{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:44:42Z","timestamp":1770983082349,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T00:00:00Z","timestamp":1762473600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Union","doi-asserted-by":"crossref","award":["CZ.10.03.01\/00\/22_003\/0000048"],"award-info":[{"award-number":["CZ.10.03.01\/00\/22_003\/0000048"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper presents a comprehensive study of nonlinear wave and oscillator dynamics under both deterministic and stochastic influences. By comparing soliton-like and dispersive waveforms, we employ spectral solvers, Darboux transformations, and nonlinear diagnostics, including Lyapunov exponents, power spectral analysis, and multidimensional phase-space reconstructions, to examine transitions from quasiperiodic motion to chaotic and stochastic regimes. The results highlight the robustness of soliton solutions in preserving energy and structure, in contrast to the degradation observed in dispersive waves under noise and damping. We also show that spectral broadening, entropy growth, and ergodic phase-space patterns are caused by the critical influence of initial conditions and noise intensity on system behavior. Incorporating control strategies such as OGY chaos control, this work provides a flexible framework for analyzing, modeling, and stabilizing nonlinear systems. Applications span nonlinear optics, fluid flows, and electrical lattices, offering insight into the interplay of nonlinearity and noise with implications for both theoretical understanding and practical system design.<\/jats:p>","DOI":"10.3390\/computation13110263","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T10:56:45Z","timestamp":1762513005000},"page":"263","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Comparative Study of Oscillator Dynamics Under Deterministic and Stochastic Influences with Soliton Robustness Darboux Transformations and Chaos Transition"],"prefix":"10.3390","volume":"13","author":[{"given":"Maham","family":"Munawar","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Engineering and Technology, Lahore 54700, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6747-425X","authenticated-orcid":false,"given":"Adil","family":"Jhangeer","sequence":"additional","affiliation":[{"name":"IT4-Innovations, VSB- Technical University of Ostrava, 70800 Ostrava-Poruba, Czech Republic"},{"name":"Center for Theoretical Physics, Khazar University, Baku AZ1096, Azerbaijan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6506-8730","authenticated-orcid":false,"given":"Mudassar","family":"Imran","sequence":"additional","affiliation":[{"name":"College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates"}]}],"member":"1968","published-online":{"date-parts":[[2025,11,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2031","DOI":"10.1364\/OL.32.002031","article-title":"Impact of two-photon absorption on self-phase modulation in silicon waveguides","volume":"32","author":"Yin","year":"2007","journal-title":"Opt. Lett."},{"key":"ref_2","unstructured":"Whitham, G.B. (2011). Linear and Nonlinear Waves, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Winfree, A.T. (1980). The Geometry of Biological Time, Springer.","DOI":"10.1007\/978-3-662-22492-2"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Kivshar, Y.S., and Agrawal, G.P. (2003). Optical Solitons: From Fibers to Photonic Crystals, Academic Press.","DOI":"10.1016\/B978-012410590-4\/50012-7"},{"key":"ref_5","unstructured":"Remoissenet, M. (2013). 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