Heteroclinic cycles in thermal convection models

This book presents a global bifurcation study of a four-dimensional system of differential equations modeling the Rayleigh-Bernard convection. The Rayleigh and Prandtl numbers are two natural parameters on which the system depends. The investigation of the model proceeds through a combination of theoretical analysis and numerical computations. There are local bifurcations, corresponding to changes in stability of steady patterns, but the main changes are governed by curves of global bifurcations involving homoclinic and heteroclinic dynamics. A numerical investigation identifies codimension-two global bifurcations that organize the bifurcation diagram. Bifurcation analysis makes clear the unfolding of these bifurcations. The book is extracted from the doctoral thesis to the Unviversity of Amsterdam, under supervision of Dr. Ale Jan Homburg.