From global to local bifurcations in a forced Taylor-Couette flow

The unfolding due to imperfections of a gluing bifurcation occurring in a periodically forced Taylor-Couette system is analyzed numerically. In the absence of imperfections, a temporal glide-reflection Z₂ symmetry exists, and two global bifurcations occur within a small region of parameter space: a heteroclinic bifurcation between two saddle two-tori and a gluing bifurcation of three-tori. As the imperfection parameter increase, these two global bifurcations collide, and all the global bifurcations become local (fold and Hopf bifurcations). This severely restricts the range of validity of the theoretical picture in the neighborhood of the gluing bifurcation considered, and has significant implications for the interpretation of experimental results.