一个新混沌系统的反同步与双同步研究

发布时间：2018-04-12 00:26

本文选题：新混沌系统 + 反同步　；参考：《暨南大学》2015年硕士论文

【摘要】：混沌是非线性领域中非线性科学的重要组成部分。它不仅存在于自然界中,而且也广泛的存在于社会生活中。本文主要在已有混沌系统的基础上提出了一个新的混沌系统,通过理论分析和数值仿真研究了它的一些动力学特征。除此之外,由于混沌系统在各行各业的广泛应用,本文也研究了它的自结构和不同维异结构的反同步和双同步问题。文中主要内容如下:第一章绪论部分,简单的阐述了一下混沌理论的产生发展,混沌的基本定义和一些经典的混沌系统以及混沌系统的反同步、双同步问题。第二章稳定性理论部分,阐述了一下Lyapunov稳定性理论,给出了判别稳定性的方法李雅普诺夫函数判别法以及直接判别法。第三章在已知系统的基础上提出了一个新的三维自治混沌系统,通过理论推导以及数值仿真,如系统的耗散性、吸引子的存在性、平衡点的稳定性、Lyapunov指数、Lyapunov维数、对初值的敏感性以及功率谱分析来验证提出的新混沌系统确实具有非常丰富的混沌特性。第四章主要研究了混沌系统的反同步。一方面通过设计非线性控制器来实现新混沌系统的反同步;另一方面,通过扩维并且设计非线性控制器来实现了不同维数的超混沌Lorenz系统和新混沌系统的反同步,并且都通过不同于以往基于Lyapunov稳定性理论的V函数判别法而应用了拉普拉斯变换方法选择了直接判别法理论进行了证明,最后也都通过数值仿真验证了上述所设计控制器的合理性和可行性。第五章主要研究了混沌系统的双同步,通过设计合理的控制方法,选取合适的增益向量来使得混沌系统达到双同步;其次以同维数的新混沌系统和Chen混沌系统为实例进行了理论证明和数值仿真来验证该方法的合理性和可行性;最后为进一步验证此方法的有效性,又通过不同维数的新混沌系统和超混沌Lorenz系统进行了双同步的验证。最后都证明了此方法的正确性。
[Abstract]:Chaos is an important part of nonlinear science in nonlinear field.It exists not only in nature, but also in social life.In this paper, a new chaotic system is proposed on the basis of the existing chaotic system. Some dynamic characteristics of the chaotic system are studied by theoretical analysis and numerical simulation.In addition, due to the wide application of chaotic systems in various industries, this paper also studies the anti-synchronization and dual-synchronization problems of its self-structure and different dimensional structures.The main contents of this paper are as follows: the first chapter introduces the development of chaos theory, the basic definition of chaos, some classical chaotic systems and anti-synchronization and double synchronization of chaotic systems.In the second chapter, the stability theory of Lyapunov is expounded, and the methods of discriminating stability are given, such as Lyapunov function discriminant and direct discriminant.In chapter 3, a new three-dimension autonomous chaotic system is proposed on the basis of known systems. Through theoretical derivation and numerical simulation, for example, the dissipation of the system, the existence of attractors, the stability of the equilibrium point and the Lyapunov dimension.The sensitivity to the initial values and the power spectrum analysis are used to verify that the proposed new chaotic system has very rich chaotic characteristics.In chapter 4, the anti-synchronization of chaotic system is studied.On the one hand, the anti-synchronization of the new chaotic system is realized by designing a nonlinear controller; on the other hand, the hyperchaotic Lorenz system with different dimensions and the new chaotic system are de-synchronized by expanding the dimension and designing the nonlinear controller.Moreover, the direct discriminant theory is used to prove that the Laplace transformation method is different from the previous V function discriminant method based on Lyapunov stability theory.Finally, the rationality and feasibility of the designed controller are verified by numerical simulation.The fifth chapter mainly studies the double synchronization of chaotic system. By designing reasonable control method and selecting appropriate gain vector, the chaotic system can achieve double synchronization.Secondly, taking the new chaotic system of the same dimension and the Chen chaotic system as examples, the theoretical proof and numerical simulation are carried out to verify the rationality and feasibility of the method.The new chaotic system with different dimensions and the hyperchaotic Lorenz system are verified by double synchronization.Finally, the correctness of this method is proved.
【学位授予单位】：暨南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O415.5;O231

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