Chimera dynamics in nonlocally coupled moving phase oscillators

Chimera states, a symmetry-breaking spatiotemporal pattern in nonlocally coupled dynamical units, prevail in a variety of systems. However, the interaction structures among oscillators are static in most of studies on chimera state. In this work, we consider a population of agents. Each agent carries a phase oscillator. We assume that agents perform Brownian motions on a ring and interact with each other with a kernel function dependent on the distance between them. When agents are motionless, the model allows for several dynamical states including two different chimera states (the type-I and the type-II chimeras). The movement of agents changes the relative positions among them and produces perpetual noise to impact on the model dynamics. We find that the response of the coupled phase oscillators to the movement of agents depends on both the phase lag α, determining the stabilities of chimera states, and the agent mobility D. For low mobility, the synchronous state transits to the type-I chimera state for α close to π/2 and attracts other initial states otherwise. For intermediate mobility, the coupled oscillators randomly jump among different dynamical states and the jump dynamics depends on α. We investigate the statistical properties in these different dynamical regimes and present the scaling laws between the transient time and the mobility for low mobility and relations between the mean lifetimes of different dynamical states and the mobility for intermediate mobility.     

Virial Theorem for a Class of Quantum Nonlinear Harmonic Oscillators

In this paper,the Virial Theorem based on a class of quantum nonlinear harmonic oscillators is presented.This relationship has to do with parameter λ and ∂/∂λ,where the λ is a real number.When λ=0,the nonlinear harmonic oscillator naturally reduces to the usual quantum linear harmonic oscillator,and the Virial Theorem also reduces to the usual Virial Theorem.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.     

Explorations of the Phase-Space Linearization Method for Deterministic and Stochastic Nonlinear Dynamical Systems

A new numeric-analytic phase-space linearization (PSL) schemefor a class of nonlinear oscillators with continuous vector fields isinvestigated in this study. The essence of the PSL method is to replacethe nonlinear vector field by a set of conditionally linear ones, eachvalid either over a short segment of the evolving trajectory or(equivalently) over a sufficiently small interval of time. This conceptmay be usefully exploited to arrive at certain explicit and implicitintegration schemes for analyses and simulations. The explicit schemes,which are found to have ready extensions to systems under stochasticinputs, are first numerically implemented for a few oft-used nonlineardynamical systems under (deterministic) sinusoidal inputs. An estimateof an upper bound to the local error in terms of the chosen time stepsize is provided. The explicit scheme of local linearization is nextextended to nonlinear oscillators under stochastic excitations, namelywhite noise processes, which are formal derivatives of one or acombination of Gauss–Markov processes. Since the PSL approach is todecompose the nonlinear operator into a set of linear operators, theprinciples of linear random vibration may be suitably exploited toarrive at a faster Monte-Carlo scheme for computing the responsestatistics, both in stationary and nonstationary regimes. A fewexamples, based on Ueda's and Duffing–Holmes' oscillators, arepresented and compared with exact solutions, whenever available, toverify the correctness and versatility of the proposed schemes.     

Transitions from strongly to weakly-nonlinear dynamics in a class of exactly solvable oscillators and nonlinear beat phenomena

In this paper, a regular perturbation tool is suggested to bridge the gap between weakly and strongly nonlinear dynamics based on exactly solvable oscillators with trigonometric characteristics considered by Nesterov (Proc. Mosc. Inst. Power Eng. 357:68–70, 1978). It is shown that the corresponding action-angle variables linearize the original oscillators with no special functions involved. As a result, linear and strongly nonlinear areas of the dynamics are described within the same perturbation procedure. The developed tool is applied then to analyzing the nonlinear beat and energy localization phenomena in two linearly coupled Duffing oscillators. It is shown that the principal phase variable describing the beat phenomena is governed by the hardening Nesterov oscillator with some perturbation due to qubic nonlinearity and coupling between the oscillators. As a result, the above class of strongly nonlinear oscillators is given clear physical meaning, whereas a closed form analytical solution is obtained for nonlinear beat and localization dynamics. Based on this solution, necessary and sufficient conditions for onset of energy localization are obtained.     

Liouville Integrability of Conservative Peakons for a Modified CH equation

The modified Camassa-Holm (also called FORQ) equation is one of numerous cousins of the Camassa-Holm equation possessing non-smoth solitons (peakons) as special solutions. The peakon sector of solutions is not uniquely defined: in one peakon sector (dissipative^a) the Sobolev H¹ norm is not preserved, in the other sector (conservative), introduced in [2], the time evolution of peakons leaves the H¹ norm invariant. In this Letter, it is shown that the conservative peakon equations of the modified Camassa-Holm can be given an appropriate Poisson structure relative to which the equations are Hamiltonian and, in fact, Liouville integrable. The latter is proved directly by exploiting the inverse spectral techniques, especially asymptotic analysis of solutions, developed elsewhere [3].     

Generation of squeezed vacuum on cesium D2 line down to kilohertz range

We report the experimental generation of a squeezed vacuum at frequencies ranging from 2.5 kHz to 200 kHz that is resonant on the cesium D2 line by using a below-threshold optical parametric oscillator(OPO). The OPO is based on a periodically-poled KTiOPO_4(PPKTP) crystal that is pumped using a bow-tie four-mirror ring frequency doubler. The phase of the squeezed light is controlled using a quantum noise locking technique. At a pump power of 115 mW, maximum quadrature phase squeezing of 3.5 d B and anti-squeezing of 7.5 d B are detected using a home-made balanced homodyne detector. This squeezed vacuum at an atomic transition in the kilohertz range is an ideal quantum source for quantum metrology of enhancing measurement precision, especially for ultra-sensitive measurement of weak magnetic fields when using a Cs atomic magnetometer in the audio frequency range.     

基于DFB腔注入锁定效应的可调谐光电振荡器

提出一种基于分布反馈光注入锁定效应的可调谐光电振荡器,其环路主要由马赫曾德尔调制器、光电探测器、环形器、分布反馈激光器和射频放大器顺接而成,分布反馈激光器是系统关键器件,通过分布反馈激光器光注入锁定效应,分布反馈腔在光域实现了微波光子滤波器功能,无需传统光电振荡器必须的射频带通滤波器.同时,由于分布反馈激光器注入锁定提高了环路Q值,因此系统可采用短环路结构,从而降低了光纤因温度敏感对微波信号稳定性的影响并减小了整个系统的尺寸.另外,通过调节注入光波长和功率可改变该微波光子滤波器的中心频率,从而可实现系统的可调谐性.理论分析了该光电振荡器的原理和微波光子滤波器的调谐性,在此基础上开展了实验验证.结果表明该光电振荡器能够产生18.7～21.6 GHz的可调微波信号,在1 kHz频偏处的相位噪声为-90 dBc/Hz.     

Approximate analytical solutions to a conservative oscillator using global residue harmonic balance method

In the current research paper, a conservative system comprising of a mass grounded by linear and nonlinear springs in series connection is studied. The equation of motion for the aforementioned system has been derived as a nonlinear ordinary differential equation with inertia and static–type cubic nonlinearities. The global residue harmonic balance method is applied to obtain an approximate analytical frequency and periodic solution of the problem. Using the obtained analytical expressions, the influences of the hardening and softening nonlinear spring on the non–dimensional frequency are investigated. The results show that developing the system nonlinearity leads the displacement of the mass and the deflection of linear spring to approach each other. Moreover, comparison of the results obtained using the proposed procedure with those achieved by other methods such as numerical method, variational iteration method and harmonic balance approach demonstrates the accuracy and advantages of the current approach.     

Mutual Interdependence of Partitions Functions in Vicinity T g of Transition

The solid—liquid transition is described by use of the model incorporating the non-linear interactive oscillators. The individual non-linear oscillators are formed from the mechanical units of about the monomer size and produce the vibrations on the lower amplitude level, for the solid phase, either in amorphous or in crystal-like form. As the temperature starts to overpass the Vogel's temperature, the vibrations of individual units are big enough to cause the permanent displacements of the individual vibrating particles; the material starts to flow and the process of diffusion begins as well. As the temperature is passing through T _g vicinity, the large mechanical heterogeneity's start to appear as the small percentage of oscillators enlarge their amplitude of vibrations enormously and act as the local stress perturbations centers. These centers are responsible for the destruction of original matrixes and the sharp onset of fluidity and diffusion takes place. The upper amplitude of vibration motion is the basic property of a liquid state. The whole system of vibrations in matrix is described by use of techniques of deterministic chaos theories. It is shown as well, how the mutual interplay of the partition functions (vibration and cohesive), plays the important role in transition from liquid to solid states.This revised version was published online in November 2005 with corrections to the Cover Date.