Little More Than Kin and Less Than Kind: Distinguishing Dynamical Systems byTheir Time Series

摘要

In this thesis, the following specific problem is investigated: the authors havetime series data from a direct numerical simulation (using partial differential equations) of a fluid dynamics experiment, and they have time series from a system of ordinary differential equations, which approximate the system of partial differential equations. The question is: do the time series display the same kind of long-term behavior. In chapter 2 necessary definitions are made, the fundamental theorem about attractor reconstruction is stated, and a couple of time series characteristics are introduced. The next chapter shows how these concepts work in two simple cases: The Henon map and the Lorenz differential system. Chapter 4 then shows the results for the fluid dynamics data, and chapter 5 contains the conclusions.