复混沌系统的稳态控制

混沌系统的多稳态具有复杂性和非预期性,引起了人们的极大关注,如何针对混沌系统进行稳态控制还没有有效的方法.混沌吸引子是复混沌系统典型的动态特性.本文的主要目标是选择合适的控制方法使复混沌系统在预定的位置范围获得期望的稳态吸引子.本文即针对复混沌稳态吸引子的控制问题,提出了分段函数控制器和比例正弦函数控制器,分别用于实现稳态吸引子的位置控制和形状控制,其中混沌吸引子的位置由分段函数的间隔控制,混沌吸引子的形状由系统参数或正弦函数控制.这两种控制器简单可行,易于实现.最后,通过复Lorenz混沌系统和一个物理实例Duffing振子仿真实验验证了所提出控制器的有效性.     

Analysis,synchronisation and circuit design of a new highly nonlinear chaotic system

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master–slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.     

新混沌系统及其特性分析

提出了一个新的不同于Lorenz系统和Chen系统的三维自治混沌系统。这个混沌系统的奇怪吸引子与Lorenz、Chen系统、Ln系统以及Liu系统不同,存在六个平衡点,其拓扑结构与它们的拓扑结构也完全不同。该系统含有五个参数,其中三个方程中均含有非线性顷。分析了该新系统的混沌吸引子相图、平衡点及其性质、Lyapunov指数和分形维数等非线性动力学特性。     

A new 3D chaotic system with golden proportion equilibria: Analysis and electronic circuit realization

This article introduces a new three-dimensional quadratic continuous autonomous chaotic system with golden proportion equilibria, which can generate single folded attractor. Some basic dynamical behaviors and the dynamical structure of the new chaotic system are investigated either analytically or numerically. Finally, the chaos generator of the new chaotic system was designed, simulated and experimentally confirmed via a novel electronic circuit design. A good qualitative agreement is illustrated between the simulations and the experimental results. It is convenient to use the new system to purposefully generate chaos in chaos applications. The new system has eight terms, two quadratic nonlinearities and two parameters (a and b). The new chaotic attractor equations have three equilibrium points and more interestingly the equilibrium points have golden proportion values.     

混沌吸引子不稳定周期轨道控制方法研究

提出一种控制混沌吸引子不稳定周期轨道的新方法,该方法先从系统映射图中找出混沌吸引子不稳定不动点的近似值,然后利用非线性反馈达到控制混沌的目的,这种方法的主要特点是不需要知道混沌系统的具体模型,而且可以在混沌态的任意时刻施加控制作用,另外,该方法还具有很强的抗干扰能力和非常快的收敛速度,控制结构简单,易于实现,仿真结果表明了该方法的有效性。     

一个三维非线性系统的混沌运动及其控制

通过数值计算、理论推导分析了一个三维类Lorenz混沌系统的基本动力学特性, 并通过数值仿真、相图、Poincare截面图和功率谱研究了这个系统的混沌行为. 然后, 构建一个受控系统并利用Lyapunov指数谱、分叉图分析了该系统混沌吸引子的形成机制, 通过对控制参数的改变, 系统的混沌运动可以得到有效控制.     

混沌系统的RBF神经网络控制设计

对镇定一嵌入在混沌吸引子内的不稳定平衡点上的混沌轨道提出了一种新的混沌系统神经网络补偿控制方法，探讨了用神经网络估计混沌系统不确定性的途径，给出了神经补偿控制器的设计方法，并证明了闭环系统的稳定性。以三阶Ｌｏｒｅｎｚ方程为例给出了仿真结果。     

Nonlinear Sprott94 Case A chaotic equation: Synchronization and masking communication applications

The nonlinear autonomous Sprott94 Case A chaotic equations are algebraically simple but can generate a complex chaotic attractor. In this paper, the Sprott94 Case A system is found suitable for chaotic synchronization circuits and chaotic masking communication circuits using Matlab–Simulink® and Orcad–PSpice® programs. Simulation results are used to visualize and illustrate the effectiveness of Sprott94 Case A chaotic system in synchronization and secure communication. The applicability of chaos to secure communication is verified by all simulation results performed on Sprott94 Case A chaotic system.     

单核单涡旋混沌系统定平面折返控制法

基于混沌细胞模型理论,提出适用于单核单涡旋混沌系统的定平面折返控制法.让混沌系统的运动轨线在确定的平面折返,并用一线性系统取代混沌系统作折返运动,从而大大降低了系统的随机性.适当选择折返平面,可控制混沌系统稳定运行于某些周期轨道上.用该控制方法对多个典型混沌系统进行数字仿真实验,获得了稳定的周期1、周期2和周期4轨道.     

基于DSP Builder的四维时滞混沌系统数字电路设计与仿真

以Lorenz混沌系统为基础,通过线性反馈扩展系统维数,设计一个四维混沌系统,分析系统的动力学特性。在引入时滞量后,进一步观察这个系统的动力学行为。为了克服模拟电路设计混沌系统的固有缺陷,将混沌系统进行离散化处理,提出基于DSP Builder软件设计时滞混沌吸引子的方法。通过数字电路的优化设计,参数的合理配置,该系统的信号幅度控制合理,计算机仿真结果表明在DSPBuilder下与MatLab下结果一致,从而使得基于FPGA混沌系统的开发变得快速、便捷,具有实际应用价值。