{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T01:18:30Z","timestamp":1775179110781,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,26]],"date-time":"2025-07-26T00:00:00Z","timestamp":1753488000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Shimizu\u2013Morioka dynamical system is analytically investigated in this paper by means of the Optimal Auxiliary Functions Method (OAFM). This system has a chaotic dynamical behavior, specified for more physical applications as chaos synchronization, an attractive phenomenon involving various real-life processes. Semi-analytical solutions for the Shimizu\u2013Morioka system are provided. A comparative analysis between the obtained results via the OAFM method and the corresponding numerical solution highlights the accuracy and efficiency of the involved method. The choice of the OAFM method is justified by the performance in comparison with the iterative method with 7\u201310 iterations. The physical parameters\u2019 influence is investigated on damped oscillations and periodical behaviors of the obtained solutions.<\/jats:p>","DOI":"10.3390\/axioms14080580","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T09:53:02Z","timestamp":1753696382000},"page":"580","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Semi-Analytical Solutions for the Shimizu\u2013Morioka Dynamical System"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1679-1498","authenticated-orcid":false,"given":"Remus-Daniel","family":"Ene","sequence":"first","affiliation":[{"name":"Department of Mathematics, Politehnica University of Timisoara, 300006 Timisoara, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7051-6753","authenticated-orcid":false,"given":"Nicolina","family":"Pop","sequence":"additional","affiliation":[{"name":"Department of Physical Foundations of Engineering, Politehnica University of Timisoara, 300223 Timisoara, Romania"}]},{"given":"Rodica","family":"Badarau","sequence":"additional","affiliation":[{"name":"Department of Mechanical Machines, Equipment and Transportation, Politehnica University of Timisoara, 300222 Timisoara, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"105101","DOI":"10.1016\/j.cnsns.2019.105101","article-title":"Integrability analysis of the Shimizu-Morioka system","volume":"84","author":"Huang","year":"2020","journal-title":"Commun. 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