Phys. Rev. E 62, R29 (2000)] claim that the angular velocity of the phase point moving along the chaotic trajectory in a properly chosen projection (the instantaneous frequency) is intermittent. Using the same examples, namely the Rössler and the Lorenz systems, we show the absence of intermittency in the dynamics of the instantaneous frequency. This is confirmed by demonstrating that the phase dynamics exhibits normal diffusion. We argue that the nonintermittent behavior is generic.

Dynamic localization of Lyapunov vectors in Hamiltonian lattices.

The convergence of the Lyapunov vector toward its asymptotic shape is investigated in two different one-dimensional Hamiltonian lattices: the so-called Fermi-Pasta-Ulam and Phi(4) chains. In both cases, we find an anomalous behavior, i.e., a clear difference from the previously conjectured analogy with the Kardar-Parisi-Zhang equation. The origin of the discrepancy is eventually traced back to the existence of nontrivial long-range correlations both in space and time. As a consequence of this anomaly, we find that, in a Hamiltonian lattice, the largest Lyapunov exponent is affected by stronger finite-size corrections than standard space-time chaos.

Controlling oscillator coherence by delayed feedback.

We demonstrate that the coherence of a noisy or chaotic self-sustained oscillator can be efficiently controlled by the delayed feedback. We develop a theory of this effect, considering noisy systems in the Gaussian approximation. We obtain a closed equation system for the phase diffusion constant and the mean frequency of oscillation. For weak feedback and strong noise, the theory is in good agreement with the numerics. We discuss possible applications of the effect for the synchronization control.

Detecting direction of coupling in interacting oscillators.

We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.

Lyapunov exponents in disordered chaotic systems: avoided crossing and level statistics.

The behavior of the Lyapunov exponents (LEs) of a disordered system consisting of mutually coupled chaotic maps with different parameters is studied. The LEs are demonstrated to exhibit avoided crossing and level repulsion, qualitatively similar to the behavior of energy levels in quantum chaos. Recent results for the coupling dependence of the LEs of two coupled chaotic systems are used to explain the phenomenon and to derive an approximate expression for the distribution functions of LE spacings. The depletion of the level spacing distribution is shown to be exponentially strong at small values. The results are interpreted in terms of the random matrix theory.

Comment on "Phase synchronization in discrete chaotic systems".

Chen et al. [Phys. Rev. E 61, 2559 (2000)] recently proposed an extension of the concept of phase for discrete chaotic systems. Using the newly introduced definition of phase they studied the dynamics of coupled map lattices and compared these dynamics with phase synchronization of coupled continuous-time chaotic systems. In this paper we illustrate by two simple counterexamples that the angle variable introduced by Chen et al. fails to satisfy the basic requirements to the proper phase. Furthermore, we argue that an extension of the notion of phase synchronization to generic discrete maps is doubtful.

Transcritical riddling in a system of coupled maps.

The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.

From multiplicative noise to directed percolation in wetting transitions.

A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behavior observed along the transition line changes from a directed-percolation type to a multiplicative-noise type. Numerical simulations allow for a quantitative study of the multicritical point separating the two regions. Mean-field arguments and the mapping on yet a simpler model provide some further insight on the overall scenario.