Generalized projective synchronization of a class of chaotic （hyperchaotic） systems with uncertain parameters

In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.

A new four-dimensional hyperchaotic Chen system and its generalized synchronization

Based on the Chen chaotic system, a new four-dimensional hyperchaotic Chen system is constructed, and the basic dynamic behaviours of the system were studied, and the generalized synchronization has been observed in the coupled four-dimensional hyperchaotic Chen system with unknown parameters. The Routh Hurwitz theorem is used to derive the conditions of stability of this system. Furthermore based on Lyapunov stability theory, the control laws and adaptive laws of parameters are obtained to make generalized synchronization of the coupled new four-dimensional hyperchaotic Chen systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

Bidirectional Partial Generalized Synchronization in Chaotic and Hyperchaotic Systems via a New Scheme

In this paper, a bidirectional partial generalized （lag, complete, and anticipated） synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized （lag, complete, and anticipated） synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic Tamasevicius Namajunas-Cenys system to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. It is interesting that partial chaos synchronization not only can take place between two chaotic systems, but also can take place between chaotic and hyperchaotic systems. The proposed scheme can also be extended to research bidirectional partial generalized （lag, complete, and anticipated） synchronization between other dynamical systems.

Modified Cascade Synchronization Scheme for Discrete-Time Hyperchaotic Systems

In this paper, the modified cascade synchronization scheme is proposed to investigate the synchronization in discrete-time hyperchaotic systems. By choosing a general kind of proportional scaling error functions and based on rigorous control theory, we take the discrete-time hyperchaotic system due to Wang and 3D generalized Henon map as two examples to achieve the modified cascade synchronization, respectively. Numerical simulations are used to verify the effectiveness of the proposed technique.

Function Projective Synchronization between Two Discrete-Time Hyperchaotic Systems Using Backstepping Method

We realize the function projective synchronization (FPS) between two discrete-time hyperchaotic systems, that is, the drive state vectors and the response state vectors can evolve in a proportional scaling function matrix. In this paper, a systematic scheme is explored to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems using the backstepping method. Additionally, FPS of two different hyperchaotic systems is also realized. Numeric simulations are given to verify the effectiveness of our scheme.

The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system

This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a threedimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross-product term. Some basic properties of the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter a or b is varied. The system is hyperchaotic in several different regions of the parameter b. Especially, the two positive Lyapunov exponents are both larger, and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying a. The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincaré sections.

Linear generalized synchronization of chaotic systems with uncertain parameters

A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.

Generalized synchronization between different chaotic maps via dead-beat control

This paper presents a new scheme to achieve generalized synchronization（GS） between different discrete-time chaotic（hyperchaotic） systems.The approach is based on a theorem,which assures that GS is achieved when a structural condition on the considered class of response systems is satisfied.The method presents some useful features：it enables exact GS to be achieved in finite time（i.e.,dead-beat synchronization）;it is rigorous,systematic,and straightforward in checking GS;it can be applied to a wide class of chaotic maps.Some examples of GS,including the Grassi-Miller map and a recently introduced minimal 2-D quadratic map,are illustrated.

A novel hyperchaotic map with sine chaotification and discrete memristor

Discrete memristor has become a hotspot since it was proposed recently.However,the design of chaotic maps based on discrete memristor is in its early research stage.In this paper,a memristive seed chaotic map is proposed by combining a quadratic discrete memristor with the sine function.Furthermore,by applying the chaotification method,we obtain a high-dimensional chaotic map.Numerical analysis shows that it can generate hyperchaos.With the increase of cascade times,the generated map has more positive Lyapunov exponents and larger hyperchaotic range.The National Institute of Standards and Technology(NIST)test results show that the chaotic pseudo-random sequence generated by cascading two seed maps has good unpredictability,and it indicates the potential in practical application.

Adaptive Generalized Eigenvector Estimating Algorithm for Hermitian Matrix Pencil

Generalized eigenvector plays an essential role in the signal processing field.In this paper,we present a novel neural network learning algorithm for estimating the generalized eigenvector of a Hermitian matrix pencil.Differently from some traditional algorithms,which need to select the proper values of learning rates before using,the proposed algorithm does not need a learning rate and is very suitable for real applications.Through analyzing all of the equilibrium points,it is proven that if and only if the weight vector of the neural network is equal to the generalized eigenvector corresponding to the largest generalized eigenvalue of a Hermitian matrix pencil,the proposed algorithm reaches to convergence status.By using the deterministic discretetime(DDT)method,some convergence conditions,which can be satisfied with probability 1,are also obtained to guarantee its convergence.Simulation results show that the proposed algorithm has a fast convergence speed and good numerical stability.The real application demonstrates its effectiveness in tracking the optimal vector of beamforming.

Generalized Consensus of Discrete-Time Multi-Agent Systems with Directed Topology and Communication Delay

Compared with traditional consensus,this paper studies the generalized consensus problem for discrete-time multi-agent systems with directed topology and communication delay.Novel distributed consensus protocols with and without communication delay are designed.Based on the analysis of error dynamical system and graph theory,the generalized consensus is globally asymptotically achieved under suitable conditions without changing the zero row-sums property of Laplacian matrix in networks.Moreover,the sufficient conditions for generalized consensus of communication delay are obtained under directed connections.Finally,some simulations have been provided to verify the theoretical results.

ASYMPTOTICAL STABILITY OF NON-AUTONOMOUS DISCRETE-TIME NEURAL NETWORKS WITH GENERALIZED INPUT-OUTPUT FUNCTION

In this paper, we first introduce the model of discrete-time neural networkswith generalized input--output function and present a proof of the existence of afixed point by Schauder fixed-point principle. Secondly, we study the uniformlyasymptotical stability of equilibrium in non-autonomous discrete--time neuralnetworks and give some sufficient conditions that guarantee the stability of itby using the converse theorem of Lyapunov function. Finally, several examplesand numerical simulations are given to illustrate and reinforce our theories.

A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH J-VACATION POLICY AND GENERAL RETRIAL TIMES

The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times.As soon as the orbit is empty,the server takes a vacation.However,the server is allowed to take a maximum number J of vacations,if the system remains empty after the end of a vacation.If there is at least one customer in the orbit at the end of a vacation,the server begins to serve the new arrivals or the arriving customers from the orbit.For this model,the authors focus on the steady-state analysis for the considered queueing system.Firstly,the authors obtain the generating functions of the number of customers in the orbit and in the system.Then,the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size.Besides,the relationship between this discrete-time model and the corresponding continuous-time model is also investigated.Finally,some numerical results are provided.

基于双超混沌映射的伪随机序列发生器设计

有限精度下的混沌退化问题影响伪随机序列发生器性能。本文基于2D-SLIM和2D-LSCM超混沌系统提出一种迭代序列耦合的伪随机序列发生器方案。首先采用随机周期扰动方式防止混沌退化,随后对迭代序列进行耦合输出,并构建伪随机序列发生器模型。然后采用SP800-22 Revision 1a测试标准对生成序列进行随机性检测。实验结果表明,伪随机序列具有良好的随机性能。此外,基于方案生成的伪随机序列发生器设计了一种音频数据加密方案并对其进行仿真验证。

分数阶超混沌系统的线性广义同步观测器设计

首先利用分数阶的常微分动力系统的稳定性理论,通过判断线性化后平衡点的稳定不变特性、辅助以分岔图分析等数值手段,给出了新近提出的改进型超混沌L櫣系统对应分数阶系统产生混沌现象的阶次参数范围;进一步,设计了一类广义线性同步观测器,该观测器的动力学行为能与原系统实现任意的线性关系的广义同步,而经典的完全同步、反相同步以及投影同步可以视为本文提出方法的特例.最后的数值仿真进一步证实了本文提出的观测器设计方案的有效性.

异结构不确定混沌系统的广义投影同步

针对一类参数随时间变化的不确定混沌系统,用鲁棒自适应方法实现异结构混沌系统的广义投影同步和参数辨识。基于李亚普诺夫稳定性理论,设计了鲁棒自适应控制器和参数自适应律。通过改变广义投影同步的比例矩阵,获得所有状态变量任意比例于原驱动系统的混沌信号,并辨识出系统所有未知参数。以Rssler超混沌系统和Lü超混沌系统为例,数值仿真验证了所设计方法的有效性和可行性。

广义Hénon系统的广义超混沌同步

提出实现广义混沌或超混沌同步的一种构造响应系统的方法.该方法从已知的混沌或超混沌驱动系统出发,拆分并保留系统稳定的线性部分,通过对驱动系统变量的线性变换构造出响应系统.以具有超混沌特性的广义H啨non离散系统为例,理论分析和数值计算的结果完全一致,表明该方法对于构造广义混沌和超混沌同步系统十分有效.

基于改进观测器的分数阶超混沌Chen系统广义同步

基于分数阶微积分的预估-校正算法,研究了分数阶超混沌Chen系统,并进行了数值仿真.仿真结果表明,分数阶超混沌Chen系统存在超混沌的最低阶数为3.8阶.根据分数阶稳定性理论,设计了一种改进的状态观测器,利用解析的方法求得广义同步的响应系统,从理论上证明了广义同步方法的可行性.最后,利用该同步方法实现了3.8阶超混沌Chen系统的广义同步,数值仿真结果证实了它的有效性.

新型超混沌系统的改进自适应广义投影同步

基于Lyapunov稳定性理论,设计合适的非线性控制器以及参数更新规则,实现一类混沌系统以及超混沌系统的改进自适应广义投影同步。该方法可以使得驱动系统和响应系统渐近地达到所有对应状态向量,按照不同的比例进行同相位或者反相位投影同步,同时既可以对响应系统中的未知参数进行辨识,也可以对驱动系统中的未知参数进行辨识,当然,该方法也可以适用于不包含未知参数的混沌系统广义投影同步。以新型的四维超混沌Lorenz系统和超混沌Chen系统为例,数值模拟结果表明了所设计控制器的有效性。

广义Hénon超混沌系统的同步及在保密通信中的应用

研究了一类超混沌系统——广义Hénon超混沌系统的同步问题.基于精确线性化和不变流形理论,针对广义Hénon超混沌系统,提出了新的混沌同步方法.其优点在于控制器的设计完全由系统输出值及其时延值来构造,避免了其他状态变量的不可测性,更有利于在实际工程中的应用.在此基础上,提出此同步系统在保密通信中的应用方案.计算机仿真结果表明了上述方法的有效性以及保密通信方案的可行性.