Nonlinear parametric oscillations in certain stochastic systems: A random van der Pol oscillator

Astochastic model for some class ofnonlinear oscillators, which includes a van der Pol-type oscillator with random parameters, is analyzed in thediffusion limit. That is, small random fluctuations and long time are considered, while the nonlinearity is also assumed to be small. We show that there existstationary distributions, independent of the phase of the oscillator, a result proved earlier by R. L. Stratonovich assuming the random perturbations of the frequency to be delta correlated. The time behavior of the moments of the displacement of the oscillator from its rest position is also investigated and the results are compared with the corresponding ones for the linear random oscillator. A numerical study is also performed for the first two moments and plots are given.on leave from the University of Padua, Italy.     

计算相位响应曲线的方波扰动直接算法

通过相位响应曲线可对具有极限环周期运动的动力系统的性质有更为深入的理解.神经元是一个典型的动力系统,因此相位响应曲线提供了一种研究神经元重复周期放电行为的新思路.本文提出一种求解相位响应曲线的方法,即方波扰动的直接算法,通过Hodgkin-Huxley,Fitz Hugh-Nagumo,Morris-Lecar和Hindmarsh-Rose神经元模型验证该算法可计算周期峰放电、周期簇放电的相位响应曲线.该算法克服了其他算法在运用过程中的局限性.利用该算法计算结果表明:周期峰放电的相位响应曲线类型是由其分岔类型所决定;在Morris-Lecar模型中发现一种开始于Hopf分岔终止于鞍点同宿轨道分岔的阈上周期振荡,其相位响应曲线属于第二类型.通过大量的相位响应曲线的计算发现相位响应的相对大小及正负性仅取决于扰动所施加的时间,而且周期簇放电的相位响应曲线比周期峰放电的相位响应曲线更为复杂.     

重复频率可调谐的超低抖动光窄脉冲源的研究

提出了一种新型的基于光电振荡器的重复频率可调谐的超低抖动光窄脉冲源. 光电振荡器系统可以产生超低相位噪声的微波信号; 被该信号调制的直调光经过两次相位调制之后, 使光脉冲的啁啾增强; 再通过一段色散补偿光纤, 光脉冲被进一步压窄. 实验中使用YIG可调滤波器, 可以得到8–12 GHz内步进为200 MHz的可调谐微波信号, 因此光脉冲的重复频率具有可调谐性. 当微波信号即脉冲重复频率为9.6 GHz时, 测得脉冲宽度为3.7 ps, 相位噪声为-130.1 dBc/Hz@10 kHz. 由此得出光脉冲的瞬时抖动为60.1 fs (100 Hz–1 MHz), 因此该方案产生的光窄脉冲源具有超低的抖动.     

A geometric theory of chaotic phase synchronization

A rigorous mathematical treatment of chaotic phase synchronization is still lacking, although it has been observed in many numerical and experimental studies. In this article we address the extension of results on phase synchronization in periodic oscillators to systems with phase coherent chaotic attractors with small phase diffusion. As models of such systems we consider special flows over diffeomorphisms in which the neutral direction is periodically perturbed. A generalization of the Averaging Theorem for periodic systems is used to extend Kuramoto's geometric theory of phase locking in periodically forced limit cycle oscillators to this class of systems. This approach results in reduced equations describing the dynamics of the phase difference between drive and response systems over long time intervals. The reduced equations are used to illustrate how the structure of a chaotic attractor is important in its response to a periodic perturbation, and to conclude that chaotic phase coherent systems may not always be treated as noisy periodic oscillators in this context. Although this approach is strictly justified for periodic perturbations affecting only the phase variable of a chaotic oscillator, we argue that these ideas are applicable much more generally.     

Relative timing jitter measurements with an indirect phase comparison method

We propose and demonstrate experimentally a method for the sensitive measurement of the relative timing jitter of two mode-locked lasers, which can be either free-running or timing-synchronized to a common reference oscillator. The method is based on the indirect comparison of the phases of two photodetector outputs, using a microwave oscillator, the noise of which does not affect the results, electronic mixers, and a sampling oscilloscope. We carefully analyze and experimentally demonstrate the potential of this method. Compared to phase detector methods, it has a broader scope of applications and a lower sensitivity to intensity noise. We also obtained data on the coupling of intensity to timing noise in photodetectors. PACS 42.50.Lc; 42.60.Fc     

Monolithic 0–f Scheme-Based Frequency Comb Directly Driven by a High-Power Ti:Sapphire Oscillator

A monolithic O-f scheme-based femtosecond optical frequency comb directly driven by a high-power Ti:sapphire laser oscillator is demonstrated.The spectrum covering from 650 nm to 950 nm is generated from the Ti:sapphire oscillator with a repetition rate of 170 MHz.The average output power up to 630 mW is delivered under the pump power of 4.5 W.A 44-dB signal-to-noise ratio(SNR) of the carrier-envelope phase offset(CEO) beat note is achieved under the resolution of 100 kHz and is long-term stabilized to a reference source at 20 MHz.The integrated phase noise(IPN) in the range from 1 Hz to 1 MHz is calculated to be 138 mrad,corresponding to the timing jitter of 63 as at the central wavelength of 790 nm.     

Progress toward controlling in vivo fibrillating sheep atria using a nonlinear-dynamics-based closed-loop feedback method

We describe preliminary experiments on controlling in vivo atrial fibrillation using a closed-loop feedback protocol that measures the dynamics of the right atrium at a single spatial location and applies control perturbations at a single spatial location. This study allows investigation of control of cardiac dynamics in a preparation that is physiologically close to an in vivo human heart. The spatial-temporal response of the fibrillating sheep atrium is measured using a multi-channel electronic recording system to assess the control effectiveness. In an attempt to suppress fibrillation, we implement a scheme that paces occasionally the cardiac muscle with small shocks. When successful, the inter-activation time interval is the same and electrical stimuli are only applied when the controller senses that the dynamics are beginning to depart from the desired periodic rhythm. The shock timing is adjusted in real time using a control algorithm that attempts to synchronize the most recently measured inter-activation interval with the previous interval by inducing an activation at a time projected by the algorithm. The scheme is "single-sided" in that it can only shorten the inter-activation time but not lengthen it. Using probability distributions of the inter-activation time intervals, we find that the feedback protocol is not effective in regularizing the dynamics. One possible reason for the less-than-successful results is that the controller often attempts to stimulate the tissue while it is still in the refractory state and hence it does not induce an activation. (c) 2002 American Institute of Physics.     

Equalization-enhanced phase noise induced timing jitter

In electronic digital signal processing based optical communication systems, digital equalization for chromatic dispersion interacts with local oscillator phase noise to produce equalization-enhanced phase noise (EEPN). In addition to both phase and intensity noises, EEPN also induces timing jitter to the equalized signal. For a 100?Gbit/s quadrature-phase-shift keying signal with laser linewidth of 300?kHz, the timing jitter is up to 20% of the symbol interval for a transmission distance of 1500?km.     

Measurement of mode-locked laser timing jitter by use of phase-encoded optical sampling

The phase-noise characteristics of a harmonically mode-locked fiber laser are investigated with a new measurement technique called phase-encoded optical sampling. A polarization-maintaining ring laser is mode locked by use of the short-pulse electrical output of a resonant-tunneling diode oscillator, enabling it to produce 30-ps pulses at a 208-MHz repetition rate. The interferometric phase-encoded sampling technique provides 60-dB suppression of amplitude-jitter noise and allows supermode phase noise to be observed and quantified. The white-noise pulse-to-pulse timing jitter and the rms supermode timing jitter of the laser are measured to be less than 50 and 70 fs, respectively.     

Diode laser frequency-noise suppression by >50dB by use of electro-optic parametric master oscillators

We demonstrate a novel frequency-stabilization scheme for laser diodes that is capable of linewidth reduction by more than 5 orders of magnitude. In this master-slave scheme the diode laser emission is frequency-offset phase locked to the emission of an electro-optic parametric oscillator (EOPO), and the laser diode is simultaneously used as the EOPO pump source. As a result the initial frequency fluctuations of the pump are reduced to the intrinsic noise level of the EOPO, which can be extremely small. We demonstrate that subhertz linewidths of the beat notes of the signals of two of these systems can be readily achieved if acoustic perturbations are suppressed.     

Phase-rectified signal averaging for the detection of quasi-periodicities and the prediction of cardiovascular risk

We present the phase-rectified signal averaging (PRSA) method as an efficient technique for the study of quasi-periodic oscillations in noisy, nonstationary signals. It allows the assessment of system dynamics despite phase resetting and noise and in relation with either increases or decreases of the considered signal. We employ the method to study the quasi-periodicities of the human heart rate based on long-term ECG recordings. The center deflection of the PRSA curve characterizes the average capacity of the heart to decelerate (or accelerate) the cardiac rhythm. It can be measured by a central wavelet coefficient which we denote as deceleration capacity (DC). We find that decreased DC is a more precise predictor of mortality in survivors of heart attack than left ventricular ejection fraction, the current "gold standard" risk predictor. In addition, we discuss the dependence of the DC parameter on age and on diabetes.     

钛宝石飞秒激光振荡器的稳定性改善

对钛宝石飞秒激光器脉冲序列的强度和时间的稳定性进行了分析.实验比较了钛宝石飞秒激光器底板有无水冷的条件下,输出锁模脉冲序列的稳定性以及中心波长和光谱宽度的变化.结果表明对钛宝石飞秒激光器底板施加水冷可改善锁模脉冲的稳定性. 关键词： 钛宝石激光器 稳定性 飞秒脉冲     

Double Poincaré sections of a quasi-periodically forced,chaotic attractor

A nonlinear mechanical oscillator is forced with two incommensurate harmonic signals and chaotic vibrations are experimentally observed. The fractal nature of this strange attractor in four-dimensional phase space is revealed by using a double Poincaré section. This section involves a narrow timing pulse on one harmonic driving signal and a wider phase window on the other forcing harmonic signal. The resulting two-dimensional map shows a Cantor set structure characteristic of strange attractors. The transition from quasi-periodic to chaotic vibrations is also observed.     

Phase resetting and dynamics in isolated atrioventricular nodal cell clusters

In the heart, the AV node is the primary conduction pathway between the atria and ventricles and subserves an important function by virtue of its rate-dependent properties. Cell clusters isolated from the rabbit atrioventricular (AV) node beat with a stable rhythm (cycle length: 300-520 ms) and are characterized by slow action potential upstroke velocities (7 to 30 V/s). The goal of this study is to better characterize the phase resetting and the rhythms during periodic stimulation of this slow inward current system. Single or periodic depolarizing pulses (20 ms in duration) were injected into AV nodal cell clusters using glass microelectrodes. Phase resetting curves of both strong, weak as well as discontinuous types were obtained by applying single current pulses of different intensities and latencies following every ten action potentials. Graded responses were elicited in a wide range of stimulus phases and amplitudes. A single premature stimulus caused a transient prolongation of the cycle length. Sustained periodic stimulation, at rates faster than the intrinsic beat rate, resulted in various N:M (stimulus frequency: action potential frequency) entrainment rhythms as well as periodic or irregular changes in action potential morphology. The changes in action potential characteristics were evaluated by computing the area under the action potential trace and above a fixed threshold (-45 mV). We show that the variations in action potential morphology play a major role in the onset of complicated dynamics observed in this experimental preparation. In this context, the prediction of entrainment rhythms using techniques based on the iteration of phase resetting curves (PRCs) is inadequate since the PRC does not carry information directly related to the changes in action potential morphology. This study demonstrates the need to consider graded events which, though not propagated, have important implications in the understanding of dynamical diseases of the heart. (c) 1995 American Institute of Physics.     

Mode-locked laser pulse trains with subfemtosecond timing jitter synchronized to an optical reference oscillator

We independently phase lock the repetition rates of two femtosecond lasers at their approximately 456, 000th harmonic to a common optical oscillator. The timing jitter of each individual laser relative to the optical reference is only 0.45 fs in a 100-Hz bandwidth. Our method takes advantage of the tremendous leverage that is possible when stability is transferred from the optical to the microwave domain. The low timing jitter is commensurate with the independently measured fractional frequency instability in the repetition rates of < or = 2.3 x 10(-15) in 1-s averaging time, limited by the measurement system. The microwave signals at 1 GHz that are extracted by photodetection of the pulse trains have a 10-times-greater instability, confirming the presence of excess noise in the photodetection.     

Berry phase of primordial scalar and tensor perturbations in single-field inflationary models

In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes in terms of the Lewis–Riesenfeld phase. We conclude by discussing the discrepancy in the results of Pal et al. (2013) [21] for these Berry phases, which is resolved to yield agreement with our results.     

Observation of quantum-limited timing jitter in an active, harmonically mode-locked fiber laser

We report on the observation of quantum-limited timing jitter in a harmonically mode-locked soliton fiber laser with an ultralow-noise local oscillator. The effects of amplitude and phase modulation on the spectrum are described and compared with theory.     

Phase resetting effects for robust cycles between chaotic sets

In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated, owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena, including that of robust attractors showing chaotic itinerancy. At the simplest level this is an attracting heteroclinic cycle between equilibria, but cycles between more general invariant sets are also possible. In this paper we introduce and discuss an instructive example of an ordinary differential equation where one can observe and analyze robust cycling behavior. By design, we can show that there is a robust cycle between invariant sets that may be chaotic saddles (whose internal dynamics correspond to a R?ssler system), and/or saddle equilibria. For this model, we distinguish between cycling that includes phase resetting connections (where there is only one connecting trajectory) and more general non(phase) resetting cases, where there may be an infinite number (even a continuum) of connections. In the nonresetting case there is a question of connection selection: which connections are observed for typical attracted trajectories? We discuss the instability of this cycling to resonances of Lyapunov exponents and relate this to a conjecture that phase resetting cycles typically lead to stable periodic orbits at instability, whereas more general cases may give rise to "stuck on" cycling. Finally, we discuss how the presence of positive Lyapunov exponents of the chaotic saddle mean that we need to be very careful in interpreting numerical simulations where the return times become long; this can critically influence the simulation of phase resetting and connection selection.