Phase fluctuations of transient self-sustained oscillations

We experimentally traced time evolution of phase fluctuation which occurred in the phase shift keying.     

The influence of external fluctuations on self-sustained temporal oscillations

The influence of external fluctuations on the bifurcational behavior of two-dimensional dynamical systems exhibiting limit cycles is investigated. Studying both exactly and approximately solvable examples it is shown that the variances of the external fluctuations occur as additional bifurcation parameters. The threshold values for soft as well as for hard self-excitation of oscillations are affected by the external fluctuations. To classify bifurcations of dynamical systems in the presence of fluctuations some aspects of catastrophe theory are applied to the corresponding stationary probability distributions.     

Stochastic self-sustained oscillations of non-autonomous systems

In the present minireview, we analyze autonomous and non-autonomous oscillations of dynamical and stochastic systems in the framework of common concepts. We introduce the definition of an attractor for a non-autonomous system. We also propose the definition of self-sustained oscillations, which can be applied for both autonomous and non-autonomous systems. We consider noise-induced oscillations and formulate the definition of stochastic self-sustained oscillations for this case. All the statements made in this work are illustrated by particular examples.     

Effect of the fraction of semiconducting inclusions on the properties of self-sustained oscillations in a metal-semiconductor system

A model of self-sustained oscillations in a heterophase system consisting of metal and semiconductor layers is constructed. It is shown that parameters of self-sustained oscillations (amplitude and period) can be controlled by varying the fraction of metal inclusions in the semiconductor. The numerical solution of the system of equations for the heterophase system shows that, the higher the temperature coefficient of resistance of the metal, the stronger the effect of the metal impurity on the properties of the heterophase system, manifested in a decrease in the effective band gap and in suppression of self-sustained oscillations.     

Control of forced self-sustained oscillations via a backward time controller

A weakly non-linear self-sustained oscillator can be synchronized by an external force only in a certain domain of parameters. We exploit unstable periodic orbits and extend this domain via a small control perturbation. The controller is constructed as a backward time replica of the original oscillator that has the same periodic orbits but with the opposite stability properties. The control is achieved by synchronizing the original oscillator with its backward time replica. We demonstrate these ideas both theoretically and experimentally.     

Dominant phase-advanced driving analysis of self-sustained oscillations in biological networks

Oscillatory behaviors can be ubiquitously observed in various systems. Biological rhythms are significant in governing living activities of all units. The emergence of biological rhythms is the consequence of large numbers of units. In this paper we discuss several important examples of sustained oscillations in biological media, where the unit composed in the system does not possess the oscillation behavior. The dominant phase-advanced driving method is applied to study the skeletons and oscillatory organizing motifs in excitable networks and gene regulatory networks.     

Contribution to harmonic balance calculations of self-sustained periodic oscillations with focus on single-reed instruments

The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.     

Self-oscillations and critical fluctuations

An active system is analyzed whose parameter space contains a bistable region of stationary states bounded by a cuspidal point. This point is somewhat analogous to the critical point of a non-symmetry-breaking phase transition (in terms of high low-frequency susceptibility, fluctuation growth, etc.). The system has not only stationary states, but also periodic oscillatory ones. When parameters change so that the oscillatory instability threshold passes through the cuspidal point, the continuous spectrum of fluctuations transforms into the discrete spectrum of periodic oscillations. The dynamics associated with this transformation are examined.     

Intermittent dynamics of critical fluctuations

We argue that the fluctuations of the order parameter in a complex system at the critical point can be described in terms of intermittent dynamics of type I. Based on this observation we develop an algorithm to calculate the isothermal critical exponent delta for a "thermal" critical system. We apply successfully our approach to the 3D Ising model. The intermittent character of these "critical" dynamics guides to the introduction of a new exponent which extends the notion of the exponent delta to nonthermal systems.     

Scaling of fluctuations and critical exponents

We present a new technique to describe the abnormal behavior of certain fluctuation observables in the critical regime of quantum statistical systems which undergo a phase transition. The idea is to rescale the local fluctuation operators by a relevant external parameter of the system, in addition to the usual scaling with the inverse square root of the volume. The scaling indices used in this scaling procedure are directly related to the critical exponents. Furthermore, it is explained that this new method of scaling preserves the CCR structure of the algebra of macroscopic fluctuations. Finally, scaling indices are computed for the relevant microscopic observables at all temperatures in a mean field approximation for a quantum anharmonic crystal. These indices yield the same critical exponents as predicted by mean field theory.     

On the Ornstein-Zernike-theory of critical fluctuations

The Ornstein-Zernike (OZ)-theory is developed entirely in Fourier space. Three different regions of temperature are considered:

1. 1.
   T≧T′, whereT′ defines the upper limit of a certain “critical region”,     
   
   

Remarks on a coordinate system for critical fluctuations

The elements of a coordinate system for critical fluctuations are expressed in terms of the correlation functions which characterize the thermodynamic behavior of the system. As well, a k-dependent generalization of Le Chatelier's principle is derived.     

Self-synchronization of nonlinear oscillations in the presence of fluctuations

A statistical mechanical theory is presented for the self-organization of a macroscopic oscillation with the presence of external fluctuations in a system of Van der Pol oscillators coupled through dissipative interactions. Starting from Langevin equations for the Van der Pol oscillators, the static and dynamic characteristics are studied. The threshold condition is given by the relative size between the fluctuation and the interaction. The transitions between synchronous and asynchronous phases are well discussed by a Landau-type equation. The steady state value of the order parameter and the onset time are compared between the theory and the computer experiments and a good agreement is obtained.     

Magnetic resonance and self-sustained oscillations in an iron-yttrium garnet film in a vortex state

Some of the magnetic excitations in an iron-yttrium garnet film in a vortex state have been studied. A narrow (about 0.05 Oe) absorption line of high-frequency energy has been revealed in the absence of a magnetic field. A mechanism of this absorption has been proposed to explain such a small width of this line.