Analysis Of Characteristics Of Chaotic Time Series And Phase Space Reconstruction

As known to all, non-linear phenomenon results from all kinds of motions and therefore it permeates into each branch of nature science and society science since the chaos theory was first established, even, in general cases, complex dynamical system cannot set up determinate mathematical model. The major reason for this is our ignorance for unknown dynamical systems, such as the complexity and volatility of parameters and boundary conditions of dynamical systems etc. As for a group of data collected on the spot from an unknown dynamical system , we must analyze and determine its nonlinearity of the obtained time series firstly for nonlinearity is a necessary condition of chaos .Based on nonlinearity of time series , we undoubtedly should turn to studying chaotic characteristics of the data qualitatively and quantitatively as a following step ,such as correlation dimension ,the largest Lyapunov exponent, Kolmogrov entropy etc. Obviously, only qualitative analysis is not enough , especially for some complex nonlinear system such as biological system , finance system etc .In view of the imperfection of qualitative analysis .phase space reconstruction present a new approach to quantitative analysis. In fact, only by quantitative analysis can we obtain the intrinstic and fundamental properties of the nonlinear dynamical system and can we resolve those difficult problem completely such as examination or diagnosis of system signal derived from complex nonlinear dynamical system.Based on the fact above, this thesis can be summarized as follows emphasis:1. The current research situation is elaborately summarized .Besides, the direction for further study in this field at present and days to come is indicated.2. The surrogate-data is applied for the nonlinearity examination , and is experimented and discussed comparatively within twins of data from different systems.3. Fundamental chaos characteristics are explained comparatively within twins of data from chaotic systems.4. The selection of parameters of phase space reconstruction is discussed and explored with analyzing the drawback within the presented methods currently. Furthermore the thought of delay vectors' sequencing is scheduled to calculate thesmallest embedding dimension. As for the calculation of a perfect time delay, a new idea is also put forward by means of the inner product of vectors. Simulation not only proved the validity of the above ideas but also showed the conciseness of its program.