{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T16:41:40Z","timestamp":1769186500854,"version":"3.49.0"},"reference-count":29,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T00:00:00Z","timestamp":1656460800000},"content-version":"vor","delay-in-days":179,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2022,1]]},"abstract":"<jats:p>\n                    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\u2010dimensionality, 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\u2010established techniques of network analysis to study the phase space of a complex system. We show the latter by introducing a new node\u2010based metric called\n                    <jats:italic>attractivity<\/jats:italic>\n                    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\u2010scale agent\u2010based social simulation model.\n                  <\/jats:p>","DOI":"10.1155\/2022\/3937475","type":"journal-article","created":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T16:35:10Z","timestamp":1656520510000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Analysis and Visualization of High\u2010Dimensional Dynamical Systems\u2019 Phase Space Using a Network\u2010Based Approach"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3537-9914","authenticated-orcid":false,"given":"Shane","family":"St Luce","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2670-5864","authenticated-orcid":false,"given":"Hiroki","family":"Sayama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,6,29]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0242875"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.techfore.2016.08.015"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2018.05.093"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1039\/C3MB70331B"},{"key":"e_1_2_9_5_2","doi-asserted-by":"crossref","unstructured":"LuceS.andSayamaH. Phase spaces of the strategy evolution in the El Farol bar problem Proceedings of the ALIFE 2020: The 2020 Conference On Artificial Life Volume ALIFE 2020: The 2020 Conference on Artificial Life March2020 Montr\u00e9al Canada 558\u2013566.","DOI":"10.1162\/isal_a_00339"},{"key":"e_1_2_9_6_2","first-page":"243","volume-title":"On the Concept of Attractor","author":"Milnor J.","year":"2004"},{"key":"e_1_2_9_7_2","first-page":"137","volume-title":"Computing and complexity \u2014 networks, nature and virtual world In Hooker, C., editor, Philosophy Of Complex Systems, Volume 10 of Handbook Of the Philosophy Of Science","author":"Green D. G.","year":"2011"},{"key":"e_1_2_9_8_2","unstructured":"RenY. LuY. LvJ. andChenZ. 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Graph Fractal Dimension and Structure of Fractal Networks: A Combinatorial Perspective 2019 https:\/\/arxiv.org\/abs\/1912.11385."},{"key":"e_1_2_9_21_2","unstructured":"VettelschossB. FreibergerM. andDambreJ. Self-organized dynamic attractors in recurrent neural networks Proceedings of the ESANN 2020 European Symposium on Artificial Neural Networks Computational Intelligence and Machine Learning oct2020 Bruges Belgium."},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(00)00311-3"},{"key":"e_1_2_9_23_2","doi-asserted-by":"crossref","unstructured":"DeverashettiM.andPradhanS. Identification of topologies by using harmonic centrality in huge social networks Proceedings of the 2018 3rd International Conference on Communication and Electronics Systems (ICCES) 2018october Coimbatore India 443\u2013448.","DOI":"10.1109\/CESYS.2018.8724042"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1186\/s40649-020-00081-w"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1162\/artl_a_00347"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"e_1_2_9_27_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2017\/4037682","article-title":"A new 3d autonomous continuous system with two isolated chaotic attractors and its topological horseshoes","author":"Zhou P.","year":"2017","journal-title":"Complexity"},{"key":"e_1_2_9_28_2","first-page":"1","article-title":"A new 4d chaotic system with two-wing, four-wing, and coexisting attractors and its circuit simulation","author":"Huang L.","year":"2019","journal-title":"Complexity"},{"key":"e_1_2_9_29_2","unstructured":"Wikimedia Commons Lorenz attractor yb.svg April2021 https:\/\/commons.wikimedia.org\/wiki\/File:Lorenz_attractor_yb.svg."}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/3937475","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/2022\/3937475","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2022\/3937475","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T21:14:38Z","timestamp":1769116478000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2022\/3937475"}},"subtitle":[],"editor":[{"given":"Atila","family":"Bueno","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,1]]},"references-count":29,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["10.1155\/2022\/3937475"],"URL":"https:\/\/doi.org\/10.1155\/2022\/3937475","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1]]},"assertion":[{"value":"2022-02-19","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-06-04","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-06-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"3937475"}}