Time-Modulated Oscillatory Convection

Abstract

We investigate the effect of temporal modulation on the spatial patterns produced by a spatially extended system undergoing a Hopf bifurcation. It is shown that physically this modulation can stabilize standing waves, which would otherwise be stable to traveling waves. Mathematically a codimension-3 point is naturally introduced which encompasses a Takens-Bogdanov codimension-2 point with vanishing Hopf frequency. Experimentally this setup is attractive since the three relevant parameters are easily accessible and the steady bifurcation can be made forward as well as backward near a codimension-2 point.