Hopf bifurcation for two-dimensional doubly diffusive convection

Abstract

In this article, we present a stability analysis of the Hopf bifurcation for a doubly diffusive problem. It is proved that there exist both continuous and jump transitions and that these are determined explicitly by the variation of certain physically relevant, non-dimensional parameters.

Keywords:

• doubly diffusive convection
• thermohaline ocean circulation
• attractor bifurcation
• stability
• structural stability
• saddle-node bifurcation
• hysteresis
• roll structure

AMS Subject Classifications::

• 35B32
• 35B35
• 35B41
• 35K50
• 35Q35
• 76E20
• 76R05
• 86A05

Acknowledgements

The work was supported in part by the Office of Naval Research, the National Science Foundation and the National Science Foundation of China. C. Hsia was supported in part the Kenda Foundation and by the National Science Council of Taiwan.