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We study nonlinear dynamics in a system of two coupled oscillators,describing the motion of two interacting microbubble contrast agents. In thecase of identical bubbles, the corresponding symmetry of the governing systemof equations leads to the possibility of existence of asymptotically stablesynchronous oscillations. However, it may be difficult to create absolutelyidentical bubbles and, moreover, one can observe in experiments regimes thatare unstable with respect to perturbations of equilibrium radii of bubbles.Therefore, we investigate the stability of various synchronous and asynchronousdynamical regimes with respect to the breaking of this symmetry. We show thatthe main factors determining stability or instability of a synchronousattractor are the presence/absence and the type of an asynchronous attractorcoexisting with the synchronous attractor. On the other hand, asynchronoushyperchaotic attractors are stable with respect to the symmetry breaking in allthe situations we have studied. Therefore, they are likely to be observed inphysically realistic scenarios and can be beneficial for suitable applicationswhen chaotic behavior is desirable.

Synchronous oscillations and symmetry breaking in a model of two interacting ultrasound contrast agents