Analysis and Visualization of High-Dimensional Dynamical Systems’ Phase Space Using a Network-Based Approach

Shane St Luce, Hiroki Sayama and Atila Bueno

Complexity, 2022, vol. 2022, 1-11

Abstract: The concept of attractors is considered critical in the study of dynamical systems as they represent the set of states that a system gravitates toward. However, it is generally difficult to analyze attractors in complex systems due to multiple reasons including chaos, high-dimensionality, and stochasticity. This paper explores a novel approach to analyzing attractors in complex systems by utilizing networks to represent phase spaces. We accomplish this by discretizing phase space and defining node associations with attractors by finding sink strongly connected components (SSCCs) within these networks. Moreover, the network representation of phase space facilitates the use of well-established techniques of network analysis to study the phase space of a complex system. We show the latter by introducing a new node-based metric called attractivity which can be used in conjunction with the SSCC as they are highly correlated. We demonstrate the proposed method by applying it to several chaotic dynamical systems and a large-scale agent-based social simulation model.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/complexity/2022/3937475.pdf (application/pdf)
http://downloads.hindawi.com/journals/complexity/2022/3937475.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:3937475

DOI: 10.1155/2022/3937475

Access Statistics for this article

More articles in Complexity from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem (mohamed.abdelhakeem@hindawi.com).