Re-Entrant Hexagons and Locked Turing–Hopf Fronts in the CIMA Reaction

Abstract

Aspects of the mode-interaction and pattern-selection processes in far-from-equilibrium chemical reaction-diffusion systems are studied through numerical simulation of the Lengyel-Epstein model. By varying the feed concentrations, a transition is observed in which hexagons are replaced by stripes and these again by inverted hexagons. The competition between Hopf oscillations and Turing stripes is investigated by following the propagation of a front connecting the two modes. In certain parameter regimes, mode-locking is found to occur. The front then moves an integer number of Turing stripes during an integer number of Hopf oscillations. This phenomenon can be seen as arising from depinning of the Turing front under influence of the Hopf mode.

Hexagons and triangles in the Rayleigh–Bénard problem: quintic-order equations on a hexagonal lattice

“…As stable Turing patterns, Ouyang & Swinney (1991a,b) first observed re-entrant hexagons in a chloriteiodide-malonic acid (CIMA) reaction. Borckmans et al (1992) and Verdasca et al (1992) obtained the re-entrant hexagons for the two-dimensional Brusselator model, Dufiet & Boissonade (1992a) for the Schnackenberg model, Dufiet & Boissonade (1992b) for an activator-substrate depletion model, Dewel et al (1996) for a FitzHugh-Nagumo-type model and Mosekilde et al (1998) for the Lengyel-Epstein model related to the CIMA reaction, for example. As stable convection patterns, on the other hand, Dewel et al (1995) and Hilali et al (1995) obtained re-entrant hexagons in the generalized Swift-Hohenberg equation.…”