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oai:recercat.cat:2117/4554142026-03-09T04:11:47Zcom_2072_1033col_2072_452950

Nested Feigenbaum cascades and Shil’nikovlike dynamics in convection of binary mixtures Sánchez Umbría, Juan Net Marcé, Marta Universitat Politècnica de Catalunya. Departament de Física Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics Thermal convection Binary mixtures Periodic orbits Stability Period-doubling and saddle-node bifurcations Cyclic and chaotic nearly-heteroclinic orbits Numerical continuation and stability analysis of periodic orbits are used to analyze, under a dynamical systems point of view, the time dependent dynamics that arise from the steady convection of a H2 -Xe gas mixture, driven by lateral temperature and low concentration gradients. Both Soret and Dufour effects are taken into account. A bifurcation diagram consisting of sequences of period-doubling and saddle-node bifurcations is unfold. They give rise to a series of nested Feigenbaum cascades in a narrow region of the parameter space. Several types of cyclic and chaotic solutions close to heteroclinic orbits were found in the interval of the control parameter where the periodic orbits are unstable. The relations between them are established. This research has been supported by the Spanish Ministry of Science and Innovation and the European Regional Development Fund, under Grant No. PID2021-125535NB-I00. We would like to acknowledge the interest and support by the late Àngel Jorba Monte during most of the development of this study. Many thanks as well to Edgar Knobloch for his helpful comments. Peer Reviewed Postprint (published version) 2026-02-12 Article Sanchez, J.; Net, M. Nested Feigenbaum cascades and Shil'nikovlike dynamics in convection of binary mixtures. «Communications in nonlinear science and numerical simulation», 12 Febrer 2026, article 109829. 1878-7274 https://hdl.handle.net/2117/455414 10.1016/j.cnsns.2026.109829 https://hdl.handle.net/2117/455414 eng https://www.sciencedirect.com/science/article/pii/S1007570426001899 info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-125535NB-I00/ES/METODOS ANALITICOS Y COMPUTACIONALES EN SISTEMAS DINAMICOS/ http://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access Attribution-NonCommercial-NoDerivatives 4.0 International 25 p. application/pdf Elsevier