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.     

Noise enhanced phase synchronization and coherence resonance in sets of chaotic oscillators with weak global coupling

The effect of noise on phase synchronization in small sets and larger populations of weakly coupled chaotic oscillators is explored. Both independent and correlated noise are found to enhance phase synchronization of two coupled chaotic oscillators below the synchronization threshold; this is in contrast to the behavior of two coupled periodic oscillators. This constructive effect of noise results from the interplay between noise and the locking features of unstable periodic orbits. We show that in a population of nonidentical chaotic oscillators, correlated noise enhances synchronization in the weak coupling region. The interplay between noise and weak coupling induces a collective motion in which the coherence is maximal at an optimal noise intensity. Both the noise-enhanced phase synchronization and the coherence resonance numerically observed in coupled chaotic R?ssler oscillators are verified experimentally with an array of chaotic electrochemical oscillators.     

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.     

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.     

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     

Automatic control of phase synchronization in coupled complex oscillators

We present an automatic control method for phase locking of regular and chaotic nonidentical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, the approach presented here supposes the existence of a special controller, which allows to change the parameters of the controlled systems. First we discuss general principles of automatic phase synchronization (PS) for arbitrary coupled systems with a controller whose input is given by a special quadratic form of coordinates of the individual systems and its output is a result of the application of a linear differential operator. We demonstrate the effectiveness of our approach for controlled PS on several examples: (i) two coupled regular oscillators, (ii) coupled regular and chaotic oscillators, (iii) two coupled chaotic Rössler oscillators, (iv) two coupled foodweb models, (v) coupled chaotic Rössler and Lorenz oscillators, (vi) ensembles of locally coupled regular oscillators, (vii) ensembles of locally coupled chaotic oscillators, and (viii) ensembles of globally coupled chaotic oscillators.     

Synchronization transition of limit-cycle system with homogeneous phase shifts

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated when phase shifts are considered. In the system of coupled oscillators, phase shifts are the same between different oscillators. Synchronization and synchronization transition are revealed with different phase shifts. Phase shifts play an important role for this kind of system. When the phase shift α<0.5π, the synchronization state can be attained by increasing the coupling, and the system cannot reach the synchronization state while α≥q0.5π. A clear scaling between complete synchronization critical coupling strength K_pc and α-0.5π is found.     

Collective Directional Transport in Symmetric Periodic Potentials by Breaking the Coupling Symmetry

Collective unidirectional motion of an asymmetrically coupled array of oscillators in symmetric periodic potentials is studied. A directed current is observed when the drift coupling is presented, while no external biased force is applied. Negative directed current is found when varying system parameters. An addition of a periodic rocking force may enhance the efficiency of directed transport. Resonant steps of the current are found and interpreted as the mode locking between the array and the ac force. Noise-assisted transport is observed, and an optimal noise intensity can give rise to a most efficient transport. The directed transport thus can be optimized and furthermore controlled by suitably adjusting the parameters of the system.     

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.     

Extreme sensitivity to detuning for globally coupled phase oscillators

We discuss the sensitivity of a population of coupled oscillators to differences in their natural frequencies, i.e., to detuning. We argue that for three or more oscillators, one can get great sensitivity even if the coupling is strong. For N globally coupled phase oscillators we find there can be bifurcation to extreme sensitivity, where frequency locking can be destroyed by arbitrarily small detuning. This extreme sensitivity is absent for N = 2, appears at isolated parameter values for N = 3 and N = 4, and can appear robustly for open sets of parameter values for N > or = 5 oscillators.     

Power delivered by an array of Van der Pol oscillators coupled to a resonant cavity

An array of Van der Pol oscillators coupled to an RLC load is considered both theoretically and experimentally. It is found that the oscillators are active when the capacitance of the capacitor coupling the array to the load is below a critical value increasing with the number of oscillators. The power delivered to the load by the array of active oscillators increases with the number of oscillators till a limiting value increasing with the quality factor of the load. Good agreement is obtained between the theoretical and experimental results.     

Ring intermittency in coupled chaotic oscillators at the boundary of phase synchronization

A new type of intermittent behavior is described to occur near the boundary of the phase synchronization regime of coupled chaotic oscillators. This mechanism, called ring intermittency, arises for sufficiently high initial mismatches in the frequencies of the two coupled systems. The laws for both the distribution and the mean length of the laminar phases versus the coupling strength are analytically deduced. Very good agreement between the theoretical results and the numerically calculated data is shown. We discuss how this mechanism is expected to take place in other relevant physical circumstances.     

Interplay of noise and coupling in heterogeneous ensembles of phase oscillators

We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise can also be heterogeneous, representing diversity in the individual responses to external fluctuations. We show that the desynchronization transition induced by noise may be completely suppressed, even for arbitrarily large noise intensities, is the distribution of coupling strengths decays slowly enough for large couplings. Equivalently, if the response to noise of a sufficiently large fraction of the ensemble is weak enough, desynchronization cannot occur. The two effects combine with each other when the response to noise and the coupling strength of each oscillator are correlated. This combination is quantitatively characterized and illustrated with explicit examples.     

耦合分数阶双稳态振子的同步、反同步与振幅死亡

研究了耦合分数阶振子的同步、反同步和振幅死亡等问题. 基于P-R振子在特定参数下的双稳态特性, 利用最大条件Lyapunov指数、最大Lyapunov指数和分岔图等数值方法分析发现, 通过选取初始条件和耦合强度, 可以控制耦合振子呈现混沌同步、混沌反同步、全部振幅死亡同步、全部振幅死亡反同步和部 分振幅死亡等丰富的动力学现象. 基于蒙特卡罗方法的原理, 在初始条件相空间中随机选取耦合振子的初始位置, 计算不同耦合强度下耦合振子的全部振幅死亡态、部分振幅死亡态和非振幅死亡态的比例, 从统计学角度表征了耦合分数阶双稳态振子的动力学特征. 几种有代表性的双稳态振子的吸引域进一步证明了统计方法的计算结果. 关键词： 振幅死亡 吸引域 双稳态     

Phase locking and chaotic synchronization in an array of three lasers

A linear array of three lasers that are coupled mutually in space is investigated. It is shown that the phase of the laser fields is locked with intermediate coupling while the laser intensities are totally chaotic and chaotically synchronized. When the intensities of lasers reenter the regime of chaotic synchronization at smaller coupling constant, the laser fields show low degree of phase locking. The phase differences in the fields between three lasers show rich patterns when the coupling is changed. Received 3 August 2001 and Received in final form 27 September 2001     

Clustering and Synchronization in an Array of Repulsively Coupled Phase Oscillators

Clustering and synchronization in an array of repulsively coupled phase oscillators are numerically investigated. It is found that oscillators are divided into several clusters according to the symmetry in the structure.Synchronization occurs between oscillators in each cluster, while those oscillators belonging to different clusters remain asynchronous. Such synchronization may collapse for all clusters when the dynamics of only one oscillator is altered properly. The synchronous state may return back after a short period of transient process. This is determined by the strength of the oscillator altered. Its application in the communication of one-to-several is suggested.     

Clustering and Synchronization in an Array of Repulsively Coupled Phase Oscillators

Clustering and synchronization in an array of repulsively coupled phase oscillators are numerically investigated. It is found that oscillators are divided into several clusters according to the symmetry in the structure. Synchronization occurs between oscillators in each cluster, while those oscillators belonging to different clusters remain asynchronous. Such synchronization may collapse for all clusters when the dynamics of only one oscillator is altered properly. The synchronous state may return back after a short period of transient process. This is determined by the strength of the oscillator altered. Its application in the communication of one-to-several is suggested.     

Resonance tongues in a system of globally coupled FitzHugh-Nagumo oscillators with time-periodic coupling strength

We investigate the dynamics of a population of globally coupled FitzHugh-Nagumo oscillators with a time-periodic coupling strength. While for synchronizing global coupling, the in-phase state is always stable, the oscillators split into several cluster states for desynchronizing global coupling, most commonly in two, irrespective of the coupling strength. This confines the ability of the system to form n:m locked states considerably. The prevalence of two and four cluster states leads to large 2:1 and 4:1 subharmonic resonance regions, while at low coupling strength for a harmonic 1:1 or a superharmonic 1:m time-periodic coupling coefficient, any resonances are absent and the system exhibits nonresonant phase drifting cluster states. Furthermore, in the unforced, globally coupled system the frequency of the oscillators in a cluster state is in general lower than that of the uncoupled oscillator and strongly depends on the coupling strength. Periodic variation of the coupling strength at twice the natural frequency causes each oscillator to keep oscillating with its autonomous oscillation period.     

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.