Loss enhanced phase locking in coupled oscillators

Phase locking, which is achieved by transferring some energy from one oscillator to the others, strongly depends on the coupling strength between the oscillators. Typically, the coupling strength must be above a certain threshold in order to achieve phase locking. Here we show how this threshold can be significantly reduced when phase-dependent losses are introduced into the oscillators. Specifically, the coupling strength can be reduced by at least an order of magnitude, thereby substantially decreasing the needed transfer of energy between oscillators. The resulting enhancement of phase locking does not only influence the laser research area, but also affects many other areas that involve coupled ensembles.     

Analysis of synchronized regimes for injection-locked spin-transfer nano-oscillators

The large-angle magnetization dynamics of an injection-locked spin-transfer nano-oscillator (STNO) is studied. The magnetic system is subject to the action of time-varying spin-polarized currents and external magnetic fields. The uniform mode theory is developed and describes the hysteretic synchronization mechanism in terms of bifurcations of equilibria and limit cycles of appropriate dynamical systems. Analytical predictions of control parameters for the synchronization between the magnetization self-oscillation and the external microwave excitations (current, field) are provided. The effect of temperature on the locking band and the hysteretic character of the oscillation response is analyzed. An analytical approach is developed to determine the thermally induced sidebands in the power spectral density of phase-locked oscillations as a function of control parameters. The analytical predictions are in good agreement with the results of numerical simulations.     

Design optimization for microwave coupling structures of a digital-to-analog converter based on series arrays of high-temperature superconducting Josephson junctions

A new coupling scheme of the external microwave signal for a digital-to-analog converter based on series arrays of high-temperature superconducting Josephson junctions has been proposed. It is suggested to couple the meander-like array inductively to a parallel microwave transmission line. Within the resistively shunted junction model different types of microwave coupling structures were analyzed with the goal to reduce the mutual phase locking and to achieve high output power and phase-locking stability. A harmonic balance technique was used to derive an analytic expression connecting the amplitudes of microwave voltages and currents in the array and the frequency of the external signal. Numerical simulations were performed to determine the boundaries of stable locking as a function of circuit parameters.     

Repulsive synchronization in an array of phase oscillators

We study the dynamics of a repulsively coupled array of phase oscillators. For an array of globally coupled identical oscillators, repulsive coupling results in a family of synchronized regimes characterized by zero mean field. If the number of oscillators is sufficiently large, phase locking among oscillators is destroyed, independently of the coupling strength, when the oscillators' natural frequencies are not the same. In locally coupled networks, however, phase locking occurs even for nonidentical oscillators when the coupling strength is sufficiently strong.     

Suppression of Chaos and Phase Locking in Two Coupled Nonidentical Neurons under Periodic Input

Dynamical behaviour of two coupled neurons with at least one of them being chaotic is presented. Bifurcation diagrams and Lyapunov exponents are calculated to diagnose the dynamical behaviour of the coupled neurons with the increasing coupling strength. It is found that when the coupling strength increases, a chaotic neuron can be controlled by the coupling between neurons. At the same time, phase locking is studied by the maxima of the differences of instantaneous phases and average frequencies between two coupled neurons, and the inherent connection of phase locking and the suppression of chaos is formulated. It is observed that the onset of phase locking is closely related to the suppression of chaos. Finally, a way for suppression of chaos in two coupled nonidentical neurons under periodic input is suggested.     

利用全光纤耦合环实现三路光纤激光器的相位锁定

利用三个2×2的光纤耦合器按一定规则联接成一个全光纤耦合环,该耦合环将三个独立的掺铒光纤激光器连成一个锁相阵列. 由于耦合环的引入,锁相阵列的整体损耗减小,且三个单元激光器之间可以进行有效的能量相互注入耦合,进而实现阵列的锁相输出. 实验中观察到的远场干涉图样和锁相前后的输出光谱均表明三路光纤激光器实现了相位锁定,当三路抽运源的功率均为100 mW时,获得了92 mW的稳定相干输出. 关键词： 光纤激光器 相干合成 光纤耦合器 相位锁定     

Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin-Huxley neuronal networks

In this paper, we study the effect of time-periodic coupling strength (TPCS) on the spiking coherence of Newman-Watts small-world networks of stochastic Hodgkin-Huxley (HH) neurons and investigate the relations between the coupling strength and channel noise when coherence resonance (CR) occurs. It is found that, when the amplitude of TPCS is varied, the spiking induced by channel noise can exhibit CR and coherence bi-resonance (CBR), and the CR moves to a smaller patch area (bigger channel noise) when the amplitude increases; when the frequency of TPCS is varied, the intrinsic spiking can exhibit CBR and multiple CR, and the CR always occurs when the frequency is equal to or multiple of the spiking period, manifesting as the locking between the frequencies of the intrinsic spiking and the coupling strength. These results show that TPCS can greatly enhance and optimize the intrinsic spiking coherence, and favors the spiking with bigger channel noise to exhibit CR. This implies that, compared to constant coupling strength, TPCS may play a more efficient role for improving the time precision of the information processing in stochastic neuronal networks.     

Synchronization in a chain of nearest neighbors coupled oscillators with fixed ends

We investigate a system of coupled phase oscillators with nearest neighbors coupling in a chain with fixed ends. We find that the system synchronizes to a common value of the time-averaged frequency, which depends on the initial phases of the oscillators at the ends of the chain. This time-averaged frequency decays as the coupling strength increases. Near the transition to the frozen state, the time-averaged frequency has a power law behavior as a function of the coupling strength, with synchronized time-averaged frequency equal to zero. Associated with this power law, there is an increase in phases of each oscillator with 2pi jumps with a scaling law of the elapsed time between jumps. During the interval between the full frequency synchronization and the transition to the frozen state, the maximum Lyapunov exponent indicates quasiperiodicity. Time series analysis of the oscillators frequency shows this quasiperiodicity, as the coupling strength increases.     

振幅耦合动态网络中相邻结点间的相同步

研究用适当的量化指标来刻画动态网络的相同步,为此定义了新的量化指标:相邻结点的网络平均锁相值和网络平均相频差.动态网络结点选择的是多旋转中心的Lorenz混沌振子,对Lorenz系统进行柱面坐标变换,用振幅耦合方法构造动态网络.分别对星形网络和小世界网络进行了仿真计算,结果表明随着耦合强度的增大,网络中相邻结点的两个系统之间存在相同步现象,而且相同步行为与定义的量化指标之间存在较准确的对应关系.     

Synchronization with an arbitrary phase shift in a pair of synaptically coupled neural oscillators

The phase dynamics of a pair of spiking neural oscillators coupled by a unidirectional nonlinear connection has been studied. The synchronization effect with the controlled relative phase of spikes has been obtained for various coupling strengths and depolarization parameters. It has been found that the phase value is determined by the difference between the depolarization levels of neurons and is independent of the synaptic coupling strength. The synchronization mechanism has been studied by means of the construction and analysis of one-dimensional phase maps. The phase locking effect for spikes has been interpreted in application to the synaptic plasticity in neurobiology.     

Phase—Locking Dynamics in Coupled Circle—Map Lattices

The phase-locking dynamics in 1D and 2D lattices of non-identical coupled circle maps is explored.A global phase locking can be attained via a cascade of clustering processes with the increase of the coupling strength.Collective spatiotemporal dynamics is observed when a global phase locking is reached.Crisis-induced desynchronization is found,and its consequent spatiotemporal chaos is studied.     

Modulation-free optical locking of an external-cavity diode laser to a filter cavity

Optical locking to a filter cavity is an effective method to eliminate the limitations of an external-cavity diode laser, such as broad spontaneous emission backgrounds and frequency jitters. Stable operation of the optical locking requires simultaneous control of the feedback phase and the diode-laser frequency. Frequency dither is usually used to extract the two error signals, but this causes extra frequency modulation in the output beam. A modulation-free method for deriving the error signals by modulating the laser-cavity coupling strength is demonstrated with a violet diode laser. A modulation-free linewidth upper limit of about 7 kHz for a 1 s measurement is realized by the method.     

Spin transfer nano-oscillator based on synthetic antiferromagnetic skyrmion pair assisted by perpendicular fixed magnetic field

As a microwave generator, spin transfer nano-oscillator (STNO) based on skyrmion promises to become one of the next-generation spintronic devices. However, there still exist a few limitations to the practical applications. In this paper, we propose a new STNO based on synthetic antiferromagnetic (SAF) skyrmion pair assisted by a perpendicular fixed magnetic field. It is found that the oscillation frequency of this kind of STNO can reach up to 5.0 GHz, and the multiple oscillation peak with higher frequency can be realized under a fixed out-of-plane magnetic field. Further investigation shows that the skyrmion stability is improved by bilayer antiferromagnetic coupling, which guarantees the stability process of skyrmion under higher spin-polarized current density. Our results provide the alternative possibilities for designing new skyrmion-based STNO to further improve the oscillation frequency, and realize the output of multiple frequency microwave signal.     

利用一种改进模型研究谐振器耦合时的约瑟夫森结的响应(英文)

提出了一种改进的谐振器耦合时的约瑟夫森结模型,模型考虑了结与谐振器之间的耦合强度。利用这种模型,研究了谐振器耦合时的约瑟夫森结的响应,包括单结的电压自锁定和结阵列的相位互锁定现象。研究了耦合强度、谐振器的品质因数和谐振频率对电压自锁定的影响,并给出了合理的解释。此外,还对结阵列的相位互锁定强度对锁定电压和结数量的依赖关系进行了研究,并与理论值进行了比较。所得结果对谐振器耦合下的约瑟夫森结的应用具有指导意义。     

Phase stability theory of Bloch eigenstates in active photonic lattices with coupled microlaser arrays

An generic model for the lattice dynamics of coupled microlaser arrays is employed for the lattice stability analysis. Nonlinear cross-cavity gain-coupling effects, characterizing active lattices, are included via the gain dependence on carrier depletion and cross-cavity hole burning. Passive near neighbor interactions (inter-cavity absorption and mirror reflection interference) are also included. The introduction of lattice-orthogonal modes simplifies the derivation of the coupled rate equations. The interaction phase among sites exhibits spontaneous long range “crystallization" into periodic Bloch states whereby the cavity radiation envelopes behave as laser “macro-atoms". The sign of the coupling coefficients as a function of geometry determines in- vs. out-of-phase locking and has practical implications for array design. Emphasis is placed on the stability analysis of Bloch states by including earlier omitted [1] effects of phase perturbations. The importance of the linewidth factor ι is uncovered: unconditional stability results for ι ≤1, otherwise a stability threshold exists for the coupling strength among sites. Choice of low ι gain material permits phase stability with high coupling strength, beneficial in overcoming manufacturing variations among array cavity parameters.     

Phase diagram for the Winfree model of coupled nonlinear oscillators

In 1967 Winfree proposed a mean-field model for the spontaneous synchronization of chorusing crickets, flashing fireflies, circadian pacemaker cells, or other large populations of biological oscillators. Here we give the first bifurcation analysis of the model, for a tractable special case. The system displays rich collective dynamics as a function of the coupling strength and the spread of natural frequencies. Besides incoherence, frequency locking, and oscillator death, there exist hybrid solutions that combine two or more of these states. We present the phase diagram and derive several of the stability boundaries analytically.     

约瑟夫森结(阵列)与谐振器的耦合效应研究

利用一种新的电路模型系统研究了约瑟夫森结(阵列)与谐振器的耦合效应.以结的电压自锁定台阶幅度ΔI为目标值,得到了谐振电路的电阻R、谐振频率fr对耦合的影响规律,并给出了合理解释;以结阵列的相位互锁定强度IL为目标,研究了IL对锁定电压VL的依赖关系,同时,通过相关计算将其与通常电路模型下得到的结果进行了比较.     

Spiking behavior in a noise-driven system combining oscillatory and excitatory properties

We show that firing activity (spiking) can be regularized by noise in a FitzHugh-Nagumo (FHN) neuron model when operating slightly beyond the supercritical Hopf bifurcation (in the "canard" region). We also provide the conditions for imperfect phase locking between interspike intervals and low amplitude quasiharmonic oscillations. For the imperfect phase locking no need exists of an external signal as it follows from the FHN intrinsic dynamics.     

高温超导混频器在锁相稳频源中的应用

基于小型脉冲管制冷机,设计并改善了与其配套的锁相混频系统,用约瑟夫森颗粒边界结实现了高温超导3mm波段96次谐波混频,完成了60次谐波下压控振荡器的锁相稳频实验。首次实现了基于小型脉冲管制冷机的实用高温超导混频器3mm锁相稳频源。