【摘要】：生物模型如生物神經(jīng)網(wǎng)絡(luò)、流行病模型、肌型血管模型等均是高度復(fù)雜的混沌系統(tǒng),屬生物醫(yī)學(xué)工程領(lǐng)域中的一個(gè)重要研究分支。近些年來,關(guān)于混沌理論在生物模型中的應(yīng)用研究,逐步引起人們的興趣和關(guān)注,并取得了較為豐碩的成果,但還有許多未知的領(lǐng)域尚待探索。為此,本文研究了混沌理論在生物模型中的若干應(yīng)用,即生物模型的混沌控制、同步及其在保密通信的應(yīng)用。具體內(nèi)容如下： (1)幾類混沌系統(tǒng)和生物模型的同步。針對(duì)超混沌系統(tǒng)、帶有未知參數(shù)混沌系統(tǒng)、分?jǐn)?shù)階混沌系統(tǒng)、時(shí)空耦合混沌系統(tǒng),研究了它們的混沌特性；通過設(shè)計(jì)參數(shù)更新律,實(shí)現(xiàn)了對(duì)上述系統(tǒng)的同步；針對(duì)不同種類的混沌系統(tǒng),設(shè)計(jì)了基于混沌掩蓋方法的保密通信系統(tǒng),研究了帶有未知參數(shù)混沌系統(tǒng)和分?jǐn)?shù)階混沌系統(tǒng)在混沌保密通信中的應(yīng)用；采用自適應(yīng)Backstepping控制等方法,研究了混沌同步在肌型血管、流行病和神經(jīng)元中的應(yīng)用及其在臨床上的意義。其中,關(guān)于分?jǐn)?shù)階系統(tǒng)的同步,現(xiàn)有研究多采用一些常規(guī)方法,如自適應(yīng)、反饋、滑膜等控制方法,本文提出了一種新的基于Laplace變換的同步控制器；關(guān)于時(shí)空耦合混沌系統(tǒng)的同步,目前研究多集中在單向時(shí)空耦合混沌系統(tǒng),本文對(duì)單向和雙向時(shí)空耦合同步系統(tǒng)均進(jìn)行了研究,設(shè)計(jì)了投影同步控制器；關(guān)于混沌同步在肌型血管、流行病和神經(jīng)元中的應(yīng)用,本文應(yīng)用混沌理論更接近實(shí)際地描述了臨床上對(duì)冠狀動(dòng)脈的治療,理論上分析了對(duì)于麻疹流行病無病控制方法,考慮實(shí)際神經(jīng)信號(hào)的傳遞延遲,更真實(shí)地反映了神經(jīng)元間的同步。理論推導(dǎo)證明了上述控制器設(shè)計(jì)的正確性,數(shù)值仿真進(jìn)一步驗(yàn)證了有效性。 (2)基于開環(huán)加非線性閉環(huán)(Open Plus Nonlinear Closed Loop,OPNCL)、時(shí)間延遲反饋(Time Delay Feedback,TDF)方法的生物神經(jīng)網(wǎng)絡(luò)和肌型血管模型的混沌控制與同步�；贠PNCL方法,實(shí)現(xiàn)了時(shí)滯混沌細(xì)胞神經(jīng)網(wǎng)絡(luò)的混沌控制、兩種不同時(shí)滯神經(jīng)網(wǎng)絡(luò)的異結(jié)構(gòu)混沌同步,并應(yīng)用于混沌掩蓋保密通信中；基于TDF方法,實(shí)現(xiàn)了時(shí)滯神經(jīng)網(wǎng)絡(luò)的混沌反控制、兩種不同時(shí)滯神經(jīng)網(wǎng)絡(luò)的異結(jié)構(gòu)混沌同步,并設(shè)計(jì)了相關(guān)同步方案,將其應(yīng)用于混沌掩蓋保密通信中;基于OPNCL方法,運(yùn)用李雅普諾夫(Lyapunov)穩(wěn)定性理論設(shè)計(jì)出全局漸近穩(wěn)定的混沌同步控制器,研究了痙攣狀態(tài)的血管與正常狀態(tài)的血管的同步行為及其在臨床上的意義。其中,OPNCL方法迄今較為廣泛地運(yùn)用于混沌系統(tǒng),但在神經(jīng)網(wǎng)絡(luò)領(lǐng)域中的運(yùn)用很少得見,本文通過該方法,把網(wǎng)絡(luò)系統(tǒng)的解穩(wěn)定地傳遞到選定的目標(biāo),使得對(duì)網(wǎng)絡(luò)的控制變得更為靈活,對(duì)于任何目標(biāo),所控制混沌系統(tǒng)的傳遞域(Basins of Entrainment)是全局的,這樣就避免了開環(huán)控制和線性閉環(huán)控制的一些限制因素,以及有關(guān)確定傳遞域范圍的繁瑣計(jì)算；TDF方法目前在揭示混沌系統(tǒng)的研究中運(yùn)用得較為普遍,但在神經(jīng)網(wǎng)絡(luò)研究領(lǐng)域亦很鮮見,本文基于該方法,設(shè)計(jì)了控制器,成功地實(shí)現(xiàn)了時(shí)滯神經(jīng)網(wǎng)絡(luò)的反控制,同時(shí)通過改變控制器參數(shù),可以對(duì)神經(jīng)網(wǎng)絡(luò)混沌性的強(qiáng)弱進(jìn)行調(diào)節(jié)；OPNCL方法當(dāng)下在肌型血管模型混沌同步研究中的運(yùn)用同樣甚少(通常運(yùn)用自適應(yīng)方法),本文通過該方法,使處于痙攣混沌狀態(tài)下的血管的壓力差和內(nèi)徑變化可以與正常的血管有效實(shí)現(xiàn)同步；或當(dāng)發(fā)生血流不穩(wěn)時(shí),通過同步控制使得血管的血液流動(dòng)速度處于波動(dòng)的混沌狀態(tài)與正常的血流速度運(yùn)動(dòng)迅速達(dá)到同步。 (3)其它幾種控制與同步方法的應(yīng)用研究�；赥-S模糊模型(T-S Faintness Model),實(shí)現(xiàn)了混沌系統(tǒng)的廣義同步和異結(jié)構(gòu)混沌同步；基于追蹤控制方法,實(shí)現(xiàn)了時(shí)滯雙向聯(lián)想記憶模型(Memory Model Of Doubleaction, BAM)的反步投影同步,時(shí)滯神經(jīng)網(wǎng)絡(luò)的廣義同步和肌型血管的完全同步；基于徑向基函數(shù)網(wǎng)絡(luò)(Radial Basis Function Neural Networks, RBFNs)方法,實(shí)現(xiàn)了時(shí)滯BAM模型的完全同步和時(shí)滯神經(jīng)網(wǎng)絡(luò)的投影同步；基于追蹤控制方法,運(yùn)用Lyapunov穩(wěn)定性理論設(shè)計(jì)出全局漸近穩(wěn)定的混沌同步控制器,研究處于痙攣狀態(tài)血管與正常狀態(tài)血管的同步行為及其在臨床上的意義。其中,首次基于追蹤控制方法,設(shè)計(jì)了時(shí)滯神經(jīng)網(wǎng)絡(luò)的反步投影同步控制器,其控制器是由兩部分組成的,一部分是耦合系統(tǒng)中的反步投影同步控制器v,另一部分是驅(qū)動(dòng)-響應(yīng)系統(tǒng)中的追蹤控制器u;基于RBFNs控制方法,設(shè)計(jì)了線性狀態(tài)反饋控制器,成功地將可調(diào)的時(shí)滯神經(jīng)網(wǎng)絡(luò)系統(tǒng)的混沌行為轉(zhuǎn)變?yōu)槠谕繕?biāo)位置或周期軌道運(yùn)動(dòng)；基于追蹤控制方法,首次應(yīng)用于肌型血管模型的混沌同步,并設(shè)置了相應(yīng)的控制器,較通常運(yùn)用的自適應(yīng)方法,其實(shí)現(xiàn)同步的效果更加完美。理論證明了上述控制器的正確性,數(shù)值模擬實(shí)驗(yàn)進(jìn)一步驗(yàn)證了所提控制器的有效性。 本文得到國家自然科學(xué)基金(61370145,61173183,60973152),高等學(xué)校博士點(diǎn)專項(xiàng)科研基金(20070141014),遼寧省高等學(xué)校優(yōu)秀人才支持計(jì)劃資助(LR2012003),遼寧省自然科學(xué)基金(20082165),中央高�；究蒲谢�(DUT12JB06)的聯(lián)合資助。
[Abstract]:Biological models, such as biological neural network, epidemic model, muscle type vascular model, are highly complex chaotic systems, and belong to an important research branch in the field of biomedical engineering. In recent years, the research on the application of chaos theory to biological models has gradually aroused people's interest and attention, and has achieved fruitful results. However, there are still many unknown fields to be explored. Therefore, this paper studies some applications of chaos theory in biological models, namely, the chaos control of biological models, synchronization and its application in secure communication.
(1) synchronization of several kinds of chaotic systems and biological models. For hyperchaotic systems, chaotic systems with unknown parameters, fractional chaotic systems and spatio-temporal coupled chaotic systems are studied, and the synchronization of these systems is realized by designing parameter updating law, and chaos based on chaos system is designed based on chaos. The application of chaotic systems with unknown parameters and fractional chaotic systems in chaotic secure communication is studied, and the application of chaotic synchronization to the muscle blood vessels, epidemics and neurons and its clinical significance are studied by adaptive Backstepping control. Among them, the fractional order system is used. In the current research, some conventional methods, such as adaptive, feedback and synovium control methods, are used in the current research. A new synchronous controller based on Laplace transformation is proposed in this paper. The synchronization of spatio-temporal coupled chaotic systems is mainly focused on unidirectional spatiotemporal coupled chaotic systems. The system has been studied and the projection synchronization controller is designed, and the application of the chaotic synchronization in the muscular blood vessels, the epidemic and the neurons. In this paper, the chaos theory is applied to describe the clinical treatment of the coronary artery. In theory, the method of disease control for measles epidemic disease is theoretically analyzed, and the transmission of actual neural signals is considered. The delay is more true to reflect the synchronization between neurons. Theoretical derivation proves the correctness of the controller design, and numerical simulation further validates the effectiveness.
(2) chaos control and synchronization of biological neural network and muscle type vascular model based on open loop plus nonlinear closed loop (Open Plus Nonlinear Closed Loop, OPNCL), time delay feedback (Time Delay Feedback, TDF) method. Based on OPNCL method, the chaos control of time delay chaotic cellular neural networks is realized, and the difference between two different time-delay neural networks is different. The structure chaos synchronization is applied to chaos concealment communication. Based on the TDF method, the chaotic back control of time delay neural networks is realized. Two different time-delay neural networks are synchronized with different structures, and the related synchronization scheme is designed to apply it to the chaotic conceal secret communication. Based on the OPNCL method, the Lee Yap Andrianof (Lyapuno) method is used. V) the stability theory is designed to design a globally asymptotically stable chaotic synchronization controller. The synchronous behavior of blood vessels in spasmodic state and the normal state blood vessels and its clinical significance are studied. Among them, OPNCL method is widely used in chaotic systems so far, but it is seldom used in the field of neural network. This method is used in this paper. The stable transmission of the network system to the selected target makes the control of the network more flexible. For any target, the Basins of Entrainment of the controlled chaotic system is global, thus avoiding some limiting factors of open loop control and linear closed loop control, as well as the propagation of the scope of the transfer domain. The TDF method is widely used in the study of chaotic systems, but it is very rare in the field of neural network. Based on this method, the controller is designed, and the back control of the time delay neural network is successfully realized, and the chaos of the neural network can be adjusted by changing the parameter of the controller. The application of the OPNCL method in the study of the chaotic synchronization of the muscular vascular model is very small (usually using the adaptive method). By this method, the pressure difference and the inner diameter of the blood vessels in the state of the spasmodic chaos can be synchronized effectively with the normal blood vessel, or when the blood flow is unstable, it can be controlled by synchronous control. The blood flow velocity of the blood vessel is fluctuating chaotic, and the velocity of blood flow is rapidly synchronized.
(3) the application of several other control and synchronization methods. Based on the T-S fuzzy model (T-S Faintness Model), the generalized synchronization and the chaotic synchronization of the chaotic system are realized. Based on the tracking control method, the backstepping synchronization of the time-delay bidirectional associative memory model (Memory Model Of Doubleaction, BAM) and the time-delay neural network are realized. The generalized synchronization and the complete synchronization of the muscle type vessels are fully synchronized; based on the radial basis function network (Radial Basis Function Neural Networks, RBFNs), the complete synchronization of the time-delay BAM model and the projection synchronization of the time-delay neural network are realized. Based on the tracking control method, the global asymptotically stable chaos is designed by using the Lyapunov stability theory. The step controller studies the synchronous behavior of blood vessels in spasmodic state and the normal state blood vessels and their clinical significance. For the first time, based on the tracking control method, a backstepping synchronous controller of time delay neural network is designed. The controller consists of two parts, and a part is the backstepping synchronous controller V in the coupling system. The other part is the tracking controller u in the drive response system, and a linear state feedback controller is designed based on the RBFNs control method. The chaotic behavior of the adjustable time-delay neural network system is successfully transformed into the desired target position or the periodic orbit motion. Based on the tracking control method, the chaotic identity of the muscle type vascular model is first applied. Step, and set up the corresponding controller, compared with the usual adaptive method, the effect of the synchronization is more perfect. The theory proves the correctness of the controller, and the numerical simulation test further verifies the effectiveness of the proposed controller.
In this paper, the National Natural Science Foundation (613701456117318360973152), the special scientific research fund of the doctoral degree of Higher Education (20070141014), the support program for outstanding talents in Liaoning University (LR2012003), the Liaoning Natural Science Foundation (20082165), and the basic scientific research fund of the Central University (DUT12JB06) are jointly funded.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：R318

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