A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

TR Number
Date
2021-09-09
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI
Abstract

Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.

Description
Keywords
nonlinearity, model selection, chaos detection, change detection, model behavior mapping, dynamical similarity, causal discovery
Citation
Shea-Blymyer, C.; Roy, S.; Jantzen, B. A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics. Entropy 2021, 23, 1191.