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  本文關(guān)鍵詞： 分?jǐn)?shù)階超混沌系統(tǒng) 反饋同步 投影同步 自適應(yīng)同步 參數(shù)不確定　出處：《東北師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：本文主要研究了分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng)的同步問題。以分?jǐn)?shù)階穩(wěn)定性理論為基礎(chǔ),運用三種典型的同步方法(反饋同步法,投影同步法,自適應(yīng)同步法)對分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng)的同步問題進(jìn)行了深入研究。研究工作以理論分析為基礎(chǔ),并利用電路仿真和數(shù)值模擬對研究內(nèi)容進(jìn)行了分析和論證。首先,介紹了分?jǐn)?shù)階混沌系統(tǒng)及其同步方法在國內(nèi)外的研究現(xiàn)狀,概述了本文的研究意義。提出了分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng),理論分析證明其為超混沌系統(tǒng),系統(tǒng)的數(shù)值模擬和電路仿真進(jìn)一步顯示了其具有復(fù)雜的動力學(xué)特性,為研究工作提供依據(jù)。其次,用投影同步法、反饋同步法和自適應(yīng)同步法對分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng)的同步進(jìn)行了研究。首先,通過分?jǐn)?shù)階穩(wěn)定性理論設(shè)計出合適的同步控制器,實現(xiàn)分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng)的線性反饋、非線性反饋同步。然后,通過選取合適的同步控制器,實現(xiàn)了分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng)的廣義投影同步和修正投影同步。最終,以Lyapunov方程判定分?jǐn)?shù)階混沌系統(tǒng)穩(wěn)定為依據(jù),設(shè)計了分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng)的反饋自適應(yīng)同步控制器和未知參數(shù)的自適應(yīng)律,實現(xiàn)了系統(tǒng)的自適應(yīng)同步。電路仿真和數(shù)值模擬證明這些同步方法應(yīng)用到分?jǐn)?shù)階超混沌系統(tǒng)是有效的。最后,結(jié)合分?jǐn)?shù)階穩(wěn)定性理論,通過反饋同步法、函數(shù)投影同步法和自適應(yīng)同步法實現(xiàn)參數(shù)不確定的分?jǐn)?shù)階改進(jìn)Liu超混沌系統(tǒng)同步且辨識了系統(tǒng)的未知參數(shù),數(shù)值模擬的結(jié)果證明了同步方法可以應(yīng)用到分?jǐn)?shù)階超混沌系統(tǒng)。
[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.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O415.5;O231

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本文編號：1497786