On Several Kinds Of Chaos Control And Synchronization Methods And Their Application In Biomedical Models

Due to the nonlinear characteristics of the natural world, chaos theory is getting more and more concern. Over twenty years ago, the emergence of the chaos control and synchronization theory has attracted wide attention from researchers in many academic fields, and brought out many applications results. The phenomenon of chaos and chaotic synchronization has also been found in biomedical fields, such as the heart and vascular system, the neural networks of brain and some epidemic disease. Therefore, to study new analysis tools of chaos, improve the chaotic control and synchronization methods, inves-tigate their applications in biological and medical sciences are significant and valuable work. In this thesis, we present some new methods of impulsive control and synchroniza-tion, linear generalized synchronization, anti-synchronization and adapitive control; We apply these methods to research the chaos control and synchronization of muscular blood vessel, delayed chaotic neural networks and epidemic disease model with seasonality; We analyze their practical values in biological and medical fields. This thesis consists of five chapters, Chapter1is to summarize the background of the related issues and state the main results of the present thesis. Our main contributions are given in Chapter2through5, which include the following contents:(1) We present a new method of impulsive control and synchronization. Different from previous methods, the control gains and impulsive intervals are both variable in this method. Furthermore, the upper bound of impulsive interval for stable control and synchronization can be estimated. Effectiveness of this method is validated in a4dimen-sion hyperchaotic system and a3dimension chaotic system. Employed this method, the synchronization of mathematical model of muscular blood vessel with periodic stimulus is investigated. The results show that the behavior of the muscular blood vessel in disease states can be synchronized to that of normal blood vessel by this impulsive method. The clinical value of variable control gains and impulsive intervals is analyzed.(2) A generalized synchronization method to implement linear generalized synchro-nization of different chaotic systems is proposed. This synchronization method unifies several kinds of existing methods. When the parameters of driven system are unknown, an adaptive controller and some parameter update laws are given to realize accurate parameters identification and linear generalized synchronization.(3) We develop an anti-synchronization method of a class of delayed chaotic neural networks based on the invariance principle of differential equations. The state and non-state coupling methods are rigorously analyzed. This method employs a much smaller adaptive feedback strength compared to some known results, and can be realized without prior knowledge of the connection matrices. The anti-synchronization can be successfully achieved under the effect of noise and multi-parameter mismatch.(4) We provide some suggestions on prevention and control strategies of disease through analyzing the chaos control results of a seasonal epidemic disease model. We find that the disease prevalence can not achieve disease-free state through control only one class. And more controlled calsses does not mean better prevent results of disease.