新型双曲忆阻混沌系统的动力学分析、同步控制与应用

发布时间：2019-04-13 08:05

【摘要】：忆阻混沌系统是典型的非线性系统,由于具有对初始条件和系统参数极为敏感、具有瞬态混沌、多隐藏吸引子共存以及状态转移等与众不同的物理现象,因而有着极其复杂的动力学行为,并为混沌保密通信和实际工程应用提供了更新的有效路径。本文的研究内容具有一定的创新性和实用性,主要研究成果如下:(1)提出一个四维忆阻混沌系统,实现了其在图像加密中的应用首先,设计了一种新型双曲函数忆阻模型,并将其引入到改进的三维混沌系统中,得到了新型的四维双曲忆阻混沌电路系统,通过改变参数绘出了系统的Lyapunov指数谱和分岔图等,进而详细分析了系统的混沌演化过程。其次,设计了系统对应的硬件实验电路,实验结果与数值仿真一致;最后,将该系统的混沌序列应用到图像加密中,分析了加密直方图、相邻像素相关性以及抗攻击能力与密钥敏感性,仿真结果表明了忆阻混沌系统具有良好的图像加密效果。(2)设计了一个含两个双曲忆阻器的五维混沌振荡电路系统,并分析了其多稳态共存的特性首先,结合经典蔡氏电路,设计了具有两个双曲忆阻器的混沌振荡电路系统,并研究了系统随参数以及随忆阻初始状态变化的系统运行状态,证实了提出的双忆阻器系统不仅依赖于电路参数的变化,还极端依赖于系统初始条件的改变。此外,五维双曲忆阻混沌系统具有丰富的多稳态特性,包括了不同拓扑结构的混沌吸引子以及周期运动的共存,最多时可达到12种多隐藏吸引子共存。最后,利用幅值放大法有效地进行了系统的多稳态吸引子搜索,同样获得了不同的周期运动与混沌吸引子的共存,搜索结果与数值仿真存在较高的一致性。(3)实现了初始值不同的五维双忆阻器混沌系统的完全同步和投影同步首先,基于李雅普诺夫稳定性理论,设计了线性反馈控制器,实现了不同初始值条件下的五维双忆阻器混沌系统之间的完全同步,控制方案简单有效,易于实现。其次,利用主动同步控制法,设计了合适的非线性反馈控制器,实现了在不同初始状态下的同结构双曲忆阻混沌系统的投影同步,误差系统响应快,同步性能指标高。
[Abstract]:Memorialized chaotic system is a typical nonlinear system. Due to its sensitivity to initial conditions and system parameters, transient chaos, coexistence of multiple hidden attractors and state transition, it is different from others in physical phenomena, such as transient chaos, multi-hidden attractor coexistence and state transition. Therefore, it has extremely complex dynamic behavior, and provides a new and effective path for chaotic secure communication and practical engineering application. The main research results are as follows: (1) A four-dimensional memory chaotic system is proposed, and its application in image encryption is realized. Firstly, a new hyperbolic function memoir model is designed. By introducing it into the improved three-dimensional chaotic system, a new type of four-dimensional hyperbolic memory-resistant chaotic circuit system is obtained. By changing the parameters, the Lyapunov exponent spectrum and bifurcation diagram of the system are plotted, and the chaotic evolution process of the system is analyzed in detail. Secondly, the hardware experiment circuit of the system is designed, and the experimental results are consistent with the numerical simulation. Finally, the chaotic sequence of the system is applied to image encryption. The encrypted histogram, the correlation of adjacent pixels, the anti-attack ability and the key sensitivity are analyzed. The simulation results show that the memory-resistant chaotic system has a good image encryption effect. (2) A five-dimensional chaotic oscillatory circuit system with two hyperbolic memoirs is designed, and its multi-steady-state coexistence characteristics are analyzed. Based on the classical Cai's circuit, a chaotic oscillatory circuit system with two hyperbolic memoirs is designed, and the operating state of the system with the parameter and the initial state of the memory resistance is studied. It is proved that the proposed double-resistor system depends not only on the variation of the circuit parameters, but also on the change of the initial conditions of the system. In addition, the five-dimensional hyperbolic memory-resistant chaotic system has rich multi-stable properties, including the coexistence of chaotic attractors with different topologies and periodic motion, and the coexistence of 12 kinds of multi-hidden attractors can be achieved at most. Finally, the amplitude magnification method is used to search the multistable attractor effectively, and the coexistence of different periodic motion and chaotic attractor is also obtained. There is a high consistency between the search results and numerical simulation. (3) the complete synchronization and projection synchronization of five-dimensional double-resistor chaotic systems with different initial values are realized. Firstly, based on Lyapunov stability theory, a linear feedback controller is designed. The complete synchronization between five-dimensional double-resistor chaotic systems with different initial values is realized. The control scheme is simple, effective and easy to implement. Secondly, using the active synchronization control method, a suitable nonlinear feedback controller is designed to realize the projective synchronization of the hyperbolic memory-resistance chaotic system with the same structure in different initial states. The error system can respond quickly and the synchronization performance index is high.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O415.5;TN60

【参考文献】