【摘要】：多渦卷混沌系統(tǒng)與雙渦卷混沌系統(tǒng)相比其動(dòng)力學(xué)行為、拓?fù)浣Y(jié)構(gòu)以及密匙參數(shù)更復(fù)雜,多渦卷混沌系統(tǒng)廣泛的應(yīng)用于混沌系統(tǒng)的信息加密中,目前多渦卷混沌系統(tǒng)的產(chǎn)生主要在于構(gòu)造適當(dāng)?shù)姆蔷�性函數(shù)產(chǎn)生多渦卷混沌系統(tǒng),但對(duì)多渦卷混沌系統(tǒng)的混沌特性分析不夠充分。由于多渦卷混沌系統(tǒng)的分析難以用傳統(tǒng)的動(dòng)力學(xué)理論分析,傳統(tǒng)的控制理論較難對(duì)多渦卷混沌系統(tǒng)進(jìn)行控制研究,因此國(guó)內(nèi)外對(duì)多渦卷混沌系統(tǒng)的分析研究的文獻(xiàn)較少。但多渦卷混沌系統(tǒng)的控制與同步研究對(duì)于工程應(yīng)用具有重要理論意義和應(yīng)用價(jià)值,將多渦卷混沌系統(tǒng)應(yīng)用到工程領(lǐng)域具有很大的發(fā)展前景。本文在Jerk系統(tǒng)的基礎(chǔ)上通過(guò)由分段線性函數(shù)所組成的非線性函數(shù)產(chǎn)生多渦卷混沌系統(tǒng),與雙渦卷Jerk系統(tǒng)相比增加了系統(tǒng)在單方向的渦卷數(shù),從而增加了混沌系統(tǒng)的復(fù)雜性,數(shù)值計(jì)算了新多渦卷混沌系統(tǒng)的散度、平衡點(diǎn)、Lyapunov指數(shù)、Lyapunov維數(shù)的值,并對(duì)其Lyapunov指數(shù)譜和分岔圖進(jìn)行了基本動(dòng)力學(xué)分析,數(shù)值模擬體現(xiàn)了系統(tǒng)的多渦卷特性,電路實(shí)驗(yàn)證明了新系統(tǒng)的物理可實(shí)現(xiàn)性。同時(shí)采用非線性反饋法、滑模變結(jié)構(gòu)控制法、線性反饋滑�？刂品▽�(duì)新多渦卷混沌系統(tǒng)進(jìn)行了追蹤控制,與非線性反饋法、滑模變結(jié)構(gòu)控制法相比,線性反饋滑�？刂品ǹs短了新多渦卷混沌系統(tǒng)對(duì)目標(biāo)信號(hào)的追蹤時(shí)間,提高了追蹤效率,數(shù)值模擬和電路實(shí)驗(yàn)說(shuō)明了這三種控制方法均可實(shí)現(xiàn)新多渦卷混沌系統(tǒng)對(duì)參考信號(hào)的追蹤目標(biāo)。最后采用主動(dòng)控制法和主動(dòng)滑�？刂品�、自適應(yīng)滑模控制法、線性反饋控制法和線性反饋滑�？刂品▽�(duì)新多渦卷混沌系統(tǒng)進(jìn)行了同步研究,主動(dòng)滑�？刂品ㄅc主動(dòng)控制法相比明顯縮短了驅(qū)動(dòng)系統(tǒng)與響應(yīng)系統(tǒng)到達(dá)同步的時(shí)間,但主動(dòng)滑�？刂品ǖ目刂破鞅容^復(fù)雜,而自適應(yīng)滑�？刂品ㄅc主動(dòng)滑�？刂品ㄏ啾韧瑯涌墒箖上到y(tǒng)達(dá)到同步,且簡(jiǎn)化了控制器的復(fù)雜度,線性反饋控制法物理實(shí)驗(yàn)易于實(shí)現(xiàn),但達(dá)到同步的時(shí)間較長(zhǎng),魯棒性較弱,線性反饋滑�？刂品ㄅc主動(dòng)滑�？刂品白赃m應(yīng)滑�？刂品ㄏ啾�,極大的縮短了兩系統(tǒng)到達(dá)同步的時(shí)間,提高了同步效果,且與線性反饋法相比,具有較強(qiáng)的抗干擾能力,魯棒性較高。
[Abstract]:The dynamical behavior, topology and key parameters of multi-scroll chaotic system are more complex than that of double-scroll chaotic system. Multi-scroll chaotic system is widely used in information encryption of chaotic system. At present, the generation of multi-scroll chaotic system mainly lies in the construction of proper nonlinear function to produce multi-scroll chaotic system, but the chaotic characteristics of multi-scroll chaotic system are not sufficiently analyzed. Because the analysis of multi-scroll chaotic system is difficult to be analyzed by the traditional dynamics theory and the traditional control theory is difficult to control the multi-scroll chaotic system, there are few literatures on the analysis and research of multi-scroll chaotic system at home and abroad. However, the research on the control and synchronization of multi-scroll chaotic systems is of great theoretical significance and application value for engineering applications, and the application of multi-scroll chaotic systems to the engineering field has a great development prospect. On the basis of the Jerk system, a multi-scroll chaotic system is generated by a nonlinear function composed of piecewise linear functions. Compared with the two-scroll Jerk system, the number of vortexes in one direction is increased and the complexity of the chaotic system is increased. The divergence and the Lyapunov exponent dimension of the new multi-scroll chaotic system are numerically calculated, and the Lyapunov exponent spectrum and bifurcation diagram are analyzed. The numerical simulation shows the multi-vorticity characteristic of the system. The circuit experiment proves the physical realizability of the new system. At the same time, nonlinear feedback method, sliding mode variable structure control method and linear feedback sliding mode control method are used to track control the new multi-scroll chaotic system, compared with nonlinear feedback method and sliding mode variable structure control method. The linear feedback sliding mode control method shortens the tracking time of the new multi-scroll chaotic system and improves the tracking efficiency. Numerical simulation and circuit experiments show that these three control methods can achieve the tracking target of the reference signal in the new multi-scroll chaotic system. Finally, active control method, active sliding mode control method, adaptive sliding mode control method, linear feedback control method and linear feedback sliding mode control method are used to synchronize the new multi-scroll chaotic system. Compared with the active control method, the active sliding mode control method obviously shortens the time between the drive system and the response system, but the controller of the active sliding mode control method is more complex. Compared with the active sliding mode control, the adaptive sliding mode control method can make the two systems synchronize, and simplify the complexity of the controller. The linear feedback control method is easy to realize in physical experiments, but the synchronization time is longer and the robustness is weak. Compared with the active sliding mode control and the adaptive sliding mode control, the linear feedback sliding mode control method can greatly shorten the time between the two systems to achieve synchronization and improve the synchronization effect. Compared with the linear feedback control method, the linear sliding mode control method has stronger anti-interference ability. The robustness is high.
【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;TP13

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