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This lack of consensus presents a significant challenge to the development of accurate models of neural dynamics. However, at the foundation of dynamical systems theory lies a definition of what constitutes the \u2019state\u2019 of a system\u2014i.e., a specification of the system\u2019s future. Here, we propose to adopt this definition to establish brain states in neuroimaging timeseries by applying Dynamic Causal Modelling (DCM) to low-dimensional embedding of resting and task condition fMRI data. We find that ~90% of subjects in resting conditions are better described by first-order models, whereas ~55% of subjects in task conditions are better described by second-order models. Our work calls into question the status quo of using first-order equations almost exclusively within computational neuroscience and provides a new way of establishing brain states, as well as their associated phase space representations, in neuroimaging datasets.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011571","type":"journal-article","created":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T17:32:34Z","timestamp":1697477554000},"page":"e1011571","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":5,"title":["Establishing brain states in neuroimaging data"],"prefix":"10.1371","volume":"19","author":[{"given":"Zalina","family":"Dezhina","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Smallwood","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ting","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico E.","family":"Turkheimer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rosalyn J.","family":"Moran","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7984-8909","authenticated-orcid":true,"given":"Karl J.","family":"Friston","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Leech","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2973-1395","authenticated-orcid":true,"given":"Erik D.","family":"Fagerholm","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2023,10,16]]},"reference":[{"key":"pcbi.1011571.ref001","article-title":"function of complex brain networks","author":"Sporns O. 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