Probabilistic behavioral distance and tuning - Reducing and aggregating complex systems

• Main Authors: Hellmann, F. (Author), Kurths, J. (Author), Raisch, J. (Author), Zolotarevskaia, E. (Author)
• Format: Article
• Language: English
• Published: Institute of Physics 2023
• Subjects: behavioral theory; Behavioral theory; Complex networks; control; Dynamical systems; H∞ model reduction; Large scale systems; model reduction; Model reduction; Networked systems; Non linear; probabilistic methods; Probabilistic methods; Probabilistics; Simple system; Small networks; Specifications; Subnetworks
• Online Access: View Fulltext in Publisher; View in Scopus

 Given two dynamical systems, we quantify how similar they are with respect to their interaction with the outside world. We focus on the case where simpler systems act as a specification for a more complex one. Combining a behavioral and probabilistic perspective we define several useful notions of the distance of a system to a specification. We show that these distances can be used to tune a complex system. We demonstrate that our approach can successfully make non-linear networked systems behave like much smaller networks, allowing us to aggregate large sub-networks into one or two effective nodes. Finally, we discuss similarities and differences between our approach and H∞ model reduction. © 2023 The Author(s). Published by IOP Publishing Ltd.