分数阶改进Liu超混沌系统的同步研究

发布时间：2018-02-09 11:06

本文关键词： 分数阶超混沌系统反馈同步投影同步自适应同步参数不确定　出处：《东北师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文主要研究了分数阶改进Liu超混沌系统的同步问题。以分数阶稳定性理论为基础,运用三种典型的同步方法(反馈同步法,投影同步法,自适应同步法)对分数阶改进Liu超混沌系统的同步问题进行了深入研究。研究工作以理论分析为基础,并利用电路仿真和数值模拟对研究内容进行了分析和论证。首先,介绍了分数阶混沌系统及其同步方法在国内外的研究现状,概述了本文的研究意义。提出了分数阶改进Liu超混沌系统,理论分析证明其为超混沌系统,系统的数值模拟和电路仿真进一步显示了其具有复杂的动力学特性,为研究工作提供依据。其次,用投影同步法、反馈同步法和自适应同步法对分数阶改进Liu超混沌系统的同步进行了研究。首先,通过分数阶稳定性理论设计出合适的同步控制器,实现分数阶改进Liu超混沌系统的线性反馈、非线性反馈同步。然后,通过选取合适的同步控制器,实现了分数阶改进Liu超混沌系统的广义投影同步和修正投影同步。最终,以Lyapunov方程判定分数阶混沌系统稳定为依据,设计了分数阶改进Liu超混沌系统的反馈自适应同步控制器和未知参数的自适应律,实现了系统的自适应同步。电路仿真和数值模拟证明这些同步方法应用到分数阶超混沌系统是有效的。最后,结合分数阶稳定性理论,通过反馈同步法、函数投影同步法和自适应同步法实现参数不确定的分数阶改进Liu超混沌系统同步且辨识了系统的未知参数,数值模拟的结果证明了同步方法可以应用到分数阶超混沌系统。
[Abstract]:In this paper, the synchronization problem of fractional order improved Liu hyperchaotic system is studied. Based on fractional stability theory, three typical synchronization methods (feedback synchronization method, projection synchronization method, projection synchronization method) are used. Adaptive synchronization method) is used to study the synchronization problem of fractional order improved Liu hyperchaotic system. The research work is based on theoretical analysis, and the research content is analyzed and demonstrated by circuit simulation and numerical simulation. This paper introduces the research status of fractional order chaotic system and its synchronization methods at home and abroad, and summarizes the significance of this paper. A fractional order improved Liu hyperchaotic system is proposed and proved to be a hyperchaotic system by theoretical analysis. The numerical simulation and circuit simulation of the system further show that the system has complex dynamic characteristics, which provides the basis for the research work. Secondly, the projection synchronization method is used. Feedback synchronization method and adaptive synchronization method are used to study the synchronization of fractional order improved Liu hyperchaotic systems. Firstly, a suitable synchronization controller is designed based on fractional stability theory to realize linear feedback of fractional order improved Liu hyperchaotic systems. Nonlinear feedback synchronization. Then, the generalized projection synchronization and modified projection synchronization of fractional improved Liu hyperchaotic systems are realized by selecting appropriate synchronization controllers. Finally, based on the Lyapunov equation to determine the stability of fractional chaotic systems, The feedback adaptive synchronization controller and the adaptive law of unknown parameters for fractional order improved Liu hyperchaotic systems are designed. The adaptive synchronization of the system is realized. The circuit simulation and numerical simulation show that these synchronization methods are effective to the fractional hyperchaotic system. Finally, combining with the fractional stability theory, the feedback synchronization method is used. The function projection synchronization method and adaptive synchronization method are used to synchronize the hyperchaotic Liu systems with uncertain parameters and the unknown parameters of the system are identified. The numerical simulation results show that the synchronization method can be applied to fractional hyperchaotic systems.
【学位授予单位】：东北师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O415.5;O231

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