本文選題：新混沌系統(tǒng) + 反同步　； 參考：《暨南大學》2015年碩士論文

【摘要】：混沌是非線性領域中非線性科學的重要組成部分。它不僅存在于自然界中,而且也廣泛的存在于社會生活中。本文主要在已有混沌系統(tǒng)的基礎上提出了一個新的混沌系統(tǒng),通過理論分析和數(shù)值仿真研究了它的一些動力學特征。除此之外,由于混沌系統(tǒng)在各行各業(yè)的廣泛應用,本文也研究了它的自結構和不同維異結構的反同步和雙同步問題。文中主要內容如下:第一章緒論部分,簡單的闡述了一下混沌理論的產生發(fā)展,混沌的基本定義和一些經典的混沌系統(tǒng)以及混沌系統(tǒng)的反同步、雙同步問題。第二章穩(wěn)定性理論部分,闡述了一下Lyapunov穩(wěn)定性理論,給出了判別穩(wěn)定性的方法李雅普諾夫函數(shù)判別法以及直接判別法。第三章在已知系統(tǒng)的基礎上提出了一個新的三維自治混沌系統(tǒng),通過理論推導以及數(shù)值仿真,如系統(tǒng)的耗散性、吸引子的存在性、平衡點的穩(wěn)定性、Lyapunov指數(shù)、Lyapunov維數(shù)、對初值的敏感性以及功率譜分析來驗證提出的新混沌系統(tǒng)確實具有非常豐富的混沌特性。第四章主要研究了混沌系統(tǒng)的反同步。一方面通過設計非線性控制器來實現(xiàn)新混沌系統(tǒng)的反同步;另一方面,通過擴維并且設計非線性控制器來實現(xiàn)了不同維數(shù)的超混沌Lorenz系統(tǒng)和新混沌系統(tǒng)的反同步,并且都通過不同于以往基于Lyapunov穩(wěn)定性理論的V函數(shù)判別法而應用了拉普拉斯變換方法選擇了直接判別法理論進行了證明,最后也都通過數(shù)值仿真驗證了上述所設計控制器的合理性和可行性。第五章主要研究了混沌系統(tǒng)的雙同步,通過設計合理的控制方法,選取合適的增益向量來使得混沌系統(tǒng)達到雙同步;其次以同維數(shù)的新混沌系統(tǒng)和Chen混沌系統(tǒng)為實例進行了理論證明和數(shù)值仿真來驗證該方法的合理性和可行性;最后為進一步驗證此方法的有效性,又通過不同維數(shù)的新混沌系統(tǒng)和超混沌Lorenz系統(tǒng)進行了雙同步的驗證。最后都證明了此方法的正確性。
[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.
【學位授予單位】：暨南大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O415.5;O231

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