A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system

This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms, and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis, the Hopf bifurcation processes are proved to arise at certain equilibrium points. Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours; the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally, an analog electronic circuit is designed to physically realize the chaotic system; the existence of four-wing chaotic attractor is verified by the analog circuit realization.     

Convergence and stability of recursive damped least square algorithm

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分数阶Lorenz系统的分析及电路实现

频域传递函数近似方法不仅是常用的 分数阶混沌系统相轨迹的数值分析方法之一, 而且也是设计分数阶混沌系统电路的主要方法. 应用该方法首先研究了分数阶Lorenz系统的混沌特性, 通过对Lyapunov指数图、分岔图和数值仿真分析, 发现了其较为丰富的动态特性, 即当分数阶次从0.7到0.9以步长0.1变化时, 该分数阶Lorenz系统既存在混沌特性, 又存在周期特性, 从数值分析上说明了在更低维的Lorenz系统中存在着混沌现象. 然后又基于该方法和整数阶混沌电路的设计方法, 设计了一个模拟电路实现了该分数阶Lorenz系统, 电路中的电阻和电容等数值是由系统参数和频域传递函数近似确定的. 通过示波器观测到了该分数阶Lorenz系统的混沌吸引子和周期吸引子的相轨迹图, 这些电路实验结果与数值仿真分析是一致的, 进一步从物理实现上说明了其混沌特性. 关键词： 分数阶系统 Lorenz系统 分岔分析 电路实现     

混沌系统的自适应多变量广义预测控制与同步

提出了一种应用带时变遗忘因子的自适应多变量广义预测控制算法(β-MGPC)，对Lorenz，Rossler，Chua电路等典型混沌系统进行控制，使之跟踪任意给定参考信号，数值仿真表明了该控制算法的良好效果.这种方法的优点在于无需知道混沌系统的精确模型，便可实现混沌系统的大范围的跟踪和同步控制. 关键词： 混沌控制 混沌同步 自适应预测控制 时变遗忘因子     

Generation of on-off intermittency based on RSssler chaotic system

In this paper, one-state on-off intermittency and two-state on-off intermittency are generated in two five- dimensional continuum systems respectively. In each system, a two-dimensional subsystem is driven by the Rossler chaotic system. The parameter conditions under which the on-off intermittency occurs are discussed in detail. The statistical property of the intermittency is investigated. It is shown that the distribution of the laminar phase duration time follows a power law with an exponent of -3/2, which is a signature of on-off intermittency. Moreover, the phenomenon of intermingled basins is observed when attractors in the two symmetric invariant subspaces are stable. We provide an effective way to generate on-off intermittency based on a chaotic system, which is important for application and theoretical study.     

无限时域预测控制的直接求解算法

在预测控制中，当预测时域取为无穷大时通常可保证闭环系统的稳定性，本文通过分析和利用这种算法的本质，把上述问题转化为一个具有部分状态等式约束的二次优化过程，获得了一种直接的算法，避免了传统方法需要迭代的缺点。     

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     

Implementation of LT codes based on chaos

Fountain codes provide an efficient way to transfer information over erasure channels like the Internet. LT codes are the first codes fully realizing the digital fountain concept. They are asymptotically optimal rateless erasure codes with highly efficient encoding and decoding algorithms. In theory, for each encoding symbol of LT codes, its degree is randomly chosen according to a predetermined degree distribution, and its neighbours used to generate that encoding symbol are chosen uniformly at random. Practical implementation of LT codes usually realizes the randomness through pseudo-randomness number generator like linear congruential method. This paper applies the pseudo-randomness of chaotic sequence in the implementation of LT codes. Two Kent chaotic maps are used to determine the degree and neighbour（s） of each encoding symbol. It is shown that the implemented LT codes based on chaos perform better than the LT codes implemented by the traditional pseudo-randomness number generator.     

A dynamic epidemic control model on uncorrelated complex networks

In this paper, a dynamic epidemic control model on the uncorrelated complex networks is proposed. By means of theoretical analysis, we found that the new model has a similar epidemic threshold as that of the susceptible-infectedrecovered （SIR） model on the above networks, but it can reduce the prevalence of the infected individuals remarkably. This result may help us understand epidemic spreading phenomena on real networks and design appropriate strategies to control infections.     

Nonlinear dynamics analysis of cluster-shaped conservative flows generated from a generalized thermostatted system

The thermostatted system is a conservative system different from Hamiltonian systems,and has attracted much attention because of its rich and different nonlinear dynamics.We report and analyze the multiple equilibria and curve axes of the cluster-shaped conservative flows generated from a generalized thermostatted system.It is found that the cluster-shaped structure is reflected in the geometry of the Hamiltonian,such as isosurfaces and local centers,and the shapes of cluster-shaped chaotic flows and invariant tori rely on the isosurfaces determined by initial conditions,while the numbers of clusters are subject to the local centers solved by the Hessian matrix of the Hamiltonian.Moreover,the study shows that the cluster-shaped chaotic flows and invariant tori are chained together by curve axes,which are the segments of equilibrium curves of the generalized thermostatted system.Furthermore,the interesting results are vividly demonstrated by the numerical simulations.