March 25, 2023

Thursday, November 7, 1996


Stephen Morris, University of Toronto
Experiments on Convection Patterns (Boardroom)
Robust Heteroclinic Cycles in Symmetric Systems

Martin Krupa, Technical University, Vienna
Robust Heteroclinic Cycles in Symmetric Systems


    Stephen Morris: "Experiments on Convection Patterns"
    Fluid convection makes a nice laboratory-scale system in which to do precise studies of pattern formation under nonlinear, non-equilibrium conditions. I will describe recent work on a couple of convection experiments, Rayleigh-Benard convection in gases and electrically driven convection in smectic liquid crystals. In each case, the system makes a transition to an ordered flow pattern, followed by a second transition to a chaotic state.

    Martin Krupa: "Robust Heteroclinic Cycles in Symmetric Systems"
    Heteroclinic cycles do not normally persist in systems of differential equations without symmetry. However, in symmetric systems, heteroclinic cycles can be robust under symmetry-preserving perturbations, and can also be stable in the Liapunov sense. Evidence of such cycles has been observed in numerical simulations and physical experiments, for example in rotating convection between two plates and turbulent flows in a boundary layer. The existence of robust heteroclinic cycles has been proven theoretically in the unfoldings of some low codimension bifurcations and in forced symmetry-breaking from a larger to a smaller symmetry group. This talk will review both theoretical and applied research on robust heteroclinic cycles.