Regular and chaotic bubble oscillations in periodically driven pressure fields

The motion of a single bubble in a periodically driven pressure field is examined from a geometric point of view using Poincaré maps. It is shown that the equations of motion can be transformed to a perturbation of a Hamiltonian system. The conditions determining nonlinear resonance are found; these correspond to subharmonic bifurcations. Further it is illustrated how the resonant response interacts with the nonresonant one to produce jump bifurcations. Results are also presented indicating that the periodic response undergoes a complex bifurcation sequence and a strange attractor forms. Finally it is demonstrated how the strange attractor disappears creating horseshoe maps that are associated with transient chaos. This gives some indication of the bifurcations that form the superstructure for single bubble oscillations.