Qualitative Phase Space Reasoning Based On Nonlinear Time Series

The time series of non-linear dynamics system is the main basis of studing complicated system.The complicated non-linear dynamics system has certainty low, but in real world, its external manifestation displays characteristics such as variable evolution , the multiple echelons,and the information we get from non-linear system is incomplete and uncertainty. The structure parameters and boundary parameters of non-linear system are time-varying and complexity, so it is impossible to establish a precise mathematical model. We want to get the basic characters of bebavior in researching the non-linear system, if we use the Traditional method to analysis the time series, the basic character of behavior is overwhelm with complicated trajectory and details,and the deviation in time series also make some mistakes. So we use qualitative method to analysis time series, and reconstructing the qualitative phase space of time series based on reconstructing its phase space.This thesis discusses the reasoning method of reconstructing the qualitative phase space of non-linear time series.First we reconstruct the phase space of non-linear time series.There are many method for reconstructing phase space of non-linear time series,so for parameters, we introduce and sum up them,and use one of them calculate embedding dimension and embedding delay. Then we change the quantitative state to qualitative for the states in time series, abstract and merge the adjacent equivalent states. We define and merge equivalence trajectories, and then we can reconstruct the qualitative phase space. Finally, we use time series of the two-dimensional, three-dimensional and economics complex system to analysis, and reconstruct the qualitative phase space of them.