具有双重时滞的时变耦合复杂网络的牵制外同步研究

针对同时具有节点时滞和耦合时滞的时变耦合复杂网络的外同步问题, 提出一种简单有效的自适应牵制控制方法. 首先构建一种贴近实际的驱动-响应复杂网络模型, 在模型中引入双重时滞和时变不对称外部耦合矩阵. 进一步设计易于实现的自适应牵制控制器, 对网络中的一部分关键节点进行控制. 构造适当的Lyapunov泛函, 利用 LaSalle不变集原理和线性矩阵不等式, 给出两个复杂网络实现外同步的充分条件. 最后, 仿真结果表明所提同步方法的有效性, 同时揭示耦合时滞对同步收敛速度的影响.     

噪声环境下时滞耦合网络的广义投影滞后同步

时滞和噪声在复杂网络中普遍存在,而含有耦合时滞和噪声摄动的耦合网络同步的研究工作却极其稀少. 本文针对噪声环境下具有不同节点动力学、不同拓扑结构及不同节点数目的耦合时滞网络,提出了两个网络之间的广义投影滞后同步. 首先,构建了更加贴近现实的驱动-响应网络同步的理论框架;其次,基于随机时滞微分方程LaSalle不变性原理,严格证明了在合理的控制器作用下,驱动网络和响应网络在几乎必然渐近稳定性意义下能够取得广义投影滞后同步;最后,借助于计算机仿真,通过具体的网络模型验证了理论推理的有效性. 数值模拟结果表明,驱动网络与响应网络不但能够达到广义投影滞后同步,而且同步效果不依赖于耦合时滞和比例因子的选取,同时也揭示了更新增益和耦合时滞对同步收敛速度的显著性影响. 关键词： 复杂网络 广义投影滞后同步 随机噪声 时滞     

Master-slave synchronization criteria for horizontal platform systems using time delay feedback control

This paper is concerned with master-slave synchronization for two identical non-autonomous horizontal platform systems by using time-delay feedback control. Compared with some existing results on synchronization for horizontal platform systems, the effect of the time delay in the feedback control on master-slave synchronization is investigated. Applying a delay decomposition approach, some delay-dependent synchronization criteria are established and formulated in the form of linear matrix inequalities (LMIs). Sufficient conditions about the existence of a time delay feedback controller are derived by employing these newly obtained synchronization criteria. The controller gains can be achieved by solving a set of LMIs. One simulation example is given to illustrate the effectiveness of synchronization criteria and the design method.     

多延时互耦合半导体激光器的实时混沌同步特性

针对双延时和三延时互耦合半导体激光器系统,研究了互耦合延时和互耦合强度对实时混沌同步质量的影响,提出了双延时互耦合系统中可将其中一个互耦合延时看作反馈延时的思想,揭示了多延时互耦合半导体激光器系统实时混沌同步条件和规律.研究结果表明,多延时互耦合系统中,某两条双向链路的互耦合延时比值为2,是实现高品质实时混沌同步的基本条件;增大互耦合强度,可以改善实时混沌同步品质,且在较低的等效耦合强度条件下,双延时互耦合系统较三延时互耦合系统更易于实现良好的实时混沌同步.     

Synchronization of chaos in unidirectionally and bidirectionally coupled multiple time delay laser diodes with electro-optical feedback

We report on chaos synchronization in both unidirectionally and bidirectionally coupled multiple time delay laser diodes with electro-optical feedback. We derive existence and sufficient stability conditions for the synchronization regimes. We calculate the Lyapunov exponents, information dimension, and Kolmogorov-Sinai entropy for a single and double delay time lasers to demonstrate that multiple time delay laser system can offer higher complexity than a single time delay laser. We demonstrate that in coupled multiple time delay lasers additional feedback(s) can play a stabilizing role. We compare the synchronization quality for closed loop and open loop receiver laser configurations and find better synchronization quality for partially open loop receiver (when the receiver laser has only one feedback loop), than the open loop receiver configuration (when the receiver contains no feedback loops). We also study the effect of the feedback phase on the correlation coefficient between the interacting laser systems. Analytical results are fully supported by numerical simulations.     

Delay time modulation induced oscillating synchronization and intermittent anticipatory/lag and complete synchronizations in time-delay nonlinear dynamical systems

Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete, and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay systems having two different time-delays, that is feedback delay with a periodic delay time modulation and a constant coupling delay. Intermittent anticipatory, intermittent lag, and complete synchronizations are shown to exist in the same system with identical delay time modulations in both the delays. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay with suitable stability condition is discussed. The intermittent anticipatory and lag synchronizations are characterized by the minimum of the similarity functions and the intermittent behavior is characterized by a universal asymptotic -32 power law distribution. It is also shown that the delay time carved out of the trajectories of the time-delay system with periodic delay time modulation cannot be estimated using conventional methods, thereby reducing the possibility of decoding the message by phase space reconstruction.     

Average Synchronization and Temporal Order in a Noisy Neuronal Network with Coupling Delay

Average synchronization and temporal order characterized by the rate of firing are studied in a spatially extended network system with the coupling time delay, which is locally modelled by a two-dimensional Rulkov map neuron. It is shown that there exists an optimal noise level, where average synchronization and temporal order are maximum irrespective of the coupling time delay. Furthermore, it is found that temporal order is weakened when the coupling time delay appears. However, the coupling time delay has a twofold effect on average synchronization, one associated with its increase, the other with its decrease. This clearly manifests that random perturbations and time delay play a complementary role in synchronization and temporal order.     

基于光电负反馈的激光混沌串联同步系统研究

提出了一种新的混沌中继系统，该系统基于光电负反馈的激光混沌串联同步.对该系统的同步性以及激光器内部参数失配对其同步性的影响进行了研究，并与基于光反馈的激光混沌串联同步系统进行了比较.研究结果表明：当系统参量满足一定条件时，该系统能实现完全同步；当激光器内部参数失配时，其混沌同步性会受到一定的影响，但该系统的混沌同步性对参数失配的容忍性要比基于光反馈的系统好得多.     

Lag synchronization in time-delayed systems

We present the first analytical investigation of lag chaos synchronization between two unidirectionally coupled identical time-delayed systems in the case when these systems are governed by two characteristic times: the delay time in the coupling is generally different from the delay time in the coupled systems. Also, for the first time we demonstrate that parameter mismatches can explain the fact that the lag time is equal to the coupling delay. These findings can be helpful to explain coupling-delay lag time in chaos synchronization.     

Synchronization dynamics of chemically coupled cells with activator–inhibitor pathways

Systems of interacting cells containing an activator–inhibitor pathway, regulating naturally in their inner parts their end-product concentrations through a sequence of biochemical reactions with feedback-loops: an end-product inhibition of the first substrate, and an autocatalytic activation of the end-product through an allosteric enzyme-mediated reaction are investigated. The individual cells are considered to be identical and are described by nonlinear differential equations recently proposed following the concerted transition model. The chemical and electrical coupling types, realized by exchange of metabolites across concentration of the cells are used in order to analyze the onset of phase and complete synchronization in the biochemical system. It is found that depending on the coupling nature and the range of coupling strength, cells enter into different synchronization regimes going from low-quality to high-quality synchronization. The synchronization manifold's stability is analyzed. The results are supported by numerical simulations using indicators such as the conditional Lyapunov exponents and the rate of change of the Lyapunov function. The results indicate that the system cannot completely synchronize under the single action of the chemical coupling. The combined effect of both chemical and electrical couplings is found to be of capital importance in the onset of complete synchronization and high quality synchronization.     

Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control

The finite-time synchronization of fractional-order multi-weighted complex networks (FMCNs) with uncertain parameters and external disturbances is studied. Firstly, based on fractional calculus characteristics and Lyapunov stability theory, quantized controllers are designed to guarantee that FMCNs can achieve synchronization in a limited time with and without coupling delay, respectively. Then, appropriate parameter update laws are obtained to identify the uncertain parameters in FMCNs. Finally, numerical simulation examples are given to validate the correctness of the theoretical results.     

基于光电反馈的激光混沌并联同步系统研究

提出了基于光电反馈的激光混沌并联同步方案,对可能存在的两种同步——广义同步和完全同步进行了研究,着重讨论了激光器内部参数失配对发射与接收激光器之间以及并联接收激光器之间同步特性的影响.研究结果显示：在一定范围内,同样的内部参数失配下,并联接收激光器之间的同步效果明显优于发射激光器与接收激光器之间的同步效果. 关键词： 半导体激光器 混沌同步 光电反馈 参数失配     

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.     

Synchronization of noise-perturbed optical systems with multiple time delays

In this paper, complete synchronization and generalized synchronization between two unidirectionally coupled optical systems with multiple time delays and noise perturbation are investigated. Sufficient conditions for both complete synchronization and generalized synchronization are rigorously established. Numerical simulations fully support the theoretical results. The effect of parameter mismatch on the quality of synchronization is also explored.     

时空混沌的单向耦合同步

以耦合映象格子模型为例,提出利用单向耦合驱动时空混沌的同步方案,并进行了数值分析.结果表明,适当地选择耦合驱动强度因子和均衡系数,两个时空混沌系统可以达到准确同步.通过计算最大条件Lyapunov指数,给出了可实现时空混沌同步的最小耦合强度以及最小耦合强度与系统参数之间的关系曲线.数值模拟还证明,此方法工作鲁棒 关键词： 时空混沌 同步 单向耦合 最大条件Lyapunov指数 数值模拟     

On the complete synchronization of the Kuramoto phase model

We discuss the asymptotic complete phase-frequency synchronization for the Kuramoto phase model with a finite size N. We present sufficient conditions for initial configurations leading to the exponential decay toward the completely synchronized states. Our new sufficient conditions and decay rate depend only on the coupling strength and the diameter of initial phase and natural frequency configurations. But they are independent of the system size N, hence they can be used for the mean-field limit. For the complete synchronization estimates, we estimate the time evolution of the phase and frequency diameters for configurations. The initial phase configurations for identical oscillators located on the half circle will converge to the complete synchronized states exponentially fast. In contrast, for the non-identical oscillators, the complete frequency synchronization will occur exponentially fast for some restricted class of initial phase configurations. Our estimates are based on the monotonicity arguments of extremal phase and frequencies, which do not employ any linearization procedure of nonlinear coupling terms and detailed information on the eigenvalue of the linearized system around the complete synchronized states. We compare our analytical results with numerical simulations.     

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.     

大规模富社团网络的时空混沌同步

以Plankton时空混沌系统作为网络节点,通过非线性耦合构成富社团(rich-club,RC)网络,研究其时空混沌同步规律.首先给出了RC网络中连接节点之间的非线性耦合函数的一般性选取原则.进而基于Lyapunov稳定性定理,理论分析了实现网络同步的条件.最后,通过仿真模拟检验了网络的时空混沌同步效果.仿真研究表明,RC网络中各富节点之间以及这些富节点各自星形连接的子网络中的所有节点均实现了完全同步。     

多延时互耦合半导体激光器的实时混沌同步特性

针对双延时和三延时互耦合半导体激光器系统,研究了互耦合延时和互耦合强度对实时混沌同步质量的影响,提出了双延时互耦合系统中可将其中一个互耦合延时看作反馈延时的思想,揭示了多延时互耦合半导体激光器系统实时混沌同步条件和规律.研究结果表明,多延时互耦合系统中,某两条双向链路的互耦合延时比值为2,是实现高品质实时混沌同步的基本条件;增大互耦合强度,可以改善实时混沌同步品质,且在较低的等效耦合强度条件下,双延时互耦合系统较三延时互耦合系统更易于实现良好的实时混沌同步.     

Adaptive Synchronization of Fractional-Order Complex-Valued Uncertainty Dynamical Network with Coupling Delay

Compared with real-valued complex networks, complex-valued dynamic networks have a wider application space. In addition, considering the existence of time delay and uncertainty in the actual system, the synchronization problem of fractional-order complex-valued dynamic networks with uncertain parameter and coupled delay is studied in this paper. In particular, the uncertain parameter is correlated with time delay. By using fractional derivative inequalities and linear delay fractional order equations, the synchronization of uncertainty complex networks with coupling delay is realized. Sufficient conditions for global asymptotic synchronization are obtained. The obtained synchronization results are applicable to most complex network systems with or without delay. Finally, numerical simulations verify the effectiveness of the obtained results.