COEXISTENCE OF PATTERNS ON A RAMP OF OVERCRITICALITY

We consider nonlinear pattern-forming systems in the case when the loc al overcriticality parameter epsilon is ramped, smoothly matching the subcritical region to the overcritical one. We assume that the nonline ar interactions between spatial modes favor the roll pattern, the reso nant hexagon-generating interaction being weak as usual. If the ramp i s sufficiently small, we find that a stripe of hexagons is sandwiched between semi-infinite regions of the uniform state (corresponding to t he deeply subcritical range) and rolls (corresponding to the strongly overcritical one). At a certain threshold value of the ramp, the hexag ons disappear via a super- or subcritical bifurcation, depending upon their orientation. In the latter case, coexistence of two different pa tterns, with and without the hexagonal component, is possible. These t ransitions between different patterns can easily be realized experimen tally in terms of the classical Rayleigh-Benard convection in a slight ly non-Boussinesq fluid. (C) 1998 Elsevier Science B.V.