 Integrability analysis of a low-dimensional model for natural convection in a single-phase loopJingjia Qu and Kaiyin Huang Chaos, Solitons & Fractals, 2025, vol. 201, issue P1 Abstract: This paper investigates the integrability of the Ehrhard–Müller (EM) model, a three-dimensional dynamical system describing natural convection in a single-phase loop with asymmetric heating. The system is governed by nonlinear differential equations that exhibit delayed flow instability and self-organized periodic structures. While the EM model has been extensively studied, its integrability has not been explored. Using Darboux integrability theory, quasi-homogeneous polynomials, and the characteristic curve method, we show that for nonzero heating and friction coefficients, the EM model does not possess polynomial, rational, or Darboux first integrals. However, we show that the EM model exhibits a time-dependent first integral when the parameters satisfy two distinct conditions. Furthermore, we demonstrate that these two special cases of the EM model possess some new features: non-chaotic dynamical behavior and bi-Hamiltonian structures. Keywords: Ehrhard–Müller model; Darboux polynomials; First integrals; Non-chaos (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:201:y:2025:i:p1:s096007792501210x DOI: 10.1016/j.chaos.2025.117197 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 |
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