Bifurcation in spiral tip dynamics induced by natural convection in the Belousov-Zhabotinsky reaction

The transition to spatial-temporal complexity exhibited by spiral waves under the effect of
gravitational field in the Belousov–Zhabotinsky reaction is numerically studied on the basis of spiral
tip dynamics. Successive transformations in tip trajectories are characterized as a function of the
hydrodynamical parameter and attributed to a Ruelle–Takens–Newhouse scenario to chaos. The
analysis describes the emergence of complexity in terms of the interplay between the evolution of
the velocity field and concentration waves. In particular, i by mapping the tip motion in relation
to some hydrodynamical pseudopotentials, the general mechanism by which the velocity field
affects the tip trajectory is pointed out, and, ii by comparing the dynamical evolutions of local and
mean properties associated with the inhomogeneous structures and to the velocity field, a surprising
correlation is found. The results suggest that the reaction-diffusion-convection RDC coupling
addresses the system to some general regimes, whose nature is imposed by the hydrodynamical
contribution. More generally, RDC coupling would be formalized as the phenomenon that governs
the system and drives it to chaos.