Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory.

A general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system, using one-dimensional time series only. It is based on the introduction of angles and radii of return times maps, and on studying the dynamics of the angles. An explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data. It is valid under conditions of weak forcing. This correspondence is confirmed numerically for a nonstationary process in a forced Van der Pol system. A model describing the angles’ behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived

Bimodality and hysteresis in systems driven by confined L\'evy flights

We demonstrate occurrence of bimodality and dynamical hysteresis in a system describing an overdamped quartic oscillator perturbed by additive white and asymmetric L\'evy noise. Investigated estimators of the stationary probability density profiles display not only a turnover from unimodal to bimodal character but also a change in a relative stability of stationary states that depends on the asymmetry parameter of the underlying noise term. When varying the asymmetry parameter cyclically, the system exhibits a hysteresis in the occupation of a chosen stationary state.Comment: 4 pages, 5 figures, 30 reference

Synchronization of chaotic oscillator time scales

This paper deals with the chaotic oscillator synchronization. A new approach to detect the synchronized behaviour of chaotic oscillators has been proposed. This approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators. It has been shown that complete synchronization, phase synchronization, lag synchronization and generalized synchronization are the particular cases of the synchronized behavior called as "time--scale synchronization". The quantitative measure of chaotic oscillator synchronous behavior has been proposed. This approach has been applied for the coupled Rossler systems.Comment: 29 pages, 11 figures, published in JETP. 100, 4 (2005) 784-79

Dependence of element composition of bile of freshwater and marine fishes on some abiotic and biotic factors

Introduction: The elemental composition and physical properties of fish bile is a very important marker for ecotoxicological and physiological studies as bile is able to accumulate elements from environmental compartments. In the present study we focused on the effects of long term (seasons and years) and spatial distance (different water bodies) as well as other biotic (feeding habits, fish species, gut morphology) and abiotic (water salinity) factors on element composition of bile of 429 individuals belonging to 22 forms/species of fishes. Methods: Element composition was determined using an inductively coupled plasma optical emission spectrometry. The fishes were analyzed from one marine (the Kandalaksha Gulf of the White Sea), two freshwater oligotrophic (Teletskoye and Baunt lakes), and one freshwater eutrophic water body (Chany Lake). In parallel, we have estimated the volume and density of bile from the same fishes using an automatic pipette and electronic balance. Results and discussion: Based on fish bile density and volume data, we hypothesize that gastric fish species (those fishes that have a stomach) require a low volume of bile, but with higher density if compared to agastric fish species (those lacking a stomach) that mainly possessed large volumes of bile, but with a lower density. We have found that the concentrations of the following Na, K, Ca, Mg, S, P (major elements) and Al, Cu, Fe, Sr, Zn (trace elements) were the highest among the 28 elements studied. There were significant findings to contribute to a better understanding of the physiology of bile. First, we have determined the conditions formed in a water body in a given year (season) are more important for element composition of fish bile rather than other tested factors (feeding habits, gut morphology, etc.). Second, the feeding habits of fishes (carnivorous compared to non-carnivorous) had a significant effect based on differences among several elements. Third, the clear distinction between marine and freshwater fishes was found only for K and Na. Understanding which elements are produced as part of waste elimination and those that are present as a consequence of vital biological functions could improve the ecotoxicological study of bile as a marker of heavy metal contamination.The sample collection, expedition, and chemical analyses (for all fish except pike, perch, roach, and ide) were paid by the Russian Science Foundation (grant number 19-74-10054). The sample chemical analyses for pike and perch was supported by the Russian Foundation for Basic Research (grant number 19-34-60028) whereas for roach and ide was paid by Russian international scientific collaboration program Mega-grant (mega-grant № 075-15-2022-1134).info:eu-repo/semantics/publishedVersio

Co-occurrence of resonant activation and noise-enhanced stability in a model of cancer growth in the presence of immune response

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, the molecular fluctuations can be approximated as a realization of a Brownian dynamics for which the model reaction kinetics takes on the form of a stochastic differential equation. After eliminating a fast kinetics, the model can be rephrased into a form of a one-dimensional overdamped Langevin equation. We discuss physical aspects of environmental noises acting in such a reduced system, pointing out the possibility of coexistence of dynamical regimes where noise-enhanced stability and resonant activation phenomena can be observed together.Comment: 18 pages, 11 figures, published in Physical Review E 74, 041904 (2006

Nonlinear oscillator with parametric colored noise: some analytical results

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is colored because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (P.D.F.) of the system and to derive the behavior of physical observables in the long time limit

Current-voltage characteristic of narrow superconducting wires: bifurcation phenomena

The current-voltage characteristics of long and narrow superconducting channels are investigated using the time-dependent Ginzburg-Landau equations for complex order parameter. We found out that the steps in the current voltage characteristic can be associated with bifurcations of either steady or oscillatory solution. We revealed typical instabilities which induced the singularities in current-voltage characteristics, and analytically estimated period of oscillations and average voltage in the vicinity of the critical currents. Our results show that these bifurcations can substantially complicate dynamics of the order parameter and eventually lead to appearance of such phenomena as multistability and chaos. The discussed bifurcation phenomena sheds a light on some recent experimental findings

Generalized Chaotic Synchronizationin Coupled Ginzburg-Landau Equations

Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling betweenthe systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.Comment: 12 page