Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points

The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively. However, the coupled oscillators in practice are nonidentical, and there exist mismatched parameters. It has been proved that under certain conditions, complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points, yet other cooperative behaviors are not addressed. In this paper, we further consider two coupled nonidentical oscillators with the same equilibrium points, where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors. We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings. In the case of directed coupling,death islands appear in two-parameter spaces. The mechanism inducing these transitions is presented.     

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.     

Stable anticipation synchronization in mutually coupled vertical-cavity surface-emitting lasers system

Two vertical-cavity surface-emitting lasers(VCSELs) are mutually coupled through a partially transparent mirror (PTM) placed in the pathway. The PTM plays the role of external mirror,which controls the feedback strength and coupling strength.We numerically simulate this system by establishing a visible SIMULINK model.The results demonstrate that the anticipation synchronization is achieved and it can tolerate some extent frequency detuning.Moreover,the system shows similar chaos-pass filtering effect on unidirectionally coupled system even both VCSELs are modulated.This system allows simultaneously bidirectional secure message transmission on public channels.     

Influence of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers

We analyze theoretically the effect of polarization mode competition on the synchronization of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs). Chaos in the master laser is induced by delayed optical feedback, and the slave laser is subject to isotropic optical injection from the master VCSEL. We show that the synchronization quality can be enhanced when the chaotic regime in the master VCSEL involves both fundamental orthogonal linearly polarized modes.     

Transition from phase synchronization to complete synchronization in mutually coupled nonidentical Nd:YAG lasers

Using mutually coupled nonidentical continuous-wave Nd:YAG lasers, we experimentally confirmed the recently proposed transition route from phase synchronization to complete synchronization. As evidence of this transition we obtained the probability distribution of the intermittent synchronization time near the threshold of the complete synchronization transition.     

Polarization switching and synchronization of mutually coupled vertical-cavity surface-emitting semiconductor lasers

Polarization switching (PS) dynamics and synchronization performances of two mutually coupled vertical-cavity surface-emitting lasers (VCSELs) are studied theoretically in this paper. A group of dimensionless rate equations is derived to describe our model. While analysing the PS characteristics, we focus on the effects of coupling rate and frequency detuning regarding different mutual injection types. The results indicate that the x-mode injection defers the occurrence of PS, while the y-mode injection leads the PS to occur at a lower current. Strong enough polarization-selective injection can suppress the PS. Moreover, if frequency detuning is considered, the effects of polarization-selective mutual injection will be weakened. To evaluate the synchronization performance, the correlation coefficients and output dynamics of VCSELs with both pure mode and mixed mode polarizations are given. It is found that performance of complete synchronization is sensitive to the frequency mismatch but it is little affected by mixed mode polarizations, which is opposite to the case of injection-locking synchronization.     

Firing rates of coupled noisy excitable elements

The dynamics of coupled excitable FitzHugh Nagumo systems under external noisy driving is studied. Different from most of previous work focusing on the noise-induced regularity in the framework of coherence resonance, here the average frequency （or firing rate） of coupled excitable elements is of much more concern. We find that （i） their frequencies first increase and then decrease with the increase of the coupling, and there is a clear crossover from a rush increase to a smooth increase with the increase of noise strength, and （ii） for nonidentical cases, all elements transit to an identical frequency simultaneously only after a certain coupling strength is achieved. These first-increase-thendecrease non-monotonic frequency behavior and isochronous frequency synchronization are believed to be two basic behaviors in coupled noisy excitable systems.     

Chaos synchronization and communication of the polarization modes for two unidirectionally coupled vertical-cavity surface-emitting lasers

We theoretically investigate the synchronization performance of the polarization modes of two unidirectionally coupled vertical-cavity surface-emitting lasers (VCSELs), where the master VCSEL subjects to polarization-preserved optical feedback and the slave VCSEL subjects to polarization-preserved optical injection. We demonstrate that high synchronization can be achieved between corresponding polarization components of the master laser and the slave laser. We also analyze the influence of the internal mismatched parameters on the synchronization performance. Furthermore, this system is used to dual-channel communication and the different transmitted digital information is respectively recovered at each polarization branch of the slaver laser successfully with the encryption scheme of chaos masking (CM). The results open an opportunity for multichannel chaotic communication by utilizing different polarization components in single-mode or multi-transverse-mode VCSELs.     

Crowd synchrony and quorum sensing in delay-coupled lasers

Crowd synchrony and quorum sensing arise when a large number of dynamical elements communicate with each other via a common information pool. Previous evidence has shown that this type of coupling leads to synchronization, when coupling is instantaneous and the number of coupled elements is large enough. Here we consider a situation in which the transmission of information between the system components and the coupling pool is not instantaneous. To that end, we model a system of semiconductor lasers optically coupled to a central laser with a delay. Our results show that, even though the lasers are nonidentical due to their distinct optical frequencies, zero-lag synchronization arises. By changing a system parameter, we can switch between two different types of synchronization transition. The dependence of the transition with respect to the delay-coupling parameters is studied.     

Light polarization fingerprints on nonlinear dynamics of vertical-cavity surface-emitting lasers

In this paper we summarize the recent results on nonlinear dynamics of vertical-cavity surface-emitting lasers (VCSELs) which are bearing the fingerprints of the particular polarization properties of VCSELs. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching and polarization mode-hopping. This provides new specificities to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We unveil both experimentally and theoretically these new specificities for the case of optical feedback, optical injection, and unidirectional synchronization between VCSELs.     

Adaptive synchronization between two complex networks with nonidentical topological structures

This paper addresses the theoretical analysis of synchronization between two complex networks with nonidentical topological structures. By designing effective adaptive controllers, we achieve synchronization between two complex networks. Both the cases of identical and nonidentical network topological structures are considered and several useful criteria for synchronization are given. Illustrative examples are presented to demonstrate the application of the theoretical results.     

Enhanced chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers with polarization-preserved injection

We experimentally study chaos synchronization in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers (VCSELs) with polarization-preserved and polarization-selected optical injection. The measurements show, in agreement with theoretical predictions, that the maximum cross coefficient of 0.884 obtained with polarization-preserved optical injection is significantly higher than the maximum cross coefficient of 0.724 obtained with polarization-selected optical injection.     

Impulsive synchronization of coupled dynamical networks with nonidentical Duffing oscillators and coupling delays

This paper aims to investigate the synchronization problem of coupled dynamical networks with nonidentical Duffing-type oscillators without or with coupling delays. Different from cluster synchronization of nonidentical dynamical networks in the previous literature, this paper focuses on the problem of complete synchronization, which is more challenging than cluster synchronization. By applying an impulsive controller, some sufficient criteria are obtained for complete synchronization of the coupled dynamical networks of nonidentical oscillators. Furthermore, numerical simulations are given to verify the theoretical results.     

Synchronization of mutually versus unidirectionally coupled chaotic semiconductor lasers

Synchronization dynamics of mutually coupled chaotic semiconductor lasers are investigated experimentally and compared to identical synchronization of unidirectionally coupled lasers. Mutual coupling shows high quality synchronization in a broad range of self-feedback and coupling strengths. It is found to be tolerant to significant parameter mismatch which for unidirectional coupling would result in loss of synchronization. The advantages of mutual coupling are emphasized in light of its potential use in chaos communications.     

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.     

Chaotic synchronization through coupling strategies

Usually, complete synchronization (CS) is regarded as the form of synchronization proper of identical chaotic systems, while generalized synchronization (GS) extends CS in nonidentical systems. However, this generally accepted view ignores the role that the coupling plays in determining the type of synchronization. In this work, we show that by choosing appropriate coupling strategies, CS can be observed in coupled chaotic systems with parameter mismatch, and GS can also be achieved in coupled identical systems. Numerical examples are provided to demonstrate these findings. Moreover, experimental verification based on electronic circuits has been carried out to support the numerical results. Our work provides a method to obtain robust CS in synchronization-based chaos communications.     

Generalized synchronization of coupled chaotic systems

In this paper we briefly report some recent developments on generalized synchronization. We discuss different methods of detecting generalized synchronization. We first consider two unidirectionally coupled systems and then two mutually coupled systems. We then extend the study to a network of coupled systems. In the study of generalized synchronization of coupled nonidentical systems we discuss the Master Stability Function (MSF) formalism for coupled nearly identical systems. Later we use this MSF to construct synchronized optimized networks. In the optimized networks the nodes which have parameter value at one extreme are chosen as hubs and the pair of nodes with larger difference in parameter are chosen to create links.     

Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons

We study nontrivial effects of noise on synchronization and coherence of a chaotic Hodgkin-Huxley model of thermally sensitive neurons. We demonstrate that identical neurons which are not coupled but subjected to a common fluctuating input (Gaussian noise) can achieve complete synchronization when the noise amplitude is larger than a threshold. For nonidentical neurons, noise can induce phase synchronization. Noise enhances synchronization of weakly coupled neurons. We also find that noise enhances the coherence of the spike trains. A saddle point embedded in the chaotic attractor is responsible for these nontrivial noise-induced effects. Relevance of our results to biological information processing is discussed.     

Synchronization of chaotic VCSELs by external chaotic signal parameter modulation

Synchronization of chaotic vertical-cavity surface-emitting lasers （VCSELs） is achieved by external chaotic signal modulation successfully. Simulation indicates that we can get chaos synchronization if the intensity of external chaotic signal is large enough. First of all, we use direct current modulation to achieve the chaos of VCSELs, and determine the laser＇s chaotic state by analyzing time series of the output and the corresponding power spectrum. And then we achieve synchronization of the two chaotic systems by external chaotic signal parameter modulation. We also find that the larger the modulation intensity is, the easier it is to achieve synchronization for chaotic VCSELs. This approach can also be applied to systems with a number of modulated lasers.