The Analysis Of Chaos Synchronization With Noise Perturbed And The Application Of Support Vector Machine

In this thesis, we mainly investigate chaos synchronization with noise perturbed and the application of support vector machine (SVM) in the Holter ECG monitoring analysis based on the heart rate variability (HRV).This thesis is organized as follows: In Chapter 1, we introduce the research background and progress for chaos and chaos synchronization, the stability of stochastic differential equations and support vector machine. Also we display the overall structure of the thesis in this chapter.In the second chapter, we firstly introduce a class of functional differential equations, in which the nonlinear terms are satisfied with global Lipchitz conditions, as well as its response systems with noise perturbed. Because of existence of global Lipchitz conditions, we just need to design suitable linear coupling term to achieve chaos synchronization. Then, we employ the LaSalle invariance principle to conclude the sufficient conditions of chaos synchronization with unidirectional coupling method. In succession, we will provide the Hopfield artificial neural network(ANN) and Chua's chaotic circuits as the concrete examples with corresponding analysis and numerical simulations.In Chapter 3, we will investigate a spacial class of ordinary differential equations, which covers serval famous chaos system, such as the Lorenz system, Chen system and R(o|¨)sslar system. The most different point with systems discussed in Chapter 2 is that the nonlinear term do not satisfy the global Lipchitz conditions. We give out the ordinary nonlinear coupling terms and deduce the sufficient conditions of chaos synchronization, which require the drive systems boundedness. Besides, we also design special nonlinear coupling terms for 3 concrete chaos systems, by which we can avoid estimating the bound of the drive system.In Chapter 4, we turn to study chaos synchronization with bidirectional coupling method for the systems introduced in Chapter 2. We also investigate the probability that the two coupling systems synchronized to the original systems. As the same time, a concrete Hopfield artificial neural network(ANN) and Chua's chaotic circuits are proposed again as instances with corresponding analysis and numerical simulations.In Chapter 5, we discuss the cases of colorful noise and generalized synchronization and provide a summary of chaos synchronization with noise perturbed.In Chapter 6, we want to apply the support vector machine to the Holter ECG monitoring analysis to classify the different samples by the quantitative indexes of heart rate variability. Our tests show that the veracity and stability of support vector machine are both obviously superior to the traditional linear classifying methods. In addition, combined with compositive index of HRV, SVM can not only differentiate normal samples and abnormal samples of parasympathetic system, but also classify the normal samples and several abnormal samples of parasympathetic system. It is a new available approach to automatically diagnose the Holter ECG monitoring by computers.At the end of this thesis, we review the former results and propose some important topics and prospective work on correlative topics.