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

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  • Shane St Luce
  • Hiroki Sayama

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.

Suggested Citation

  • Shane St Luce & Hiroki Sayama, 2022. "Analysis and Visualization of High‐Dimensional Dynamical Systems’ Phase Space Using a Network‐Based Approach," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:3937475
    DOI: 10.1155/2022/3937475
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    References listed on IDEAS

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    1. Ping Zhou & Meihua Ke, 2017. "A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes," Complexity, Hindawi, vol. 2017, pages 1-7, November.
    2. Sean C. Hill, 2017. "Toward Conceptualizing Race and Racial Identity Development Within an Attractor Landscape," SAGE Open, , vol. 7(3), pages 21582440177, July.
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