Takens-Bogdanov bifurcation on the hexagonal lattice for double-layer convection

In the Benard problem for two-fluid layers, Takens-Bogdanov bifurcations ca n arise when the stability thresholds for both layers are close to each oth er. In this paper, we provide an analysis of bifurcating solutions near suc h a Takens-Bogdanov point, under the assumption that solutions are doubly p eriodic with respect to a hexagonal lattice. Our analysis focusses on perio dic solutions, secondary bifurcations from steady to periodic solutions and heteroclinic solutions arising as limits of periodic solutions. We compute the coefficients of the amplitude equations for a number of physical situa tions. Numerical integration of the amplitude equations reveals quasiperiod ic and chaotic regimes, in addition to parameter regions where steady or pe riodic solutions are observed. (C) 1999 Elsevier Science B.V. All rights re served.