NUMERICAL-STUDIES OF TURING PATTERNS SELECTION IN A 2-DIMENSIONAL SYSTEM

The Turing bifurcations of the Schnackenberg model are studied by numerical simulations. The relative stability of the striped and hexagonal patterns are determined for a large range of control parameters. We show that the stability of the triangular and honeycomb forms of hexagonal patterns are exchanged at a critical point. Striped patterns are favoured in the vicinity of this point. We also show that one of the hexagonal phase is reentrant far from the bifurcation point. Finally, we show that striped patterns develop preferentially in directions orthogonal to the walls when no-flux boundary conditions are applied.