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The estimated system enables us to reconstruct invariant sets and statistical properties as well as to infer short time-series. Our successful modeling relies on the introduction of a set of Gaussian radial basis functions to capture local structures. The proposed method is used to construct a system of ordinary differential equations whose orbit reconstructs a time-series of a variable of the well-known Lorenz system as a simple but typical example. A system for a macroscopic fluid variable is also constructed.<\/jats:p>","DOI":"10.1063\/5.0100166","type":"journal-article","created":{"date-parts":[[2022,9,12]],"date-time":"2022-09-12T16:21:19Z","timestamp":1662999679000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics"],"prefix":"10.1063","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4908-1871","authenticated-orcid":false,"given":"Natsuki","family":"Tsutsumi","sequence":"first","affiliation":[{"name":"Faculty of Commerce and Management, Hitotsubashi University 1 , Tokyo 186-8601, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3569-5896","authenticated-orcid":false,"given":"Kengo","family":"Nakai","sequence":"additional","affiliation":[{"name":"Faculty of Marine Technology, Tokyo University of Marine Science and Technology 2 , Tokyo 135-8533, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3184-0577","authenticated-orcid":false,"given":"Yoshitaka","family":"Saiki","sequence":"additional","affiliation":[{"name":"Graduate School of Business Administration, Hitotsubashi University 3 , Tokyo 186-8601, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2022,9,12]]},"reference":[{"key":"2023080921180337500_c1","first-page":"366","volume-title":"Detecting Strange Attractors in Turbulence","year":"1981"},{"key":"2023080921180337500_c2","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1007\/BF01053745","article-title":"Embedology","volume":"65","year":"1991","journal-title":"J. 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