Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

By a small-size complex network of coupled chaotic Hindmarsh-Rose circuits, we study experimentally the stability of network synchronization to the removal of shortcut links. It is shown that the removal of a single shortcut link may destroy either completely or partially the network synchronization. Interestingly, when the network is partially desynchronized, it is found that the oscillators can be organized into different groups, with oscillators within each group being highly synchronized but are not for oscillators from different groups, showing the intriguing phenomenon of cluster synchronization. The experimental results are analyzed by the method of eigenvalue analysis, which implies that the formation of cluster synchronization is crucially dependent on the network symmetries. Our study demonstrates the observability of cluster synchronization in realistic systems, and indicates the feasibility of controlling network synchronization by adjusting network topology.     

Experimental synchronization of single-transistor-based chaotic circuits

This work deals with nonautonomous chaotic circuits and, in particular, with the experimental characterization of the synchronization properties of two simple nonautonomous circuits. Two single-transistor chaotic circuits, which are among the simplest chaotic oscillators, are investigated. We studied synchronization of these circuits and found that the most appropriate technique to synchronize two single-transistor chaotic circuits is that based on the design of an inverse circuit.     

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.     

Phase synchronization in bi-directionally coupled chaotic ratchets

We show the existence of phase synchronization in bi-directionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states. A transition from a regime where the phases rotate with different velocities to a synchronous state where the phase difference is bounded was observed as the coupling was increased. In addition, the region of synchronization in which the system is permanently phase locked was identified. In this regime, the transverse Lyapunov exponent corresponding to both phases remain positive. Our calculations show that the transition to a synchronized state occurs via a crisis transition to an attractor filling the whole phase space.     

Phase synchronization in two coupled chaotic neurons

Chaotically-spiking dynamics of Hindmarsh–Rose neurons are discussed based on a flexible definition of phase for chaotic flow. The phase synchronization of two coupled chaotic neurons is in fact the spike synchronization. As a multiple time-scale model, the coupled HR neurons have quite different behaviors from the Rössler oscillators only having single time-scale mechanism. Using such a multiple time-scale model, the phase function can detect synchronization dynamics that cannot be distinguished by cross-correlation. Moreover, simulation results show that the Lyapunov exponents cannot be used as a definite criterion for the occurrence of chaotic phase synchronization for such a system. Evaluation of the phase function shows its utility in analyzing nonlinear neural systems.     

Generalized chaotic synchronization in coupled Ginzburg-Landau equations

Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling between the systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.     

Phase synchronization in unidirectionally coupled chaotic ratchets

We study chaotic phase synchronization of unidirectionally coupled deterministic chaotic ratchets. The coupled ratchets were simulated in their chaotic states and perfect phase locking was observed as the coupling was gradually increased. We identified the region of phase synchronization for the ratchets and show that the transition to chaotic phase synchronization is via an interior crisis transition to strange attractor in the phase space.     

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.     

Controlling projective synchronization in coupled chaotic systems

In this paper, a new method for controlling projective synchronization in coupled chaotic systems is presented. The control method is based on a partially linear decomposition and negative feedback of state errors. Firstly, the synchronizability of the proposed projective synchronization control method is proved mathematically. Then, three different representative examples are discussed to verify the correctness and effectiveness of the proposed control method.     

Transmission of information and synchronization in a pair of coupled chaotic circuits: An experimental overview

We propose a rationale for experimentally studying the intricate relationship between the rate of information transmission and synchronization level in active networks, applying theoretical results recently proposed. We consider two non-identical coupled Chua’s circuit with non-identical coupling strengths in order to illustrate the proceeding for experimental scenarios of very few data points coming from highly non-coherent coupled systems, such that phase synchronization can only be detected by methods that do not rely explicitely on the calculation of the phase. A relevant finding is to show that for the coupled Chua’s circuit, the larger the level of synchronization the larger the rate of information exchanged between both circuits. We further validate our findings with data from numerical simulations, and discuss an extension to arbitrarily large active networks.     

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.     

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.     

Global synchronization in lattices of coupled chaotic systems

Based on the concept of matrix measures, we study global stability of synchronization in networks. Our results apply to quite general connectivity topology. In addition, a rigorous lower bound on the coupling strength for global synchronization of all oscillators is also obtained. Moreover, by merely checking the structure of the vector field of the single oscillator, we shall be able to determine if the system is globally synchronized.     

强耦合混沌系统中的近似同步

以单向驱动耦合Lorenz振子一维链为研究对象，研究振子间的混沌同步行为. 数值计算结果表明，对于变量y驱动x的耦合方式，在合适的耦合强度下，会出现第一个振子和第二个振子不同步，而与次近邻非直接连接的振子(如第三个振子)近似同步. 进一步研究表明，出现这一现象的原因是在大耦合强度下，对于这种驱动方式，第一个振子和第二个振子间出现驱动单变量近似同步；虽然它们之间未出现所有变量的完全同步，但是驱动信号事实上已经传递下去了. 关键词： Lorenz振子 混沌同步 近似同步     

Impulsive synchronization of nonlinear coupled chaotic systems

The issue of impulsive synchronization of the nonlinear coupled chaotic systems is investigated. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. To illustrate the effectiveness of the new scheme, a numerical example is given.     

耦合分数阶混沌振荡器的主-从同步

近年来对分数阶系统的动力学研究得到了较为广泛的关注。本文研究了基于主-从耦合同步法的同步技术并实现了两个耦合的分数阶振荡器的混沌同步。仿真结果表明：在适当的耦合强度的调节下，该方法可实现两个耦合分数阶混沌振荡器的准确同步，且分数阶混沌振荡器的同步率明显慢于整数阶混沌振荡器的同步率；而耦合分数阶混沌振荡器在实现同步的过程中，随着阶数的提高，同步误差曲线变得平滑，这表明，系统阶数的提高改善了耦合混沌振荡器实现同步的平稳性。     

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.     

Fuzzy modeling and synchronization of different memristor-based chaotic circuits

This Letter is concerned with the problem of fuzzy modeling and synchronization of memristor-based Lorenz circuits with memristor-based Chua?s circuits. In this Letter, a memristor-based Lorenz circuit is set up, and illustrated by phase portraits and Lyapunov exponents. Furthermore, a new fuzzy model of memristor-based Lorenz circuit is presented to simulate and synchronize with the memristor-based Chua?s circuit. Through this new fuzzy model, two main advantages can be obtained as: (1) only two linear subsystems are needed; (2) fuzzy synchronization of these two different chaotic circuits with different numbers of nonlinear terms can be achieved with only two sets of gain K. Finally, numerical simulations are used to illustrate the effectiveness of these obtained results.     

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.     

Complete synchronization induced by disorder in coupled chaotic lattices

The effect of phase disorder in external forces introduced into two-dimensional lattices of coupled chaotic pendulums is investigated. As the increase of the disorder, we find complete synchronization between the pendulums in each chain and different periodic synchronized patterns, while the chain remains asynchronous if all driving forces have the same phase. Applying the master stability function method, an analytic solution is given to support the numerical results. All these findings may provide further insight into chaos control and synchronization in nonlinear systems.