  We study nonlinear dynamics in a model of three interacting encapsulated gas
bubbles in a liquid. The model is a system of three coupled nonlinear
oscillators with an external periodic force. Such bubbles have numerous
applications, for instance, they are used as contrast agents in ultrasound
visualization. Certain types of bubbles oscillations may be beneficial or
undesirable depending on a given application and, hence, the dependence of the
regimes of bubbles oscillations on the control parameters is worth studying. We
demonstrate that there is a wide variety of types of dynamics in the model by
constructing a chart of dynamical regimes in the control parameters space. Here
we focus on hyperchaotic attractors characterized by three positive Lyapunov
exponents and strange attractors with one or two positive Lyapunov exponents
possessing an additional zero Lyapunov exponent, which have not been observed
previously in the context of bubbles oscillations. We also believe that we
provide a first example of a hyperchaotic attractor with additional zero
Lyaponov exponent. Furthermore, the mechanisms of the onset of these types of
attractors are still not well studied. We identify two-parametric regions in
the control parameter space where these hyperchaotic and chaotic attractors
appear and study one-parametric routes leading to them. We associate the
appearance of hyperchaotic attractors with three positive Lyapunov exponents
with the inclusion of a periodic orbit with a three-dimensional unstable
manifold, while the onset of chaotic oscillations with an additional zero
Lyapunov exponent is connected to the partial synchronization of bubbles
oscillations. We propose several underlying bifurcation mechanisms that explain
the emergence of these regimes. We believe that these bifurcation scenarios are
universal and can be observed in other systems of coupled oscillators.
