Testing Whether Two Chaotic One Dimensional Processes Are Dynamically Identical
Guo-Cheng Yuan, James A. Yorke, Thomas L. Carroll, Edward Ott, Louis M. Pecora · Physical Review Letters · 2000
Consider the situation where two individuals observe the same chaotic physical process but through time series of different measured variables (e.g., one individual measures a temperature and the other measures a voltage). If the two individuals now use their data to reconstruct (e.g., via delay coordinates) a map, the maps they obtain may appear quite different. In the case where the resulting maps appear one dimensional, we introduce a method to test consistency with the hypothesis that they represent the same physical process. We illustrate this method using experimental data from an electric circuit.