Researches On Several Applications Of Chaos Theory In The Biological Model

The biological model includes the biological neural network, the model of epidemic disease, the model of muscular blood vessel, etc are all the high complicated chaotic systems, that belongs to an important research ramus in the area of the engineer of biological doctor. In the past years, researches on applications of chaos theory in the biological model, that have begun to absorb the people’s fun and attention, and that have gotten the definite achievement, but that have many unknown areas to be explored. Thereinto, the dissertation researches several applications of chaos theory in the biological model, namely, control and synchronization of neural network and their application in secure communication. The material content as follows:(1) Synchronization for several kinds of chaotic systems and the biological model. Aiming at hyperchaotic chaotic system, chaotic system of cincturing unknown parameters, fractional-order chaotic system, and coupling space-time chaotic system, which researches their chaos characteristic; through designing the parameter updating rule, which realizes synchronization above systems; aiming at the different kinds of chaotic systems, which designs the secrecy correspondence systems based on chaotic concealing method, that researchs the applications of chaotic system of cincturing unknown parameters and fractional-order chaotic system in chaotic masking secure communication; adopt adaptive Backstepping control etc., that research chaos application and sense of synchronization for the muscular blood vessel, the epidemic disease and nerve cell in clinic. Thereinto, about synchronization of fraction rank system, that existing research adopts excessively some general methods, that such as control methods of self-adaptation, feedback, synovium etc., the dissertation brings forward a kind of new synchronization controller based on Laplace transformation; about synchronization of space-time coupling chaotic system, that the research has excessively concentrated unilateralism space-time coupling chaotic system at present, the dissertation carries the research through unilateralism and bidirectional space-time coupling synchronization systems, that designs projection synchronization controller; about application of synchronization for the muscular blood vessel, the epidemic disease and nerve cell in clinic, the dissertation describes more practically the treatment to the coronary artery in clinic through chaos theory, analyzes the anosis control method to the measles epidemic disease on the theory, considers the transfer lag of the practical neural signal, reflects more really synchronization between nerve cells. Theory detrusiving proves the validity of above controllers, the numerical simulation experiments are provided to further demonstrate the effectiveness.(2) Chaos control and synchronization of the biological neural network and the biological model based on Open Plus Nonlinear Closed Loop (OPNCL), Time Delay Feedback (TDF) method. Based on OPNCL method, which realizes the chaotic control of chaotic cell neural network with delays, different-structure synchronization for two kinds of neural networks with delays applied in chaotic masking secure communication; based on TDF method, which realizes the chaotic anti-control of neural network with delays, different-structure synchronization for two kinds of neural networks with delays, and design the correlation synchronization scheme, which is applied in chaotic masking secure communication; based on OPNCL method, the dissertation designs global asymptotically stable chaos synchronization controller through Lyapunov stability theory, researches synchronization behavior for the blood vessel of spasticity and the blood vessel of normal condition and its sense in clinic. Thereinto, OPNCL method has exercised diffusely chaotic system at present, but that is infrequent in the field of neural network, the dissertation passes the method, the solution of the network system can be stably transferred to the selected aim, which realizes the network’s control more agility, for any aims, that controls basins of entrainment of chaotic system to be global, which avoids some limiting factor of open loop control, linear closed loop control and the cockamamie account about confirming the bound of basins of entrainment; TDF method has been exercised in the research of posting chaotic system at large, but which is not seen in the field of researching neural network, the dissertation utilizes the method, that the controller is designed, that the negative control of neural network with delays is realized triumphantly, at the same time through changing the controller’s parameters, which can adjust the strong and weak of neural network’s chaos characteristic; OPNCL method has been used seldom (usually use self-adaptive method) in the chaos synchronization research of the model of muscular blood vessel at present, the dissertation uses the method, that realizes effectively synchronization for pressure difference, inner diameter change of vascular in the state of spasm chaos and normal vascular; or when the blood flow is unstable, that realizes quickly synchronization for blood flow velocity of vascular in fluctuant chaos state and normal blood flow velocity through synchronization control.(3) The application researches of the other several kinds of control and synchronization methods. Based on T-S faintness model method, which realizes projective and different-structrue synchronization of chaotic systems; based on tracing control method, which realizes backstepping generalized synchronization of associative memory model of doubleaction (BAM) with delays and projective synchronization of neural network with delays; based on radial basis function neural networks (RBFNs) method, which realizes synchronization of BAM model with delays and projective synchronization of neural network with delays; based on tracing control method, the dissertation designs global asymptotically stable chaos synchronization controller through Lyapunov stability theory, researches synchronization behavior for the blood vessel of spasticity and the blood vessel of normal condition and its sense in clinic. Thereinto, based on tracing control method, that the controller of backstepping generalized synchronization of neural network with delays is designed at first, that is two parts, the part is the controller v of backstepping generalized synchronization in coupling system, that part is the controller u of tracing; based on RBFNs control method, that linearity estate feedback controller is designed, that chaotic action is translate into expectation aim position or period path sport; based on tracing control method, the dissertation applies to chaos synchronization of the model of muscular blood vessel at first, sets the corresponding controller, the effect of realizing synchronization is perfecter than self-adaptive method of usual application. Theory proves the validity of aforesaid controllers, the experiment of numerical simulations are provided to further demonstrate the effectiveness of the controllers mentioned.The research is jointly supported by the National Natural Science Foundation of China (Nos:61370145,61173183, and60973152), the Doctoral Program Foundation of Institution of Higher Education of China (No:20070141014), Program for Liaoning Excellent Talents in University (No:LR2012003), the National Natural Science Foundation of Liaoning province (No:20082165) and the Fundamental Research Funds for the Central Universities (No: DUT12JB06).