Resonant heteroclinic cycles and singular hyperbolic attractors in models for skewed varicose instability

Abstract

We consider a system of differential equations proposed by Busse et al (1992 Physica D 61 94–105) to describe the development of spatio-temporal structures in Rayleigh–Bénard convection, near the skewed varicose instability. Numerical computations make it clear that the global bifurcations are organized by a codimension two bifurcation with heteroclinic cycles and a double principal stable eigenvalue at the origin. We carry out the bifurcation study and prove in particular the occurrence in the unfolding of robustly transitive strange attractors akin to Lorenz attractors. In contrast to the actual Lorenz attractors, these attractors contain two equilibria.