Qualitative Phase Space Reasoning Based on Non-linear Time Series

Phase space is a useful tool for explanations of complex system. However, in some cases, the basic patterns of behavior which is intended to be explored in phase space may be overwhelmed with details. This paper develops a method to research the qualitative phase space in non-linear time series, which decreases the number of the time serial states and predigests behavior trajectories through abstract, and reconstructs the qualitative phase space. To demonstrate this method, we use the time series which comes from the system of Lorenz with 3 variables and the result demonstrates that the method is feasible, and can reveal underlying base patterns of behavior that have not been apparent with previous methods.