Bifurcations 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.