 On an integrable family of oscillators with linear and quadratic dampingAnna R. Ishchenko and Dmitry I. Sinelshchikov Chaos, Solitons & Fractals, 2023, vol. 176, issue C Abstract: In this work we study integrability of a family of nonlinear oscillators with linear and quadratic damping. Equations from this family often appear in various applications in physics, mechanics and biology. We demonstrate that certain nonlocal transformations preserve integrating factors for the considered family of equations and provide an explicit expression that connects integrating factors of two nonlocally related oscillators. We apply these results and construct an integrable family of oscillators with linear and quadratic damping, which is connected to an equation from the Painlevé–Gambier classification. We show that members of this family possess an integrating factor, a first integral in terms of the hypergeometric function and a pair of invariant curves. In order to explicitly illustrate our results, we construct new integrable examples of two biologically and physically relevant dynamical systems. Keywords: Nonlocal transformations; Integrating factors; Painlevé–Gambier equations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923009839 DOI: 10.1016/j.chaos.2023.114082 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.