Design and implementation of a novel multi-scroll chaotic system

This paper proposes a novel approach for generating a multi-scroll chaotic system. Together with the theoretical design and numerical simulations, three different types of attractor are available, governed by constructing triangular wave, sawtooth wave and hysteresis sequence. The presented new multi-scroll chaotic system is different from the classical multi-scroll chaotic Chua system in dimensionless state equations, nonlinear functions and maximum Lyapunov exponents. In addition, the basic dynamical behaviours, including equilibrium points, eigenvalues, eigenvectors, eigenplanes, bifurcation diagrams and Lyapunov exponents, are further investigated. The success of the design is illustrated by both numerical simulations and circuit experiments.

Implementation of a novel two-attractor grid multi-scroll chaotic system

This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function. Some basic dynamical properties, such as equilibrium points, bifurcations, and phase diagrams, were studied. Furthermore, the system was experimentally confirmed by an electronic circuit. The circuit simulation results and numerical simulation results verified the feasibility of this method.

A new multi-scroll chaotic generator

In this paper a new simple multi-scroll chaotic generator is studied. The characteristic of this new multi-scroll chaotic generator is that it is easy to generate different number of scroll chaotic attractors through modifying the nature number n after fixing the suitable system parameters and it does not need complex mathematical derivation. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on Electronic Workbench （EWB）.

Adaptive generalized synchronization between Chen system and a multi-scroll chaotic system

Based on Lyapunov theory, the adaptive generalized synchronization between Chen system and a multi-scroll chaotic system is investigated. According to the form of target function a proper adaptive controller is designed, by which the controlled Chen system can be synchronized with a multi-scroll chaotic system including unknown parameters. The Lyapunov direct method is exploited to prove that the synchronization error and parameter identification error both converge to zero. Numerical simulation results verify the feasibility of the proposed method further.

A novel multi-scroll chaotic generator:Analysis, simulation, and implementation

Based on a new three-dimensional autonomous linear system and designing a specific form of saturated function series and a sign function with two variables of system, which are employed to increase saddle-focus equilibrium points with index 2, a novel multi-scroll chaotic system is proposed and its typical dynamical characteristics including bifurcation diagram, Poincare map, and the stability of equilibrium points are analyzed. The hardware circuit is designed and the experimental results are presented for confirmation.

A new multi-scroll chaotic system

This paper proposes a new simple autonomous chaotic system which can generate multi-scroll chaotic attractors. The characteristic of this new multi-scroll chaotic system is that the 4n ＋ 2rn ＋ 4-scroll chaotic attractors are generated easily with n and m vaxying under n ≤ m. Various number of scroll chaotic attractors are illustrated not only by computer simulation but also by the realization of an electronic circuit experiment on EWB （Electronics Workbench）.

Novel two-directional grid multi-scroll chaotic attractors based on the Jerk system

A new method is presented to generate two-directional (2D) grid multi-scroll chaotic attractors via a specific form of the sine function and sign function series, which are applied to increase saddle points of index 2. The scroll number in the x-direction is modified easily through changing the thresholds of the specific form of the sine function, while the scroll number in the y-direction is controlled by the sign function series. Some basic dynamical properties, such as equilibrium points, bifurcation diagram, phase portraits, and Lyapunov exponents spectrum are studied. Furthermore, the electronic circuit of the system is designed and its simulation results are given by Multisim 10.

Generating one-,two-,three-and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.

混沌理论与非线性经济系统

简述了混沌的定义、特征以及混沌系统的判定方法，并初步探讨了混沌理论在非线性经济系统中的应用。

对脑干听觉诱发电位相关维数的研究

用二维延时重构技术重构了脑干听觉诱发电位（ＢＡＥＰ）时间序列，并用Ｇｒａｓｓｂｅｒｇｅｒ－ｐｒｏｃａｃｃｉａ算法计算了正常人与有听觉障碍病人的关联积分Ｃ（ｒ）．结果表明在局部线性区域，病人的关联维数Ｄ２较正常人偏高，两者的Ｄ２均不收敛．Ｍａｃｋｅｙ－Ｇｌａｓｓ方程的数值模拟表明噪声不是影响Ｄ２的根本原因．因此，ＢＡＥＰ信号不是一个稳定的混沌吸引子，Ｄ２不能作为临床识别的标准．

四维系统中多涡卷混沌与超混沌吸引子的仿真研究

在双涡卷混沌吸引子的基础上 ,以变型蔡氏电路和四阶蔡氏电路为例 ,提出一种研究四维系统中多涡卷混沌与超混沌吸引子的新方法 .根据这一方法 ,从数学上找到了一种能产生多涡卷的递推规律 ,其特点是只需给定三个初始值ma,mb 和x1 ,由文中所导出的递推公式 ,可确定多涡卷吸引子中分段线性奇函数的各个转折点和平衡点的值 ,从而能在四维系统中产生多涡卷混沌与超混沌吸引子 ,并且这种方法可以推广到产生任意多个涡卷的情形 ,因此 ,它具有一般的规律性 .理论分析、计算机模拟和电路仿真结果证明了该方法的可行性 .