{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:12:54Z","timestamp":1753884774975,"version":"3.41.2"},"reference-count":46,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> The main objective of this study is to explore the nonlinear dynamics and chaos detecting in the three-dimensional (3D) generalized Hamiltonian Yang\u2013Mills system as coupled quartic oscillators. We investigate its Liouvillian integrability. The integrable system is obtained and its associated first integral of motion is explicitly given. Also, a variety of nonlinear phenomena could be expressed using various numerical analysis, such as the construction of the system\u2019s Poincar\u00e9 Surface of Section (PSS), the maximum Lyapunov exponent (mLE), and the modern numerical methods like the Smaller (SALI) and the Generalized (GALI) Alignment Indexes. In this context, a series of numerical simulations are appropriate in order to explore ordered and chaotic motions of the system both in two (2D) and three dimensions, and one can observe chaos\u2013order\u2013chaos transition of the system when any parameters on which the system depends vary. Finally, several numerical schemes are shown to demonstrate the effectiveness and rapidity of these proposed methods for distinguishing chaos and order states of the system. <\/jats:p>","DOI":"10.1142\/s0218127422501450","type":"journal-article","created":{"date-parts":[[2022,8,29]],"date-time":"2022-08-29T03:49:35Z","timestamp":1661744975000},"source":"Crossref","is-referenced-by-count":1,"title":["Detecting Order and Chaos by the mLE, SALI and GALI Methods in Three-Dimensional Nonlinear Yang\u2013Mills System"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2433-1563","authenticated-orcid":false,"given":"Walid","family":"Chatar","sequence":"first","affiliation":[{"name":"Laboratoire de Physique du Solide, Facult\u00e9 des Sciences Dhar El Mahraz, Universit\u00e9 Sidi Mohamed Ben Abdellah, B. 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