Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers

A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between the two lasers in the experiment and in a delay differential equation model of the system. Because the lasers are internally perturbed by spontaneous emission, we include a noise source in the model to obtain stochastic realizations of the deterministic equations. Both amplitude synchronization and phase synchronization are considered. We use the Hilbert transform to define the phase variable and compute phase synchronization. We find that synchronization increases with coupling strength in the experiment and the model. When the time series from two lasers are time shifted in either direction by the delay time, approximately equal synchronization is frequently observed, so that a clear leader and follower cannot be identified. We define an algorithm to determine which laser leads the other when the synchronization is sufficiently different with one direction of time shift, and statistics of switches in leader and follower are studied. The frequency of switching between leader and follower increases with coupling strength, as might be expected since the lasers mutually influence each other more effectively with stronger coupling.     

Dual-lag synchronization between coupled chaotic lasers due to path-delay interference

We study experimentally the synchronization dynamics of two semiconductor lasers coupled unidirectionally via two different delayed paths. The emitter laser operates in a chaotic regime characterized by low-frequency fluctuations due to optical feedback and induces a synchronized dynamical activity in the receiver laser, which operates in the continuous-wave regime when uncoupled. Different delays in the two coupling paths lead to the coexistence of two time lags in the synchronized dynamics of the oscillators. This dual-lag synchronization degrades the average synchronization quality of the system of coupled lasers and hinders the transmission of information between them. Numerical simulation results agree with the experimental observations, and allow us to explore this phenomenon in a wide parameter range, and quantify the degree of signal transmission degradation caused by this chaotic path-delay interference.     

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.     

Complete synchronization in coupled type-I neurons

For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of noise-induced complete synchronization (CS). For the inputs to the neurons, we point out that the rate of change of instantaneous frequency with the instantaneous phase of the stochastic inputs to each neuron matches exactly with that for the other in the event of CS of their outputs. Our observation can be exploited in practical situations to produce completely synchronized outputs in artificial devices. For excitatory-excitatory synaptic coupling, a functional dependence for the synchronization error on coupling and noise strengths is obtained. Finally, we report a noise-induced CS between nonidentical neurons coupled bidirectionally through random nonzero couplings in an all-to-all way in a large neuronal ensemble.     

Power emitted by an array of ultra high frequency current modulated semiconductor lasers with global coupling

We report the output power emitted by an array of ultra high frequency current modulated semiconductor lasers (CMSCL) whose elements are mutually coupled in a ring configuration and globally coupled through an external mirror. By varying the coupling strengths, we determine the domain where the in-phase state occurs. The dependence of the output power on the coupling strengths is analyzed. The power increases with the number of lasers and shows an abrupt increase or decrease as the coupling strengths increase. This particular behaviour is related to synchronization.     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper, by the help of evolutionary algorithm and using Hindmarsh-Rose (HR) neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neuron cells system. First, we build different coupling structure with N cells, and found the effect of synchronized transition contact not only closely with the topology of the system, but also with whether there exist the ring structures in the system. In particular, both the size and the number of rings have greater effects on such transition behavior. Secondly, we introduce synchronization error to qualitative analyze the effect of the topology structure. Furthermore, by fitting the simulation results, we find that with the increment of the neurons number, there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems. Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system. Biological system may gradually acquire such efficient topology structures through the long-term evolution, thus the systems' information process may be optimized by this scheme.     

GENERAL SYNCHRONIZATION OF CHAOS IN A SYSTEM OF TWO NON-IDENTICAL LASERS

General synchronization of the chaotic intensity fluctuations of two spatially coupled Nd:YAG lasers with pump modulation is investigated theoretically when the losses of the two lasers are different. It is shown that the chaotic synchronization still exists for medium coupling even though the two lasers are different. For strong coupling the system shows periodic motion of laser intensities. While for weak coupling, the two lasers oscillate independently. It is obvious that the increase of difference between the two lasers reduces the degree of chaotic synchronization.     

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.     

Synchronization of Chaotic Intensities and Phases in an Array of N Lasers

A linear array of N mutually coupled single-mode lasers is investigated. It is shown that the intensities of N lasers are chaotically synchronized when the coupling between lasers is relatively strong. The chaotic synchronization of intensities depends on the location of the lasers in the array. The chaotic synchronization appears between two outmost lasers, the second two outmost lasers, etc. There is no synchronization between nearest neighbors of the lasers. If the number of N is odd, the middle laser is never synchronized between any lasers. The chaotic synchronization of phases between nearest lasers in the array is examined by using the analytic signal and the Gaussian filter methods based on the peak of the power spectrum of the intensity. It can be seen that the message of chaotic intensity synchronization is conveyed through the phase synchronization.     

Generalized <Emphasis Type="Italic">N</Emphasis>-coupled maps with invariant measure in Bose-Mesner algebra perspective

By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with a given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a relation between the vertexes. Based on the E ₀ transverse projection operator, we addressed synchronization problem of an array of the linearly coupled map lattices of identical discrete time systems. The synchronization rate is determined by the second largest eigenvalue of the transition probability matrix. Algebraic properties of the Bose-Mesner algebra with an associated scheme with definite spectrum has been used in order to study the stability of the coupled map lattice. Associated schemes play a key role and may lead to analytical methods in studying the stability of the dynamical systems. The relation between the coupling parameters and the chaotic region is presented. It is shown that the feasible region is analytically determined by the number of couplings (i.e. by increasing the number of coupled maps, the feasible region is restricted). It is very easy to apply our criteria to the system being studied and they encompass a wide range of coupling schemes including most of the popularly used ones in the literature.      

Synchronization of chaotic semiconductor laser systems: a vectorial coupling-dependent scenario

We demonstrate the influence of vectorial coupling on the synchronization behavior of complex systems. We study two semiconductor lasers subject to delayed optical feedback which are unidirectionally coherently coupled via their optical fields. Our experimental and numerical results demonstrate a characteristic synchronization scenario in dependence on the relative feedback phase leading cyclically from chaos synchronization to almost uncorrelated states, and back to chaos synchronization. Finally, we reveal the influence of the feedback phase on the dynamics of the solitary delay system.     

Preference of Chaotic Synchronization in a Coupled Laser System

In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak.     

Preference of Chaotic Synchronization in a Coupled Laser System

In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak.     

Synchronization properties and effects of parameter mismatches in unidirectionally coupled chaotic vertical-cavity surface-emitting lasers

We numerically investigate the effects of parameter mismatches on chaos synchronization in vertical-cavity surfaceemitting lasers (VCSELs). We assume injection-locked chaos synchronization in a unidirectionally coupled and openloop optical feedback system. The accuracy of chaos synchronization is greatly affected by the mismatches of the device parameters and operation conditions between the two lasers. In particular, the oscillation frequency of the laser is one of the important parameters in a system of injection-locked chaos synchronization. However, the variations of the device characteristics of VCSELs are very large compared with those of other types of semiconductor lasers. We study the effects of parameter mismatches related to the oscillation frequency of VCSELs on chaos synchronization. We proved that mismatches in terms of the birefringence and the injection current play crucial roles for the quality of chaos synchronization.     

激光局域网络的混沌控制及并行队列同步

本文提出并研究了"单队列-双参数"光电延时反馈控制条件下的激光局域网络的混沌控制及串联的动力学行为的并行队列"交叉驱动-反馈"网络同步实现,建立了该光学局域网络的数学物理控制模型.通过含时延超越方程理论的分析,预言了该光学局域网络是可以实现混沌控制的,且网络两路结点队列是可以实现实时引导控制到多个类周期状态上的,并通过并行队列同步方程理论证明并行串联队列同步是可以获得的.结果发现在可控的激光局域网络两个并行串联队列光路上,分别实现了网络队列结点的混沌控制并能够实现多个类周期的网络结点的并行串联队列同步,实现了络网结点激光器的2周期、3周期、4周期等状态的并行队列同步,以及其他多个类周期的队列并行同步和动态同步.还发现了两个类周期并行队列网络同步控制区域.本文还给出了激光局域网络"并行多点混沌载波同步发射及其在光学超宽带通信中应用"的一个案例并成功实现.这是一种新型的激光混沌局域网络控制系统,具有光局域网络光传送与光联接核心控制技术要素,具有复杂动力学系统与网络的多变量、多空间维度及并行两路不同队列混沌控制技术特点,还具有光网络超宽带通信功能等.其研究结果对局域网络、光网络的控制与同步、激光技术以及混沌的研究具有重要的参考价值.     

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.     

Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback

The synchronization of chaotic semiconductor lasers with optical feedback is studied numerically in a one-way coupling configuration, in which a small amount of the intensity of one laser (master laser) is injected coherently into the other (slave laser). A regime of anticipated synchronization is found, in which the intensity of the slave laser is synchronized to the future chaotic intensity of the master laser. Anticipation is robust to small noise and parameter mismatches, but in this case the synchronization is not complete. It is also shown that anticipated synchronization occurs in coupled time-delay systems, when the coupling has a delay that is less than the delay of the systems.     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.     

Generalized synchronization of chaos in erbium—doped dual—ring lasers

We investigate chaotic synchronization in the generalized sense in unidirectionally coupled erbium-doped fibre dual-ring lasers. Numerical simulation shows that no matter whether the two different erbium-doped fibre dual-ring lasers are chaotic or not before coupling, they show generalized synchronization with a suitable unidirectional coupling coefficient under which the maximum condition Lyapunov exponent is negative. We also use the auxiliary system approach to detect the generalized synchronization.     

Bidirectional chaos synchronization and communication based on mutually coupled semiconductor lasers with asymmetrical bias currents

In this paper, a bidirectional chaos secret communication system, based on mutually coupled semiconductor lasers (MCSLs) with asymmetrical bias currents, is proposed, and the synchronization characteristics and the communication performances of such a system are numerically investigated. The results show that the stable leader-laggard chaos synchronization can be achieved under relatively large asymmetrical bias current levels. Meantime, the influence of the intrinsic parameter variations of the laser on the synchronization quality is also considered, and the simulation reveals that this system still possesses good robustness to the parameter variations. Moreover, the influences of delay time and mutually coupling strength between the two lasers on chaos communication performance have also been discussed. Finally, unidirectional and bidirectional secret communication performances of such a system are examined under the chaos masking (CMS) encryption scheme, and the security of this system is also discussed.