  We study the process of destruction of synchronous oscillations in a model of
two interacting microbubble contrast agents exposed to an external ultrasound
field. Completely synchronous oscillations in this model are possible in case
of identical bubbles, when the governing system of equations possess a symmetry
leading to the existence of a synchronization manifold. Such synchronous
oscillations can be destructed without breaking the corresponding symmetry of
the governing dynamical system. Here we describe the phenomenological mechanism
responsible for such destruction of synchronization and demonstrate its
implementation in the studied model. We show that the appearance and expansion
of transversally unstable areas in the synchronization manifold leads to
transformation of a synchronous chaotic attractor into a hyperchaotic one. We
also demonstrate that this bifurcation sequence is stable with respect to
symmetry breaking perturbations.
