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In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurrence of periodic solutions in cases where the classical Wilson\u2013Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations.<\/jats:p>","DOI":"10.1007\/s00422-022-00941-w","type":"journal-article","created":{"date-parts":[[2022,9,5]],"date-time":"2022-09-05T12:10:45Z","timestamp":1662379845000},"page":"527-543","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Beyond Wilson\u2013Cowan dynamics: oscillations and chaos without inhibition"],"prefix":"10.1007","volume":"116","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4647-6464","authenticated-orcid":false,"given":"Vincent","family":"Painchaud","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Doyon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7528-697X","authenticated-orcid":false,"given":"Patrick","family":"Desrosiers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,5]]},"reference":[{"issue":"18","key":"941_CR1","doi-asserted-by":"publisher","first-page":"7681","DOI":"10.1523\/JNEUROSCI.3405-12.2013","volume":"33","author":"M Avissar","year":"2013","unstructured":"Avissar M, Wittig JH, Saunders JC et al (2013) Refractoriness enhances temporal coding by auditory nerve fibers. 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