Synchronization of mutually coupled systems

General operation conditions to obtain anticipated or retarded synchronization in a mutually coupled system with feedback are analyzed. Different from a unidirectionally coupled system, which type of synchronization will occur in a mutually coupled system does not solely depend on the difference between the feedback-delay time and the coupling-delay time. We find that in addition to the feedback/coupling delay times, feedback strengths and coupling strengths all determine whether the system will preform anticipated or retarded synchronization. Experimental implementation using semiconductor lasers subject to optoelectronic feedback is provided as an example. A set of experimental data is presented and discussed.     

Nonlinear dynamics and localized synchronization in mutually coupled VCSELs

Nonlinear dynamics of mutually coupled vertical-cavity surface-emitting lasers (VCSELs) are studied theoretically. We consider both identical and nonidentical cases, respectively. For identical cases, where the device parameters and the operating conditions are the same, both lasers show the same behaviors with an identical output, and some typical nonlinear states, including period-one, period-two, multi-period and chaos, are observed. However, for nonidentical cases, the symmetric behaviors are broken. Due to the mismatch of the bias current of these two lasers, the system nonlinearity is increased and the synchronization performance is degraded greatly. Nevertheless, it is found that the coupled VCSELs can still exhibit a form of localized synchronization when they operate under the periodic state introduced by either the weak coupling or the frequency detuning.     

Spatiotemporal antiphase dynamics in coupled extended optical media

Experimental evidence of spatiotemporal antiphase dynamics is given for an extended system made of two liquid crystal slices that are optically coupled by two equal amplitude counterpropagating pumping beams. Theory and experiments carried out in a transverse one-dimensional configuration show that roll patterns are generated in each slice. These rolls are spatially in-phase or antiphase for a focusing or a defocusing nonlinearity type, respectively. These in-phase or antiphase dynamics remain robust even for complex spatiotemporal regimes such as dislocation regimes.     

Spatiotemporal dynamics in Rayleigh band of photonic quantum ring laser

Spatiotemporal dynamic simulations are carried out for the carrier-field interactions of photonic quantum ring lasers of three dimensional (3D) whispering cave modes (WCMs). We observe quantum wires-like carrier re-distributions naturally formed in the Rayleigh band region of the active quantum well plane. Apart from the regular two dimensional (2D) whispering gallery mode (WGM), the 3D WCM’s major polarization state favors a strong carrier-photon coupling for the carriers in the Rayleigh band, such that the powerful transient coupling generates photonic quantum rings (PQRs), or concentric quantum rings with a half-wavelength pitch of imminently recombinant carriers, i.e., a photonic quantum corral effect. This feature is responsible for the low threshold currents and thermally stable spectra, which opens the way for easy optical mega-pixel (‘Omega’) chip fabrications.     

Multistability in nonlinearly coupled ring of Duffing systems

In this paper we consider dynamics of three unidirectionally coupled Duffing oscillators with nonlinear coupling function in the form of third degree polynomial. We focus on the influence of the coupling on the occurrence of different bifurcation’s scenarios. The stability of equilibria, using Routh-Hurwitz criterion, is investigated. Moreover, we check how coefficients of the nonlinear coupling influence an appearance of different types of periodic solutions. The stable periodic solutions are computed using path-following. Finally, we show the two parameters’ bifurcation diagrams with marked areas where one can observe the coexistence of solutions.     

Adaptive coupled synchronization of non-autonomous systems in ring networks

The adaptive coupled synchronization method for non-autonomous systems is proposed. This method can avoid estimating the value of coupling coefficient. Under the uniform Lipschitz assumption, we derive the asymptotical synchronization for a general coupling ring network with N identical non-autonomous systems~ even when N is large enough. Strict theoretical proofs are given. Numerical simulations illustrate the effectiveness of the present method.     

Enhanced efficiency of a mutually coupled parallel spark preioniser

The enhanced efficiency, almost by a factor of 9, of preionisation when the laser is self-switched by a mutually coupled parallel spark preioniser as against its conventional operation with inductively ballasted preioniser, has been demonstrated in the operation of a TEA CO₂ laser. The increased preionisation peak current due to the near ballast free operation of the mutually coupled parallel spark channels is shown to be responsible for the observed behavior.     

Isochronous synchronization in mutually coupled chaotic circuits

This paper examines the robustness of isochronous synchronization in simple arrays of bidirectionally coupled systems. First, the achronal synchronization of two mutually chaotic circuits, which are coupled with delay, is analyzed. Next, a third chaotic circuit acting as a relay between the previous two circuits is introduced. We observe that, despite the delay in the coupling path, the outer dynamical systems show isochronous synchronization of their outputs, i.e., display the same dynamics at exactly the same moment. Finally, we give here the first experimental evidence that the central relaying system is not required to be of the same kind of its outer counterparts.     

Non-Markovian entanglement dynamics in coupled superconducting qubit systems

We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio r ≡ w_c\omega_c/w₀\omega_0 between the reservoir cutoff frequency w_c\omega_c and the system oscillator frequency w₀\omega_0,
and the energy levels split of the superconducting circuits in the non-Markovian master equation. We analyzed the entanglement sudden death (ESD) and entanglement sudden birth (ESB) by the non-Markovian master equation. Furthermore, we find that the larger the ratio r and the thermal energy k _BT , the shorter the decoherence. In this superconducting qubit system we find that the entanglement can be controlled and the ESD time can be prolonged by adjusting the temperature and the superconducting phases F_k\Phi_k which split the energy levels.     

Consequential noise-induced synchronization of indirectly coupled self-sustained oscillators

We consider the dynamics of identical self-sustained oscillators coupled via a common linear system (beam), which is perturbed by noise. We demonstrate that increasing the noise intensity induces complete synchronization between the oscillators and, surprisingly, their in-phase synchronization with the beam. This new phenomenon of in-phase synchronization of both the oscillators and the oscillating beam arises when the noise intensity exceeds a threshold value, and can not appear in the deterministic case where the beam stably oscillates in anti-phase with the synchronized oscillators (as it is in the case of the Huygens clocks synchronization). Similar behavior persists for slightly non-identical oscillators.     

Stochastic self-sustained oscillations of non-autonomous systems

In the present minireview, we analyze autonomous and non-autonomous oscillations of dynamical and stochastic systems in the framework of common concepts. We introduce the definition of an attractor for a non-autonomous system. We also propose the definition of self-sustained oscillations, which can be applied for both autonomous and non-autonomous systems. We consider noise-induced oscillations and formulate the definition of stochastic self-sustained oscillations for this case. All the statements made in this work are illustrated by particular examples.     

链式互耦合半导体激光器的实时混沌同步

通过在互耦合外腔半导体激光器之间增加中继激光器,建立了一种链式互耦合半导体激光器混沌同步系统模型.理论分析了系统的实时混沌同步条件,数值研究了注入电流、互耦合条件、反馈条件等对系统实时混沌同步品质的影响,揭示了同步质量在反馈强度和互耦合强度二维参数空间的分布规律.结果表明:注入电流较大时,满足互耦合强度和反馈强度相同,互耦合延时和反馈延时相等,系统中所有激光器之间可同时实现稳定高品质实时混沌同步;中心激光器和边激光器之间的稳定实时混沌同步分布在在互耦合强度和反馈强度较小的区域以及互耦合强度和反馈强度相近的区域;边激光器之间由于同时接收到中心激光器实施的相同注入,能够较容易的实现稳定高品质的实时混沌同步.该系统可进一步扩展成为实现远距离的双向实时混沌同步或阵列激光器系统的实时混沌同步.     

Globally coupled systems with prescribed synchronized dynamics

A system of globally coupled maps whose synchronized dynamics differs from the individual (chaotic) evolution is considered. For nonchaotic synchronized dynamics, the synchronized state becomes stable at a critical coupling intensity lower than that of the fully chaotic case. Below such critical point, synchronization is also stable in a set of finite intervals. Moreover, the system is shown to exhibit multistability, so that even when the synchronized state is stable not all the initial conditions lead to synchronization of the ensemble. Received 22 October 1999     

Synchronization of mutually coupled chaotic lasers in the presence of a shutter

Two mutually coupled chaotic diode lasers exhibit stable isochronal synchronization in the presence of self-feedback. When the mutual communication between the lasers is discontinued by a shutter and the two uncoupled lasers are subject to self-feedback only, the desynchronization time is found to scale as Adtau, where Ad>1 and tau corresponds to the optical distance between the lasers. Prior to synchronization, when the two lasers are uncorrelated and the shutter between them is opened, the synchronization time is found to be much shorter, though still proportional to tau. As a consequence of these results, the synchronization is not significantly altered if the shutter is opened or closed faster than the desynchronization time. Experiments in which the coupling between two chaotic-synchronized diode lasers is modulated with an electro-optic shutter are found to be consistent with the results of numerical simulations.     

Spatiotemporal synchronization of coupled oscillators in a laboratory plasma

The spatiotemporal synchronization between two plasma instabilities of autonomous glow discharge tubes is observed experimentally. For this purpose, two tubes are placed separately and two chaotic waves interact with each other through a coupler. When the coupling strength is changed, the coupled oscillators exhibit synchronization in time and space. This is the first experimental evidence of spatiotemporal synchronization by mutual chaotic wave interaction in plasma.     

Synchronization and basin bifurcations in mutually coupled oscillators

Synchronization behaviour of two mutually coupled double-well Duffing oscillators exhibiting cross-well chaos is examined. Synchronization of the subsystems was observed for coupling strength k > 0.4. It is found that when the oscillators are operated in the regime for which two attractors coexist in phase space, basin bifurcation sequences occur leading to n + 1, n ≥ 2 basins as the coupling is varied — a signature of Wada structure and final-state sensitivity. However, in the region of complete synchronization, the basins structure is identical with that of the single oscillators and retains its essential features including fractal basin boundaries.      

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics.This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure.By constructing a proper Poincare map of the non-smooth system,an analytical expression of the Jacobian matrix of Poincare map is given.Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method.When the period is fixed and the coupling strength changes,the system undergoes stable,periodic,quasi-periodic,and hyper-chaotic solutions,etc.Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations.     

Evolution of solid state systems containing mutually coupled dipolar and quadrupole spins: perturbation treatment

Perturbation approach to time evolution of multi-spin systems containing quadrupole and dipolar spins has been presented and discussed. The treatment comprises polarization transfer effects, field-dependent relaxation processes of dipolar as well as quadrupole spins and combined results of both of them. Complete theories dealing with various aspects of the spin dynamic processes have been proposed. Because of an educational character of this paper, relevant assumptions, limitations and even particular steps of the proposed treatments have been discussed in detail. Special emphasis is put on understanding of validity regimes of the perturbation treatment, depending on relative strengths of spin interactions and timescales of relevant motional processes affecting them. Motional regimes required for spins to be involved in essentially different evolution pathways like polarization transfers or relaxation have been illustrated by experimental examples.     

Interaction dynamics of bright solitons in linearly coupled asymmetric systems

In this research work, composite media based on metamaterials including random distribution of spherical nanoparticles in a polymeric foam host are suggested to achieve negative effective refractive index in the visible spectrum. For this purpose structures including single, two and three layer spherical particles are investigated. Based on simulation results, media including single layer spheres (metallic and dielectric particles) and two layer nanospheres (core–shell particles consist of metallic core and dielectric shell) based on superposition of nanoparticles with different sizes and fill fractions are proposed for desired result. In this work, to obtain optimized band with negative RI media, superposition of three layer nanoparticles and doped semiconductor are designed.