Phase Locking and Chaos in a Josephson Junction Array Shunted by a Common Resistance

The dynamics of a Josephson junction array shunted by a common resistance are investigated by using numerical methods. Coexistence of phase locking and chaos is observed in the system when the resistively and capacitively shunted junction model is adopted. The corresponding parameter ranges for phase locking and chaos are presented. When there are three resistively shunted junctions in the array, chaos is found for the first time and the parameter range for chaos is also presented. According to the theory of Chernikov and Schmidt, when there are four or more junctions in the array, the system exhibits chaotic behavior. Our results indicate that the theory of Chernikov and Schmidt is not exactly appropriate.     

Experimental observation of topologically protected defect states in silicon waveguide arrays

Photonic waveguide arrays provide a simple and versatile platform for simulating conventional topological systems. Here, we investigate a novel one-dimensional(1D) topological band structure, a dimer chain, consisting of silicon waveguides with alternating self-coupling and inter-coupling. Coupled mode theory is used to study topological features of such a model. It is found that topological invariants of our proposed model are described by the global Berry phase instead of the Berry phase of the upper or lower energy band, which is commonly used in the1 D topological models such as the Su–Schrieffer–Heeger model. Next, we design an array configuration composed of two dimer patterns with different global Berry phases to realize the topologically protected waveguiding. The topologically protected propagation feature is simulated based on the finite-difference time-domain method and then observed in the experiment. Our results provide an in-depth understanding of the dynamics of the topological defect state in a 1D silicon waveguide array, and may provide different routes for on-chip lightwave shaping and routing.     

Efficient Phase Locking of Fiber Amplifiers Using a Low-Cost and High-Damage-Threshold Phase Control System

We propose a low-cost and high-damage-threshold phase control system that employs a piezoelectric ceramic transducer modulator controlled by a stochastic parallel gradient descent algorithm. Efficient phase locking of two fiber amplifiers is demonstrated. Experimental results show that energy encircled in the target pinhole is increased by a factor of 1.76 and the visibility of the fringe pattern is as high as 90% when the system is in close-loop. The phase control system has potential in phase locking of large-number and high-power fiber laser endeavors.     

Chaos in Einstein—Maxwell—Dust System

We study the dynamics of the Einstein-Maxwell-dust system and find that the system presents a critical point of a centre-centre-type structure in the phase space. By performing the numerical experiments, we find that the dynamics of the Einstein-Maxwell-dust system is unstable and its chaotic behaviour is obvious when the Hamiltonian becomes smaller.     

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.     

Phase-locked laser coherent interference

A method of locking the relative phase to provide stable constructive or destructive interference between the phase-modulated sidebands from a pair of phase modulators is demonstrated. It is discussed theoretically for optimal fringe visibility related to the phase noise from faulty system. After phase locking using the phase modulating and lock-in technique,the drift of the relative phase is focalized around ±0.0016 rad and the fringe visibility is restricted to 2×10-4 .     

Tunnelling Dynamics of Bose--Einstein Condensates in a Five-Well Trap

We develop a five-well model for describing the tunnelling dynamics of Bose-Einstein condensates （BECs） trapped in 2D optical lattices. The tunnelling dynamics of BECs in this five-well model are investigated both analytically and numerically. We focus on the self-trapped states and the difference of the tunnelling dynamics among two- well, three-well and five-well systems. The criterions for the self-trapped states and the phase diagrams of the five trapped BECs in zero-phase mode and π-phase mode are obtained. We find that the criterions and the phase diagrams are largely modified by the dimension of the system and the phase difference 5etween wells. The five-well model is a good model and can give us an insight into the tunnelling dynamics of BECs trapped in 2D optical lattices.     

Phase Noise of Optically Generated Microwave Using Sideband Injection Locking

Optically generated 20-GHz microwave carriers with phase noise lower than -75 dBc/Hz at 10 kHz offset and lower than -90 dBc/Hz at 100 kHz offset are obtained using single- and double-sideband injection locking. Within the locking range, the effect of sideband injection locking can be regarded as narrow-band amplification of the modulation sidebands. Increasing the current of slave laser will increase the power of beat signal and reduce the phase noise to a certain extent. Double-sideband injection locking can increase the power of the generated microwave carrier while keeping the phase noise at a low level. It is also revealed that partially destruction of coherence between the two beating lights in the course of sideband injection locking would impair the phase noise performance.     

Elimination of spiral waves and spatiotemporal chaos by the synchronization transmission technology of network signals

A method to eliminate spiral waves and spatiotemporal chaos by using the synchronization transmission technology of network signals is proposed in this paper. The character of the spiral waves and the spatiotemporal chaos in the Fitzhugh—Nagumo model is presented. The network error evolution equation with spatiotemporal variables and the corresponding eigenvalue equation are determined based on the stability theory, and the global synchronization condition is obtained. Simulations are made in a complex network with Fitzhugh—Nagumo models as the nodes to verify the effectiveness of the synchronization transmission principle of the network signal.     

Rhythm dynamics of complex neuronal networks with mixed bursting neurons

The spatiotemporal order and rhythm dynamics of a complex neuronal network with mixed bursting neurons are studied in this paper. A quantitative characteristic, the width factor, is introduced to describe the rhythm dynamics of an individual neuron, and the average width factor is used to characterize the rhythm dynamics of a neuronal network. An r parameter is introduced to denote the ratio of the short bursting neurons in the network. Then we investigate the effect of the ratio on the rhythm dynamics of the neuronal network. The critical value of r is derived, and the neurons in the network always remain short bursting when the r ratio is larger than the critical value.     

光折变振荡器中的模式锁定及阵发混沌

用数值模拟的方法研究了光折变振荡器的一些时空行为，结果表明在简并或准简并条件下的横模空间耦合将使得光折变振荡器表现出与普通激光器相似的时空现象，例如不同横向模式间的合作频率锁定，时空周期行为及多模振荡时的阵发混沌现象等等。     

Dynamics in a tightly-focused end-pumped solid-state laser near degenerate cavity configurations

We numerically study the dynamics of a tightly-focused end-pumped solid-state laser near the degenerate cavity configurations by using the Collins integral together with a rate equation. We find that the field and gain adjust their distributions to exhibit the temporal rather than spatiotemporal instabilities in spite of the coupling of many transverse modes. These instabilities are attributed to the frequency locking but phase unlocking of the degenerate Laguerre-Gaussian modes. The phase portrait is plotted in the three dimensional space with gain, real part, and imaginary part of the field because of similar dynamics for every transverse point. Both of the portrait and the Poincare map show the peculiar features. Moreover, the route to chaos is the mixed effect of period-doubling and quasi-period as the cavity length is tuned.     

Phase reduction approach to synchronisation of nonlinear oscillators

Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are often modelled as nonlinear limit-cycle oscillators. In this article, we briefly review phase reduction theory, which is a simple and powerful method for analysing the synchronisation properties of limit-cycle oscillators exhibiting rhythmic dynamics. Through phase reduction theory, we can systematically simplify the nonlinear multi-dimensional differential equations describing a limit-cycle oscillator to a one-dimensional phase equation, which is much easier to analyse. Classical applications of this theory, i.e. the phase locking of an oscillator to a periodic external forcing and the mutual synchronisation of interacting oscillators, are explained. Further, more recent applications of this theory to the synchronisation of non-interacting oscillators induced by common noise and the dynamics of coupled oscillators on complex networks are discussed. We also comment on some recent advances in phase reduction theory for noise-driven oscillators and rhythmic spatiotemporal patterns.     

On the role of flexoeffect in synchronization of electroconvective roll oscillations in nematics

We describe the dynamics of zigzag oscillations in a system of convective rolls in a nematic liquid crystal above the electroconvection threshold under the action of an ac voltage with a biased position of the mean value. It is found that an increase in the contribution from the constant component leads to a substantial increase in the spatiotemporal ordering of zigzag rolls and their synchronization with the homogeneous twist mode. The results confirm the flexoelectric mechanism of locking.     

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.     

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.     

Chaotic behavior in transverse-mode laser dynamics

We analyze chaotic behavior found in numerical simulations of the transverse pattern dynamics of a laser demonstrating that in some cases chaos originates in phase dynamics and is of low dimension. Investigations of both a Ginzburg-Landau equation for the complex field amplitude of the laser output and a Kuramoto-Sivashinsky-type equation for only the phase of that complex field equation find the same behavior. Both equations can be expanded in terms of spatial modes and in the chaotic regime the behavior of the modal amplitudes seems relatively independent. However, the fluctuations of the modal amplitudes are sufficiently correlated so that the spatiotemporal dynamics is a form of low dimensional chaos rather than a more complex turbulent behavior or even one that might merit the term spatiotemporal chaos.     

Phase locking of short-pulse Q-switched lasers

The effects of frequency mismatch on phase locking of two passively Q-switched lasers have been studied. Stable phase locking with a high degree of spatial coherence can be obtained for frequency mismatches that are less than the spectral linewidth of the laser pulses. As the frequency mismatch increases, the transition from the phase locked to the unlocked states is characterized by a gradual loss of coincidence of the pulses from the individual elements and a reduction in the fringe contrast in the combined laser beam. An explanation for observed phenomena based on the dynamics of the transverse modes of the laser array is provided.