三维四翼广义增广Lü系统

增广Lü系统是仅含有两个控制参数的三维混沌系统,可产生一个伪四翼吸引子.利用混沌反控制方法,通过在增广Lü系统中引入一个简单的线性状态控制器,提出了一个新三维混沌系统——广义增广Lü系统.新系统实现了一个真正的具有复合结构的四翼吸引子,它包含了两个镜像对称的子系统.理论分析、数值仿真和电路实验证明了广义增广Lü系统四翼吸引子的存在性,也阐述了广义增广Lü系统有着较增广Lü系统更加丰富的动力学特性. 关键词： 广义增广Lü系统 四翼吸引子 数值仿真 电路实验     

TS fuzzy realization of chaotic Lü system

The Lü attractor is a new chaotic attractor, which connects the Lorenz attractor and the Chen attractor and represents the transition from one to the other. The Letter presents a hybrid TS fuzzy modeling approach for the newly coined chaotic Lü system. Then the abundant and fundamental dynamical behaviors of the chaotic Lü system are completely and comprehensive investigated based on this novel hybrid TS fuzzy model.     

A new hyperchaos system and its circuit simulation by EWB

This paper reports a new hyperchaotic system evolved from the three-dimensional Lü chaotic system. The Lyapunov exponents spectrum and the bifurcation diagram of this new hyperchaotic system are obtained. Hyperchaotic attractor, periodic orbit and chaotic attractor are obtained by computer simulation. A circuit is designed to realize this new hyperchaotic system by electronic workbench.     

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation.     

A Hyperchaotic Attractor Coined from Chaotic Lü System

We report a new hyperchaotic attractor coined from the chaotic Lü system by using a state feedback controller. Theoretical analyses and simulation experiments are conducted to investigate the dynamical behaviour of the proposed hyperchaotic system     

复杂超混沌Lü系统的电路实验

利用对Lü系统实施反混沌控制的方法,构建了一类关联且有多种切换方式的四维超混沌Lü系统.依据系统的分岔图确定了各个子系统都处于超混沌状态时,系统参数的取值范围.分析了超混沌Lü系统平衡点的性质、超混沌吸引子的相图和Lyapunov指数等特性,设计并实现了这类可切换超混沌Lü系统的硬件电路,利用系统选择器,同一电路可以实现多个关联子系统的功能.电路实验表明,可切换的复杂超混沌Lü系统具有丰富的动力学行为. 关键词： 超混沌Lü系统 切换 分岔图 电路实验     

超混沌Lü系统的电路实现

在三维Lü系统的基础上增加一维状态,构建了一个新的四维超混沌Lü系统,简要地分析了该系统平衡点的性质、超混沌吸引子的相图、Lyapunov指数和Lyapunov维数等特性,并设计了一种实现四维超混沌系统的实际电路. 硬件电路实验表明,超混沌Lü系统具有丰富的动力学行为. 关键词： 超混沌Lü系统 Lyapunov指数 电路实现     

Impulsive Synchronization of Lü Chaotic System Based on Small Impulsive Signal

In this Letter the issue of impulsive synchronization of the Lü chaotic system is developed. We propose an impulsive synchronization scheme of the Lü chaotic system including chaotic systems. Some new and sufficient conditions on varying impulsive distance are established in order to guarantee the synchronizability of the systems using the synchronization method. In particular, some simple conditions are derived in synchronizing the systems by equal impulsive distances. The proposed impulsive synchronization scheme is applied to the Lü chaotic system and the numerical example demonstrates the effectiveness of the method. The boundaries of the stable regions are also estimated.     

超混沌分数阶Lü系统电路实验与追踪控制

对提出的新型超混沌Lü系统,研究了其分数阶混沌系统,通过数值仿真和电路实验,证实了分数阶超混沌Lü系统的混沌行为.利用分数阶系统稳定性理论,设计简单的线性反馈控制器,成功地实现了分数阶超混沌Lü系统的所有状态向量与正弦信号和任意不动点的追踪控制.仿真结果表明了该方法的有效性. 关键词： 分数阶Lü系统 超混沌系统 电路实验 追踪控制     

Chaotic dynamics of the fractional-order Lü system and its synchronization

In this Letter we numerically investigate the chaotic behaviors of the fractional-order Lü system. A striking finding is that the lowest order for this system to have chaos is 0.3, which is the lowest-order chaotic system among all the found chaotic systems reported in the literature to date. Period-doubling routes to chaos in the fractional-order Lü system are also found. Master–slave synchronization of chaotic fractional-order Lü systems with linear coupling is also studied.     

Adaptive backstepping control of the uncertain Lü system

In this paper we investigate further the method for controlling the uncertain Lue system via adaptive backstepping.The Lue system is transformed into the so-called general strict-feedback form.Then a novel control method can overcome the sigularity problem.Numerical simulations show the effectiveness and feasibility of this approach.     

一个新的混沌系统及其性质研究

构造了一个新的不同于Lorenz系统、Chen系统和Lü系统的三维连续自治混沌系统.该系统含有四个参数，两个非线性乘积项.通过理论推导、数值仿真、Lyapunov指数谱、分岔图和Poincaré截面图研究了系统的基本动力学特性，并分析了改变不同参数时系统动力学行为的变化. 关键词： 混沌系统 混沌生成 Lorenz系统 Lyapunov指数谱     

Global exponential synchronization between Lü system and Chen system with unknown parameters and channel time-delay

This paper proposes a nonlinear feedback control method to realize global exponential synchronization with channel time-delay between the Lü system and Chen system,which are regarded as the drive system and the response system respectively.Some effective observers are produced to identify the unknown parameters of the Lü system.Based on the Lyapunov stability theory and linear matrix inequality technique,some sufficient conditions of global exponential synchronization of the two chaotic systems are derived.Simulation results show the effectiveness and feasibility of the proposed controller.     

Dynamics of a Lüders Band and Destruction of an Aluminum-Magnesium Alloy,Initiated by a Stress Concentrator

Spatio-temporal localization of deformation and the rupture of the aluminum-magnesium AlMg6 alloy, initiated by a geometrical stress concentrator, are studied in situ by video recording at a speed of 500 to 20000 frames/s. It is established that a stress concentrator in the form of a small notch with a depth about 1% of the width of a flat specimen is an attractor of bands of macrolocalized plastic deformation, starting from a Lüders band and ending with the start of the main crack. The key role of intersecting deformation macrobands in the development of the main crack is revealed. Possible micromechanisms of viscous destruction associated with the dynamics of the intersection of deformation bands are discussed.     

分数阶统一混沌系统的投影同步

改变系统参数计算了分数阶统一系统的最大Lyapunov指数和关联维数,研究了分数阶统一系统的动力学行为.基于线性系统的稳定判定准则,设计了一种同步方案,实现了分数阶统一混沌系统的投影同步.通过对分数阶Chen系统、分数阶Lü系统和分数阶类Lorenz系统投影同步的数值模拟,进一步验证了所提出方案的有效性.     

Adaptive synchronization of a hyperchaotic L system based on extended passive control

This paper investigates the adaptive synchronization of hyperchaotic Lü systems based on the method of extended passive control. By combining the feedback control, the extended passive control method with two output variables is developed, which can synchronize hyperchaotic Lü systems asymptotically and globally more easily without knowing the bound of state of the hyperchaotic system. Adaptive laws are introduced to estimate the unknown parameters as well. Simulation results show the effectiveness and flexibility of the proposed control scheme.     

Adaptive lag synchronization and parameter identification of fractional order chaotic systems

This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic Lü system is used to illustrate the validity of this theoretic method.     

分数阶混沌系统的异结构同步

基于分数阶线性系统稳定性理论,结合反馈控制和主动控制方法,提出了一种分数阶混沌系统异结构同步方法,给出了同步控制器解析式. 以分数阶Chen混沌系统和分数阶Liu混沌系统、分数阶新超混沌系统和分数阶超混沌Rssler系统的异结构同步为例, 进行了数值模拟,证实了该方法的有效性和可行性. 关键词： 分数阶混沌 异结构混沌同步 新超混沌系统 超混沌Rssler系统     

Analysis of the Δ -resonance in a finite volume<Superscript>⋆</Superscript>

We discuss Lüscher's approach for the extraction of the Δ -resonance parameters from lattice QCD data. Within this approach, we propose a novel strategy to analyze the data corresponding to the finite volume energy spectrum. By using the new method, it is further demonstrated that Lüscher's approach allows one to determine the mass and width of the Δ at a reasonable accuracy, despite the fact that the “avoided level crossing” in the energy spectrum has been washed out due to the large width of the resonance.     

A novel 3D autonomous system with different multilayer chaotic attractors

This Letter proposes a novel three-dimensional autonomous system which has complex chaotic dynamics behaviors and gives analysis of novel system. More importantly, the novel system can generate three-layer chaotic attractor, four-layer chaotic attractor, five-layer chaotic attractor, multilayer chaotic attractor by choosing different parameters and initial condition. We analyze the new system by means of phase portraits, Lyapunov exponent spectrum, fractional dimension, bifurcation diagram and Poincaré maps of the system. The three-dimensional autonomous system is totally different from the well-known systems in previous work. The new multilayer chaotic attractors are also worth causing attention.