Alternate Phase Synchronization in Coupled Chaotic Oscillators

Phase locking dynamics in coupled chaotic oscillators is investigated.For chaotic systems with a poorly coherent phase variable,the imperfect phase locking can be observed befor the onset of a complete phase synchronization.The temporal alternations among n:n phase lockings are found,which originate from an overlap of m:n Arnold tongues.     

1:1 Mode locking and generalized synchronization in mechanical oscillators

We describe the relation between the complete, phase and generalized synchronization of the mechanical oscillators (response system) driven by the chaotic signal generated by the driven system. We identified the close dependence between the changes in the spectrum of Lyapunov exponents and a transition to different types of synchronization. The strict connection between the complete synchronization (imperfect complete synchronization) of response oscillators and their phase or generalized synchronization with the driving system (the (1:1) mode locking) is shown. We argue that the observed phenomena are generic in the parameter space and preserved in the presence of a small parameter mismatch.     

Beam Recombination Characteristics in Array Laser Amplification Using Stimulated Brillouin Scattering Phase Conjugation

Beam recombination characteristics were numerically investigated in array laser amplification using stimulated Brillouin scattering phase conjugation. To clarify the effect of piston errors due to imperfect phase locking, spatial intensity profiles of the beam recombination output were calculated in both the near and the far field on the basis of Rayleigh-Sommerfeld diffraction theory. The analyses indicate that piston errors are seriously detrimental to the quality of a beam recombination output and should be eliminated by a proper phase locking. It is also found that the gap between the beam splitting-combining wedges has a negligible effect.Presented at 1996 International Workshop on Interferometry (IWI ‘96), August 27-29, Saitama, Japan.     

高功率振荡器锁相的粒子模拟

用粒子(PIC,Particle-in-Cell)模拟方法研究了当前颇感兴趣的高功率振荡器的锁相问题。给出了模拟计算结果。讨论了锁相(Phase Locking)、Priming和InjectionSeeding等概念的区别。     

Nonlinear oscillations of the FitzHugh-Nagumo equations under combined external and two-frequency parametric excitations

The continuous FitzHugh-Nagumo (FHN for short) model is transformed into modified van der Pol oscillator with asymmetry under external and two-frequency parametric excitations. At the first, the dependence of the solutions on a combined external and two-frequency parametric stimulus forcing is investigated. By using the multiple scale method, ranges of applied current and/or parametric forcing in which nonlinear oscillations are observed are described. Second, when the multiple scale method cannot be used, we numerically prove that in the modified van der Pol oscillator with asymmetry under external and two-frequency parametric excitations, chaos and periodic solution depending on the combination between different frequencies of the model should appear. We also show that the amplitude of the oscillations can be reduced or increased. To do this, we perform the study of the FHN model by choosing a range of parameters exhibiting Hopf bifurcation and two qualitative different regimes in phase portrait.     

Responses to amplitude-modulated tones in the auditory nerve of the cat.

Sinusoidally amplitude-modulated (AM) tones are frequently used in psychophysical and physiological studies, yet a comprehensive study on the coding of AM tones in the auditory nerve is lacking. AM responses of single auditory-nerve fibers of the cat are studied, systematically varying modulation depth, frequency, and sound level. Synchrony-level functions were nonmonotonic with maximum values that were inversely correlated with spontaneous rate (SR). In most fibers, envelope phase-locking showed a positive gain. Modulation transfer functions were uniformly low pass. Their corner frequency increased with characteristic frequency (CF), but changed little for CFs above 10 kHz. The highest modulation frequencies to which phase locking occurred were more than 0.8 oct lower than the highest frequencies to which phase locking to pure tones occurs. Cumulative, or unwrapped, phase increased linearly with modulation frequency: The slope was inversely related to CF, and slightly higher than group delays reported for pure tones. High SR, low CF fibers showed the poorest envelope phase locking. In some low CF fibers, phase locking increased at high levels, associated with "peak-splitting" phenomena. Changes in average rate due to modulation were small, and could be enhancement or suppression.     

两个延迟耦合FitzHugh-Nagumo系统的动力学行为

考虑了两个延迟耦合FitzHugh-Nagumo系统，首先分析两点延迟耦合的动力学行为，给出静息态的局部稳定和不稳定的参数区. 螺旋波同步、共同的静息态以及两个系统不同的状态出现在静息态稳定参数区内，在这些态的过渡耦合强度参数区内会出现很多演化图样，它们反映了螺旋波波头、波体和波尾的不同，也反映空间尺度对螺旋波的影响.讨论了静息态局部不稳定参数区内，两点延迟耦合的动力学行为和相应参数下两个延迟耦合反应-扩散系统的斑图动力学行为. 关键词： FitzHugh-Nagumo系统 螺旋波 同步     

Observation of two distinct phase states in a self-phase-locked type II phase-matched optical parametric oscillator

We demonstrate self-phase locking in a type II phase-matched optical parametric oscillator by mutual injection locking. An intracavity quarter-wave plate provides polarization mixing between the orthogonally polarized signal and idler that induces signal-idler self-phase locking when their frequency difference is within the capture range. We observed two distinct phase states that differ in their oscillator thresholds and their signal-idler phase differences, in good agreement with theory.     

Space-time considerations in the phase locking of high harmonics

The combination of several high order harmonics can produce an attosecond pulse train, provided that the harmonics are locked in phase to each other. We present calculations that evaluate the degree of phase locking that is achieved in argon and neon gases interacting with an intense, 50 fs laser pulse, for a range of macroscopic conditions. We find that phase locking depends on both the temporal and the spatial phase behavior of the harmonics, as determined by the interplay between the intrinsic dipole phase and the phase matching in the nonlinear medium. We show that, as a consequence of this, it is not possible to compensate for a lack of phase locking by purely temporal phase manipulation.     

Phase locking in a multicore fiber laser by means of a Talbot resonator

We report phase locking of a diode-pumped multicore fiber laser with a circular array of 18 Nd-doped emitters (microcores) acting as an active medium. Phase locking was achieved in a Talbot resonator configuration. We present calculations of the effective reflection coefficients that are due to self-imaging. Far-field distributions and near-field pattern of several supermodes are calculated and compared with experimental results.     

Coupling efficiency for phase locking of a spin transfer nano-oscillator to a microwave current

The phase locking behavior of spin transfer nano-oscillators (STNOs) to an external microwave signal is experimentally studied as a function of the STNO intrinsic parameters. We extract the coupling strength from our data using the derived phase dynamics of a forced STNO. The predicted trends on the coupling strength for phase locking as a function of intrinsic features of the oscillators, i.e., power, linewidth, agility in current, are central to optimize the emitted power in arrays of mutually coupled STNOs.     

Dynamics of a FitzHugh-Nagumo system subjected to autocorrelated noise

We analyze the dynamics of the FitzHugh-Nagumo (FHN) model in the presence of colored noise and a periodic signal. Two cases are considered: (i) the dynamics of the membrane potential is affected by the noise, (ii) the slow dynamics of the recovery variable is subject to noise. We investigate the role of the colored noise on the neuron dynamics by the mean response time (MRT) of the neuron. We find meaningful modifications of the resonant activation (RA) and noise enhanced stability (NES) phenomena due to the correlation time of the noise. For strongly correlated noise we observe suppression of NES effect and persistence of RA phenomenon, with an efficiency enhancement of the neuronal response. Finally we show that the self-correlation of the colored noise causes a reduction of the effective noise intensity, which appears as a rescaling of the fluctuations affecting the FHN system.     

Collective modes — An analytical model for active mode locking in the transient case

A novel concept is presented for the pulse generation in the linear regime of an actively loss modulated laser. Introducing collective laser modes, the frequency detuning of the modulator and the statistical initial situation of the laser starting from spontaneous emission become tractable. Formation of a mode-locked pulse is described by the selection of collective modes. Perfect mode locking corresponds to the survival of a single mode in the build-up process. A variety of laser properties is derived from the solution and compared with experiment. The model predicts imperfect mode locking (with a finite number of collective modes) in the transient case in agreement with experimental findings.     

Phase synchronization from noisy univariate signals

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft phase locking; another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Kármán vortex flow meters.     

Parameter estimation of the FitzHugh-Nagumo model using noisy measurements for membrane potential

This paper proposes an identification method to estimate the parameters of the FitzHugh-Nagumo (FHN) model for a neuron using noisy measurements available from a voltage-clamp experiment. By eliminating an unmeasurable recovery variable from the FHN model, a parametric second order ordinary differential equation for the only measurable membrane potential variable can be obtained. In the presence of the measurement noise, a simple least squares method is employed to estimate the associated parameters involved in the FHN model. Although the available measurements for the membrane potential are contaminated with noises, the proposed identification method aided by wavelet denoising can also give the FHN model parameters with satisfactory accuracy. Finally, two simulation examples demonstrate the effectiveness of the proposed method.     

非高斯噪声激励下FitzHugh-Nagumo神经元系统的随机共振

研究了乘性非高斯噪声和加性高斯白噪声共同激励下FitzHugh-Nagumo(FHN) 神经元系统的随机共振问题. 利用路径积分法和两态模型理论, 推导出系统信噪比的表达式. 研究结果表明: 系统参数在不同的取值条件下, FHN神经元模型出现了随机共振和双重随机共振现象. 此外, 非高斯参数q在不同的取值条件下, 乘性噪声强度和加性噪声强度对信噪比的影响是不同的. 非高斯噪声的加入有利于增强FHN神经元系统的信号响应.     

Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators

A Lyapunov function for the phase-locked state of the Kuramoto model of non-linearly coupled oscillators is presented. It is also valid for finite-range interactions and allows the introduction of thermodynamic formalism such as ground states and universality classes. For the Kuramoto model, a minimum of the Lyapunov function corresponds to a ground state of a system with frustration: the interaction between the oscillators,XY spins, is ferromagnetic, whereas the random frequencies induce random fields which try to break the ferromagnetic order, i.e., global phase locking. The ensuing arguments imply asymptotic stability of the phase-locked state (up to degeneracy) and hold for any probability distribution of the frequencies. Special attention is given to discrete distribution functions. We argue that in this case a perfect locking on each of the sublattices which correspond to the frequencies results, but that a partial locking of some but not all sublattices is not to be expected. The order parameter of the phase-locked state is shown to have a strictly positive lower bound (r 1/2), so that a continuous transition to a nonlocked state with vanishing order parameter is to be excluded.     

Experimental demonstration of coherent beam combining over a 7 km propagation path

We demonstrate coherent combining (phase locking) of seven laser beams emerging from an adaptive fiber-collimator array over a 7 km atmospheric propagation path using a target-in-the-loop (TIL) setting. Adaptive control of the piston and the tip and tilt wavefront phase at each fiber-collimator subaperture resulted in automatic focusing of the combined beam onto an unresolved retroreflector target (corner cube) with precompensation of quasi-static and atmospheric turbulence-induced phase aberrations. Both phase locking (piston) and tip-tilt control were performed by maximizing the target-return optical power using iterative stochastic parallel gradient descent (SPGD) techniques. The performance of TIL coherent beam combining and atmospheric mitigation was significantly increased by using an SPGD control variation that accounts for the round-trip propagation delay (delayed SPGD).     

A strip extracting algorithm for phase noise measurement and coherent beam combining of fiber amplifiers

We present a strip extracting algorithm (SEA) for detecting and locking the phase noise of fiber amplifiers. Based on the algorithm, the phase noise of a 10 W Yb fiber amplifier is obtained and locked with an active segment mirror (ASM) and a high-speed CCD camera. Experimental results indicate that within the first 3 seconds after turn-on transients occur the amplitude of phase noise exceeds 20 waves, whereas in thermal steady-state operation it amounts to only several waves for the same time span. After phase locking, the Peak-to-Valley (PV) value of phase noise is close to ～1/10λ (λ=1064 nm), and the control bandwidth of the system is ～25 Hz.