| During the last decade,various methods have been developed to extract useful information from time series by means of complex network approaches,which is now one hot topic in the frontier of nonlinear dynamics and complex systems.For instance,recurrence networks,visibility graphs,and transition network,etc.These methods have been successfully applied to time series in different fields,ranging from climate,sunspots,and financial market.Most of the existing methods are restricted to univariate time series analysis.However,in real systems time series are typically multivariate and interact with each other.In this thesis,we investigate two types of multivariate time series,one from theoretical model,and the other from real climate data.In the first work,we propose two methods to define ordinal patterns in order to deal with the multivariate time series from model.In addition,we construct ordinal partition transition networks,and define two entropy measures to capture the structural feature of networks.It is shown that this method can effectively characterize the transition point in chaotic phase synchronization.Furthermore,it can describe the fine structure of parameter space of the system,providing complementary information for traditional Lyapunov exponent method.Our second work studies the real time series from climate data.Here we construct regional climate networks from precipitation data in the Amazonian regions,and focus on network properties from the recent extreme drought events in 2005 and 2010.Based on network degrees of extreme drought events and normal drought conditions,we can identify regions of interest that are correlated to longer expected drought period.We also demonstrate the difference between the two drought events and determine the main factors that affect network stability.The methods proposed in thesis can be used to analyze the actual multivariate time series from different background. |
