本文選題：新超混沌系統(tǒng) + 隱藏特性　； 參考：《東北師范大學(xué)》2017年碩士論文

【摘要】：混沌作為一種復(fù)雜的運(yùn)動(dòng)形式,在非線性動(dòng)力學(xué)中廣泛存在,也以類隨機(jī)現(xiàn)象的形式在確定性系統(tǒng)中出現(xiàn)。近年來隨著學(xué)術(shù)界研究混沌現(xiàn)象的逐漸深入,混沌控制與同步已成為研究混沌的重要內(nèi)容。由于其在物理、通信、信息科學(xué)、醫(yī)學(xué)等領(lǐng)域的巨大應(yīng)用潛力和發(fā)展前景,混沌控制與同步已成為科研界研究的熱點(diǎn)之一。相比較低維系統(tǒng),超混沌系統(tǒng)具有更復(fù)雜的動(dòng)力學(xué)行為,因此,對(duì)于超混沌系統(tǒng)的控制與同步的研究更具有應(yīng)用價(jià)值。隱藏吸引子是近年來新定義的一種吸引子,與傳統(tǒng)的自激吸引子動(dòng)力學(xué)特征不完全相同,因而引起了學(xué)術(shù)界的廣泛關(guān)注。存在隱藏吸引子的混沌系統(tǒng)具有隱藏特性,近幾年來隱藏特性得到學(xué)者們的一些關(guān)注。但由于具有隱藏特性的混沌系統(tǒng)發(fā)現(xiàn)時(shí)間較晚,關(guān)于其控制與同步的研究還比較少。本文基于Sprott B系統(tǒng),設(shè)計(jì)出了一個(gè)只具有一個(gè)參數(shù)、沒有平衡點(diǎn)、存在隱藏吸引子的新五維超混沌系統(tǒng)。首先通過理論分析,研究了具有隱藏特性的新五維超混沌系統(tǒng)的動(dòng)力學(xué)特性,如:吸引子的維數(shù)、耗散性、吸引子的存在性、Lyapunov指數(shù)和分岔等,設(shè)計(jì)了具有隱藏特性的新超混沌系統(tǒng)的電路,進(jìn)行了數(shù)值模擬和電路仿真并且用硬件電路實(shí)現(xiàn)了具有隱藏特性的新超混沌系統(tǒng),驗(yàn)證了新超混沌系統(tǒng)的動(dòng)力學(xué)特性及隱藏特性。然后對(duì)參數(shù)已知的具有隱藏特性的新超混沌系統(tǒng)運(yùn)用線性反饋法、狀態(tài)觀測(cè)器法、自適應(yīng)法、Backstepping同步法,設(shè)計(jì)出相應(yīng)的控制器,并通過理論分析、數(shù)值模擬和電路實(shí)驗(yàn)對(duì)以上四種方法進(jìn)行了分析和論證。實(shí)驗(yàn)結(jié)果表明具有隱藏特性的新超混沌系統(tǒng)均實(shí)現(xiàn)了同步,證明了控制器的有效性。最后,對(duì)參數(shù)未知的具有隱藏特性的新超混沌系統(tǒng),運(yùn)用非線性反饋法、自適應(yīng)法和Backstepping法設(shè)計(jì)控制器,進(jìn)行了理論分析、數(shù)值模擬和電路仿真,結(jié)果表明,具有隱藏特性的新超混沌系統(tǒng)實(shí)現(xiàn)了同步,控制器效果良好,能夠?qū)ξ粗獏?shù)進(jìn)行有效地識(shí)別。
[Abstract]:Chaos, as a complex form of motion, exists widely in nonlinear dynamics and appears in deterministic systems in the form of random phenomena. In recent years, chaotic control and synchronization have become an important internal capacity to study chaos with the academic circles. Chaotic control and synchronization have become one of the hotspots in the field of great application and development, and chaos control and synchronization have become one of the hotspots in the research field. Compared to low dimensional systems, hyperchaotic systems have more complex dynamic behavior. Therefore, it is more valuable for the study of the control and synchronization of hyperchaotic systems. The attractor, which is not exactly the same as the dynamic characteristics of the traditional self excited attractor, has aroused widespread concern in the academic circle. The chaotic system with hidden attractors has hidden characteristics. In recent years, the hidden characteristics of the chaotic system have received some attention from scholars. In this paper, based on Sprott B system, a new five dimensional hyperchaotic system with only one parameter, no balance point and hidden attractor is designed. First, the dynamic characteristics of the new five dimensional hyperchaotic system with hidden characteristics are studied by theoretical analysis, such as the dimension, dissipation and attraction of the attractor. The existence of the sub, the Lyapunov index and the bifurcation, etc., design the circuit of a new hyperchaotic system with hidden characteristics, carry out numerical simulation and circuit simulation, and implement a new hyperchaotic system with hidden characteristics with the hardware circuit, and verify the dynamic characteristics and hidden characteristics of the new hyperchaotic system. Then the parameters are known to the system. The new hyperchaotic system with hidden characteristics is designed by linear feedback, state observer, adaptive and Backstepping synchronization. Through theoretical analysis, numerical simulation and circuit experiment, the above four methods are analyzed and demonstrated. Experimental results show that the new hyperchaotic systems with hidden characteristics are realized. The validity of the controller is proved. Finally, the new hyperchaotic system with hidden characteristics with unknown parameters is designed by nonlinear feedback, adaptive method and Backstepping method. The theoretical analysis, numerical simulation and circuit simulation are carried out. The results show that the new hyperchaos system with hidden characteristics is synchronized and controlled. The effect is good, and the unknown parameters can be identified effectively.
【學(xué)位授予單位】：東北師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O415.5;TP273

【參考文獻(xiàn)】

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本文編號(hào)：2112756