Isochronal synchronization in networks and chaos-based TDMA communication

Pairs of delay-coupled chaotic systems were shown to be able to achieve isochronal synchronization under bidirectional coupling and self-feedback. Such identical-in-time behavior was demonstrated to be stable under a set of conditions and to support simultaneous bidirectional communication between pairs of chaotic oscillators coupled with time-delay. More recently, it was shown that isochronal synchronization can emerge in networks with several hundreds of oscillators, which allows its exploitation for communication in distributed systems. In this paper, we introduce a conceptual framework for the application of isochronal synchronization to TDMA communication in networks of delay-coupled chaotic oscillators. On the basis of the stable and identical-in-time behavior of delay-coupled chaotic systems, the chaotic dynamics of distributed oscillators is used to support and sustain coordinate communication among nodes over the network. On the basis of the unique features of chaotic systems in isochronal synchronization, the chaotic signals are used to timestamp clock readings at the physical layer such that logical clock synchronization among the nodes (a prerequisite for TDMA) can be exploited using the same basic structure. The result is a standalone network communication scheme that can be advantageously applied in the context of ad-hoc networks or alike, especially short-ranged ones that yield low values of time-delay. As explored to its depths in practical implementations, this conceptual framework is argued to have potential to provide gain in simplicity, security and efficiency in communication schemes for autonomous/standalone network applications.     

Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization

This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results.     

非线性函数耦合的Chen吸引子网络的混沌同步

利用非对称非线性函数耦合混沌同步方法,讨论了Chen吸引子的混沌同步问题,数值模拟分析初始值和耦合强度因子的选择对于实现混沌同步的影响. 将非对称非线性函数耦合同步方法进一步推广发展到完全连接网络和由星形子网络构成的复杂大网络混沌同步的研究中. 提供了确定网络中神经元之间混沌同步状态稳定性的误差发展方程,并讨论各个耦合强度因子对网络同步稳定性过程的影响,给出了相应的稳定性范围. 通过数值模拟证明利用非线性函数作为耦合函数,实现完全连接网络、星形子网络构成大网络的混沌同步是有效的. 可以预测在网络的混沌同步 关键词： 非线性耦合函数 Chen吸引子 混沌同步 网络     

Dual phase and dual anti-phase synchronization of fractional order chaotic systems in real and complex variables with uncertainties

In the present article the nonlinear control method is used for dual phase and dual anti-phase synchronizations among fractional order chaotic systems with uncertainties. The control functions are designed to achieve synchronization with the help of nonlinear control technique. The nonlinear control method is found to be very effective and convenient to achieve dual phase and dual anti-phase synchronization with parametric uncertainties of the non-identical chaotic systems. The fractional order real and complex chaotic systems with parametric uncertainties are taken to illustrate dual phase and dual anti-phase synchronization process. Numerical simulation results show the possibility of dual phase and dual anti-phase synchronizations, which are carried out using Adams–Bashforth–Moulton method and graphical results are presented to display the effectiveness of the method. The striking feature of the article is the graphical demonstration of fast communication through signals between transmitter and receiver for the complex variable systems compared to the real variable systems.     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

Communicating with optical hyperchaos: information encryption and decryption in delayed nonlinear feedback systems

Recent theoretical studies and experimental demonstrations have shown the possibility of using chaos for the encryption of message signals in communication systems. Chaos is generated by systems with delayed nonlinear feedback, which feature hyperchaotic (i.e., of high dimensionality) dynamics. The different ways for the injection of the information in the emitter and the process of the synchronization of the receiver are considered. The analysis of all the possibilities can be used to choose the correct topology of communication systems and, more generally, to explain the behavior of any chaotic systems ruled by nonlinear difference-differential equations.     

State and parameter estimation in nonlinear systems as an optimal tracking problem

In verifying and validating models of nonlinear processes it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, we present a framework for connecting a data signal with a model in a way that minimizes the required coupling yet allows the estimation of unknown parameters in the model. The need to evaluate unknown parameters in models of nonlinear physical, biophysical, and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. Our approach builds on existing work that uses synchronization as a tool for parameter estimation. We address some of the critical issues in that work and provide a practical framework for finding an accurate solution. In particular, we show the equivalence of this problem to that of tracking within an optimal control framework. This equivalence allows the application of powerful numerical methods that provide robust practical tools for model development and validation.     

非一致通信时滞动力学网络上的接连滞后同步

在动力学网络中,节点与节点之间的通信通常存在时滞,并且不同节点之间的通信时滞往往是不同的(即非一致通信时滞),研究非一致通信时滞动力学网络上的接连滞后同步,更具现实意义.为此,本文首先构建含有非一致通信时滞的动力学网络模型.其次分别设计线性反馈控制和自适应反馈控制,利用Lyapunov函数方法,重点分析了该网络的接连滞后同步的稳定性,得到了同步稳定的充分条件.最后,选取蔡氏电路作为局部动力学,又分别选取了链式网络和星型网络这两种拓扑结构来验证理论结果的正确性和有效性.     

SC混沌比例投影同步方法在保密通信中的应用

利用基于线性稳定性准则的SC混沌比例投影同步方法,提出一种应用于保密通信的混沌掩盖方案.适当分离出混沌系统的线性项与非线性项,构造一个非线性驱动向量函数,混沌状态变量包含用于投影同步的比例因子,把所需传递的有用信息掩盖入其中一个分量上,得到混沌载波信号,提高加密信息的复杂度和解码的困难度.以Lorenz吸引子和超混沌Rössler吸引子为例进行数值仿真,详细分析传输的正弦信息加密解密全过程,给出简单、最优的混沌掩盖方案,数值分析证明比例投影同步方法应用于保密通信领域的有效性.     

Multi-antenna GFDM for resilient decentralized communications

Owing to the superior performance of generalized frequency division multiplexing (GFDM), in terms of enhanced spectral efficiency and lower out-of-band radiations, it is considered as a potential replacement of traditional orthogonal frequency division multiplexing (OFDM) for next generation wireless communication systems. However, non-orthogonal pulse shaping in GFDM gives rise to intrinsic self-interference complicating the receiver design. Moreover, its extension to multi-input multi-output (MIMO) designs for spatial diversity and enhanced reliability is also not straightforward as overlapping of transmitted symbols in time and frequency hinders the extension of conventional diversity techniques to MIMO GFDM. In this work, we consider a multi-antenna GFDM decentralized communication system and present a generic framework to achieve spatial transmit diversity along with a low complexity transceiver design. We extend our proposal by presenting a novel multi-antenna preamble that helps not only in acquisition of robust time and frequency synchronization but also in reliable estimation of time-varying frequency selective channels. Performance evaluation over realistic 3GPP simulation scenarios, confirms the attainment of full diversity order along with superior preamble-based time–frequency synchronization and channel estimation performance as compared to state of the art.     

Parameter estimation based synchronization for an epidemic model with application to tuberculosis in Cameroon

We propose a method based on synchronization to identify the parameters and to estimate the underlying variables for an epidemic model from real data. We suggest an adaptive synchronization method based on observer approach with an effective guidance parameter to update rule design only from real data. In order, to validate the identifiability and estimation results, numerical simulations of a tuberculosis (TB) model using real data of the region of Center in Cameroon are performed to estimate the parameters and variables. This study shows that some tools of synchronization of nonlinear systems can help to deal with the parameter and state estimation problem in the field of epidemiology. We exploit the close link between mathematical modelling, structural identifiability analysis, synchronization, and parameter estimation to obtain biological insights into the system modelled.     

Generalized chaos synchronization of a weighted complex network with different nodes

This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, Rõssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.     

非线性耦合超混沌R(o)ssler系统和网络的同步

研究两个通过非线性函数对称耦合的超混沌Roessler系统的同步问题．通过对超混沌系统的线性项与非线性项的适当分离,构造一个特殊的非线性函数,作为耦合函数,发现在耦合强度α=0．5附近的一小段区域里存在稳定的超混沌同步现象．利用线性系统的稳定性分析准则和条件Lyapunov指数来检验同步状态的稳定性,并进一步研究了由多个超混沌Roessler系统单元通过非线性函数按照完全连接形式组成的网络的混沌同步问题。显示许多耦合单元组成的网络,满足同步稳定性的耦合强度的取值范围可以仅从2个单元组成的网络的参数取值范围估计到。此外发现耦合强度的值与耦合单元数量成反比,数值模拟结果证实所提出方法对超混沌系统和网络的混沌同步是有效的。     

最近邻耦合网络的时空混沌同步研究

本文进行了最近邻网络的时空混沌同步研究.以时空混沌系统作为网络的节点,基于Lyapunov稳定性定理,通过确定网络的最大Lyapunov指数,得到了实现网络完全同步的条件.采用Fisher-Kolmogorov时空混沌系统作为网络节点实例进行了仿真模拟,获得了理想的同步效果.进一步研究了有界噪声影响下网络的同步性能,结果显示它具有较强的抗干扰能力.     

Deep-BiGRU based channel estimation scheme for MIMO–FBMC systems

Deep Learning (DL)–based wireless communication systems have the potential to improve the conventional functions and current architecture of communication systems. In this paper, we propose a novel DL-based channel estimation scheme for multiple-input multiple-output filter bank multicarrier with offset quadrature amplitude modulation (MIMO-FBMC/OQAM) systems called deep bidirectional gated-recurrent unit (BiGRU) scheme. This scheme can easily be applied to a single-input single-output (SISO) system. The proposed scheme is divided into two stages: offline and online. The network is first trained in the offline stage. The prediction of channel information and estimation of the channel matrix using the trained network is then performed in the online stage. The simulation results in terms of the normalized mean square error (NMSE) and bit error rate (BER) demonstrate that, under different time-varying channel models, the proposed DL scheme significantly improves the channel estimation performance of FBMC for single and multiple antennas compared to conventional interference approximation method (IAM) channel estimation methods.     

Secure communication through synchronization of two chaotic systems with continuous feedback method

Secure communication through synchronization of chaotic signals is experimentally demonstrated using a nonlinear hybrid optical system. We use a small-time continuous feedback method to achieve synchronization. This method does not require that the system under study be divided into subsystems.     

参数不确定量子细胞神经网络与Lorenz超混沌系统的函数投影同步研究

研究了具有不确定参数的量子细胞神经网络系统与Lorenz超混沌系统的函数投影同步.设计了自适应追踪控制器来实现两个不同系统渐进同步到已知的比例函数,并运用Lyapunov稳定性方法进行了证明.理论分析了量子细胞神经网络系统不确定参数的系数向量线性无关性,实现了不确定参数的识别和估计.数值仿真结果验证了函数投影同步和参数估计的有效性.     

参数不确定的分数阶混沌系统广义错位延时投影同步

为进一步增强通信系统中保密通信的安全性,结合广义错位投影同步和延时投影同步,提出了广义错位延时投影同步.以分数阶Chen系统和Lü系统为例,针对两系统参数都不确定,基于分数阶稳定性理论与自适应控制方法,设计了非线性控制器和参数自适应律,实现了广义错位延时同步,并辨识出驱动系统和响应系统中所有不确定参数.理论分析和数值仿真验证了该方法的可行性与有效性.     

Projective synchronization of spatiotemporal chaos in a weighted complex network

<正>Projective synchronization of a weighted complex network is studied in which nodes are spatiotemporal chaos systems and all nodes are coupled not with the nonlinear terms of the system but through a weighted connection.The range of the linear coefficient matrix of separated configuration,when the synchronization is implemented,is determined according to Lyapunov stability theory.It is found that projective synchronization can be realized for unidirectional star-connection even if the coupling strength between the nodes is a given arbitrary weight value.The Gray-Scott models having spatiotemporal chaos behaviours are taken as nodes in the weighted complex network,and simulation results of spatiotemporal synchronization show the effectiveness of the method.     

Robust impulsive synchronization of coupled delayed neural networks with uncertainties

This paper investigates the synchronization scheme of coupled neural networks with time delays. The coupling function, which can be linear or nonlinear, is subject to uncertainties in the network. By utilizing the stability theory for impulsive functional differential equations, several new criteria are obtained to ensure the robust synchronization of coupled networks via impulsive control. Furthermore, an estimation of the predicted stable region is derived to facilitate the design of the control gain. Finally, numerical simulations are presented to demonstrate the effectiveness of our results.