Generic bifurcation structures of Arnol’d tongues in forced oscillators

A detailed numerical bifurcation analysis of the forced Brusselator is performed, exposing local and global bifurcation curves that constitute the internal structure of the dominant Arnol’d tongues. The results of our analyses are presented as phase diagrams and one-parameter bifurcation diagrams. Two theorems concerning the existence of global bifurcations near generic codimension-2 bifurcation points are stated and proved. It is argued that the results are generic to a class of periodically forced self-oscillating systems.