Nested Feigenbaum cascades and Shil’nikovlike dynamics in convection of binary mixtures

Abstract

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)