混沌理论在生物模型中的若干应用研究
发布时间：2018-07-20 17:12
【摘要】：生物模型如生物神经网络、流行病模型、肌型血管模型等均是高度复杂的混沌系统,属生物医学工程领域中的一个重要研究分支。近些年来,关于混沌理论在生物模型中的应用研究,逐步引起人们的兴趣和关注,并取得了较为丰硕的成果,但还有许多未知的领域尚待探索。为此,本文研究了混沌理论在生物模型中的若干应用,即生物模型的混沌控制、同步及其在保密通信的应用。具体内容如下： (1)几类混沌系统和生物模型的同步。针对超混沌系统、带有未知参数混沌系统、分数阶混沌系统、时空耦合混沌系统,研究了它们的混沌特性；通过设计参数更新律,实现了对上述系统的同步；针对不同种类的混沌系统,设计了基于混沌掩盖方法的保密通信系统,研究了带有未知参数混沌系统和分数阶混沌系统在混沌保密通信中的应用；采用自适应Backstepping控制等方法,研究了混沌同步在肌型血管、流行病和神经元中的应用及其在临床上的意义。其中,关于分数阶系统的同步,现有研究多采用一些常规方法,如自适应、反馈、滑膜等控制方法,本文提出了一种新的基于Laplace变换的同步控制器；关于时空耦合混沌系统的同步,目前研究多集中在单向时空耦合混沌系统,本文对单向和双向时空耦合同步系统均进行了研究,设计了投影同步控制器；关于混沌同步在肌型血管、流行病和神经元中的应用,本文应用混沌理论更接近实际地描述了临床上对冠状动脉的治疗,理论上分析了对于麻疹流行病无病控制方法,考虑实际神经信号的传递延迟,更真实地反映了神经元间的同步。理论推导证明了上述控制器设计的正确性,数值仿真进一步验证了有效性。 (2)基于开环加非线性闭环(Open Plus Nonlinear Closed Loop,OPNCL)、时间延迟反馈(Time Delay Feedback,TDF)方法的生物神经网络和肌型血管模型的混沌控制与同步。基于OPNCL方法,实现了时滞混沌细胞神经网络的混沌控制、两种不同时滞神经网络的异结构混沌同步,并应用于混沌掩盖保密通信中；基于TDF方法,实现了时滞神经网络的混沌反控制、两种不同时滞神经网络的异结构混沌同步,并设计了相关同步方案,将其应用于混沌掩盖保密通信中;基于OPNCL方法,运用李雅普诺夫(Lyapunov)稳定性理论设计出全局渐近稳定的混沌同步控制器,研究了痉挛状态的血管与正常状态的血管的同步行为及其在临床上的意义。其中,OPNCL方法迄今较为广泛地运用于混沌系统,但在神经网络领域中的运用很少得见,本文通过该方法,把网络系统的解稳定地传递到选定的目标,使得对网络的控制变得更为灵活,对于任何目标,所控制混沌系统的传递域(Basins of Entrainment)是全局的,这样就避免了开环控制和线性闭环控制的一些限制因素,以及有关确定传递域范围的繁琐计算；TDF方法目前在揭示混沌系统的研究中运用得较为普遍,但在神经网络研究领域亦很鲜见,本文基于该方法,设计了控制器,成功地实现了时滞神经网络的反控制,同时通过改变控制器参数,可以对神经网络混沌性的强弱进行调节；OPNCL方法当下在肌型血管模型混沌同步研究中的运用同样甚少(通常运用自适应方法),本文通过该方法,使处于痉挛混沌状态下的血管的压力差和内径变化可以与正常的血管有效实现同步；或当发生血流不稳时,通过同步控制使得血管的血液流动速度处于波动的混沌状态与正常的血流速度运动迅速达到同步。 (3)其它几种控制与同步方法的应用研究。基于T-S模糊模型(T-S Faintness Model),实现了混沌系统的广义同步和异结构混沌同步；基于追踪控制方法,实现了时滞双向联想记忆模型(Memory Model Of Doubleaction, BAM)的反步投影同步,时滞神经网络的广义同步和肌型血管的完全同步；基于径向基函数网络(Radial Basis Function Neural Networks, RBFNs)方法,实现了时滞BAM模型的完全同步和时滞神经网络的投影同步；基于追踪控制方法,运用Lyapunov稳定性理论设计出全局渐近稳定的混沌同步控制器,研究处于痉挛状态血管与正常状态血管的同步行为及其在临床上的意义。其中,首次基于追踪控制方法,设计了时滞神经网络的反步投影同步控制器,其控制器是由两部分组成的,一部分是耦合系统中的反步投影同步控制器v,另一部分是驱动-响应系统中的追踪控制器u;基于RBFNs控制方法,设计了线性状态反馈控制器,成功地将可调的时滞神经网络系统的混沌行为转变为期望目标位置或周期轨道运动；基于追踪控制方法,首次应用于肌型血管模型的混沌同步,并设置了相应的控制器,较通常运用的自适应方法,其实现同步的效果更加完美。理论证明了上述控制器的正确性,数值模拟实验进一步验证了所提控制器的有效性。 本文得到国家自然科学基金(61370145,61173183,60973152),高等学校博士点专项科研基金(20070141014),辽宁省高等学校优秀人才支持计划资助(LR2012003),辽宁省自然科学基金(20082165),中央高校基本科研基金(DUT12JB06)的联合资助。
[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.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：R318
本文编号：2134192
[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.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：R318
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