含有忆阻器的时滞混沌电路的动力学分析及其同步控制

The chaotic circuit based on memristor has a wide range of application background in engineering, research on the dynamic characteristics and the mechanism of those has become one of the hot topics in fields of nonlinear dynamics and control at home and abroad. Due to the ubiquitous existence of time-delay in real circuit, in this project, mathematical model of time-delay chaotic circuit with memristor will be established based on Chua 's circuit via modern non-linear theory and method as well as the stability of the system is to be analyzed. The dynamical behaviors of the circuit system, such as equilibrium points, attractors, cluster oscillations and bifurcation, are to be investigated. The influence on the dynamical behavior with mechanism of system parameters and topology structure of circuit system will be revealed. Effects of time-delay, impulse and boundary conditions of the circuit system on the dynamic behavior of the system are to be explored. Chaotic synchronization schemes of chaotic circuit system under the influence of external disturbances and noise are to be given. The sufficient conditions for the system to achieve synchronization are to be obtained. Synchronization of the circuit system with different parameters or different topology in limited time is to be solved. The results of the research will not only enrich and develop the theory of nonlinear dynamics, but also has important engineering application value for physical realization of chaotic circuit and provide important theoretical support for the application of chaotic circuit with memristor in practical engineering, such as design of soft switching .

基于忆阻器的混沌电路有着广泛的工程应用背景，其动力学特性及其机理的研究成为当前国内外非线性动力学和控制领域的热点问题之一。由于实际电路系统中普遍存在时滞，本项目将利用现代非线性理论和方法，在蔡氏电路的基础上构建含有忆阻器的时滞混沌电路的数学模型，对系统的稳定性进行分析；分析系统的周期振荡、簇发振荡、混沌吸引子及分岔等动力学行为，揭示系统的参数、状态变量初值及拓扑结构等因素对系统动力学行为的影响及其机理；探索时滞、脉冲以及电路的边界条件等对系统动力学行为的影响；研究含有忆阻器的时滞混沌电路在外部干扰和噪声影响下的混沌同步方案以及系统实现同步的条件，探讨不同参数、不同拓扑结构下系统在有限时间内的同步问题。研究结果不仅能够丰富和发展非线性动力学的相关理论，而且对忆阻混沌电路的物理实现具有重要的工程应用价值，为忆阻混沌电路在软开关设计等领域的应用提供重要的理论支撑。

基于忆阻器的混沌电路有着广泛的工程应用背景，其动力学特性及其机理的研究成为当前国内外非线性动力学和控制领域的热点问题之一。由于实际电路系统中普遍存在时滞，本项目利用现代非线性理论和方法，在蔡氏电路的基础上构建了含有忆阻器的时滞混沌电路的数学模型，对系统的动力学行为进行了研究和探讨。分析了含有忆阻器的时滞混沌电路的动力学特性及其诱发机制，得到了系统的不同分岔模式，尤其是依赖于初始条件和时滞所呈现的多稳定性。揭示了不同系统参数、不同拓扑结构、不同耦合方式以及噪声和周期激励等因素对含有忆阻器的时滞混沌电路动力学行为的影响及其诱发机理。得到了不同系统参数、不同拓扑结构、不同耦合方式以及噪声和周期激励等因素对含有忆阻器的时滞混沌电路的同步效应的影响。利用含有忆阻器的时滞混沌电路的动力学特性构建了具有实际应用价值的物理电路，为软开关电路设计等工程应用提供理论支撑。