One-dimensional Discontinuous Image Based On Recursive Graph Method And Time Series Analysis Of EEG Signals

In many scientific disciplines, more attention has been paid to analyse the characteristics of complex dynamics of system by using the modern data analysis techniques. Methods for estimating fractal or correlation dimensions, Lyapunov exponents, and mutual information have been widely used. However, most of these methods require long data series and in particular their uncritical application, especially to real-world data, may often lead to pitfalls. Therefore, the method of. recurrence plot has been developed an approach to describe complex dynamics due to its advantages on analyzing short time series. In this thesis, this method is applied to analyze the time series of one dimensional discontinuous map and electroencephalograph (EEG) data.The dynamics of many practical systems often shows abrupt change, and their dynamics can be described by discontinuous maps. In this kind of systems, the dynamic behaviors induced by border-collision bifurcations are very different from those observed in the maps which is smooth everywhere. Therefore, the investigation on the dynamics of discontinuous maps is a very important research fields. Based on the recurrence plot method, the complex network approach is employed to study the dynamical behavior of one dimensional discontinuous map. There are P independent full-linked networks for an arbitrary P-period attractor and many independent complex networks of different sizes for a chaotic attractor. Meanwhile, the control parameter dependence of the link density, the clustering coefficient and the average length of the shortest paths for the complex networks are calculated and discussed. The correlation of these characteristic quantities with the dynamics of the system is analyzed. The result shows that the link density shows a discontinuous change for different periodic attractor and a non-smooth change at the transition point between a periodic attractor and a chaotic attractor; the non-smooth changes of the clustering coefficient and the average length of the shortest paths appear at the transition point between periodic and chaotic attractors, and the merging point of chaotic attractors, respectively. These phenomena imply that the characteristic quantities might be proper indexes to describe the dynamical states and exhibit their transitions. Moreover, they may help to check out the periodic attractors when they are coexistence with some other attractors.As the development of the brain science, the study on EEG signals has attracted great attention. The recurrence plot method is used to distinguish and detect different emotional states hidden in the EEG data. Under different emotional states, the recurrence plots of the EEG signals collected through the FPZ electrodes are drawn. The result shows the recurrence plots are able to qualitatively distinguish the EEGs of different emotional states. In order to count and uncover the information of the recurrence plots, we introduce some characteristic measures for the recurrence quantification analysis, in which the normalized laminarity shows an obvious advantage for distinguishing or detecting different emotional states from EEGs.