Dimension of interaction dynamics.
A method allowing one to distinguish interacting from noninteracting systems based on available time series is proposed and investigated. Some facts concerning generalized Rényi dimensions that form the basis of our method are proved. We show that one can find the dimension of the part of the attractor of the system connected with interaction between its parts. We use our method to distinguish interacting from noninteracting systems on the examples of logistic and Hénon maps. A classification of all possible interaction schemes is given.
Journal Article↗