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Integrability analysis of a low-dimensional model for natural convection in a single-phase loop

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  • Qu, Jingjia
  • Huang, Kaiyin

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.

Suggested Citation

  • Qu, Jingjia & Huang, Kaiyin, 2025. "Integrability analysis of a low-dimensional model for natural convection in a single-phase loop," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p1:s096007792501210x
    DOI: 10.1016/j.chaos.2025.117197
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    References listed on IDEAS

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    1. da Silva, Angela & Rech, Paulo C., 2018. "Numerical investigation concerning the dynamics in parameter planes of the Ehrhard–Müller system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 152-157.
    2. Yang, Shuangling & Qu, Jingjia, 2021. "On first integrals of a family of generalized Lorenz-like systems," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Andrew J Reagan & Yves Dubief & Peter Sheridan Dodds & Christopher M Danforth, 2016. "Predicting Flow Reversals in a Computational Fluid Dynamics Simulated Thermosyphon Using Data Assimilation," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-19, February.
    4. Freddy Dumortier & Jaume Llibre & Joan C. Artés, 2006. "Qualitative Theory of Planar Differential Systems," Springer Books, Springer, number 978-3-540-32902-2, January.
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