{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T08:28:07Z","timestamp":1778401687835,"version":"3.51.4"},"reference-count":49,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T00:00:00Z","timestamp":1749772800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003069","name":"Consejo Nacional de Humanidades, Ciencias, y Tecnolog\u00edas (CONAHCyT)","doi-asserted-by":"publisher","award":["SIP-20251347"],"award-info":[{"award-number":["SIP-20251347"]}],"id":[{"id":"10.13039\/501100003069","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper presents an analytical exploration of how diverse dynamical systems, arising from different scientific domains, can be reformulated (under specific approximations and assumptions) into a common set of equations formally equivalent to the Lorenz system originally derived to model atmospheric convection. Unlike previous studies that focus on analyzing or applying the Lorenz equations, our objective is to show how these equations emerge from distinct models, emphasizing the underlying structural and dynamical similarities. The mathematical steps involved in these reformulations are included. The systems examined include Lorenz\u2019s original atmospheric convection model, the chaotic water wheel, the Maxwell\u2013Bloch equations for lasers, mechanical gyrostat, solar dynamo model, mesoscale reaction dynamics, an interest rate economic model, and a socioeconomic control system. This work includes a discussion of the unifying features that lead to similar qualitative behaviors across seemingly unrelated systems. By highlighting the Lorenz system as a paradigmatic limit of a broad class of nonlinear models, we underscore its relevance as a unifying framework in the study of complex dynamics.<\/jats:p>","DOI":"10.3390\/axioms14060465","type":"journal-article","created":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T09:51:24Z","timestamp":1749808284000},"page":"465","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["From Different Systems to a Single Common Model: A Review of Dynamical Systems Leading to Lorenz Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7134-0190","authenticated-orcid":false,"given":"Juan Carlos","family":"Chimal-Egu\u00eda","sequence":"first","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"given":"Florencio","family":"Guzm\u00e1n-Aguilar","sequence":"additional","affiliation":[{"name":"Escuela Superior de C\u00f3mputo, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1312-5294","authenticated-orcid":false,"given":"V\u00edctor Manuel","family":"Silva-Garc\u00eda","sequence":"additional","affiliation":[{"name":"Centro de Innovaci\u00f3n y Desarrollo Tecnol\u00f3gico en C\u00f3mputo, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"given":"H\u00e9ctor","family":"B\u00e1ez-Medina","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8810-9921","authenticated-orcid":false,"given":"Manuel Alejandro","family":"Cardona-L\u00f3pez","sequence":"additional","affiliation":[{"name":"Centro de Investigaci\u00f3n en Computaci\u00f3n, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"},{"name":"Escuela Superior de Ingenier\u00eda Mec\u00e1nica y El\u00e9ctrica Unidad Zacatenco, Instituto Polit\u00e9cnico Nacional, Mexico City 07738, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic Nonperiodic Flows","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. 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