Bifurcation in Doubly-Diffusive Systems. II. Time Periodic Solutions
Wayne Nagata, James W. Thomas · SIAM Journal on Mathematical Analysis · 1986
We study a system of double-diffusive convection equations which describe a layer of fluid heated and salted from below. For suitable parameter values Hopf bifurcations of time periodic solutions occur in roll-like, square and hexagonal convection cell patterns. A version of the center manifold theorem suitable for partial differential equations is used to prove the existence of the bifurcating time periodic solutions, and the stability of these solutions is determined from the Poincare normal form of the reduced equations on the center manifold.