Emergence of collective self-oscillations in minimal lattice models with feedback.

The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in the setting of dynamical systems, this phenomenon is not well understood in the context of out-of-equilibrium phase transitions in many-body systems. Here we consider three classical lattice models, namely the Ising, the Blume-Capel, and the Potts models, provided with a feedback among the order and control parameters.

Bubbling transition as a mechanism of destruction of synchronous oscillations of identical microbubble contrast agents.

We study the process of the 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 the 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.

Hyperchaos and multistability in the model of two interacting microbubble contrast agents.

We study nonlinear dynamics of two coupled contrast agents that are micrometer size gas bubbles encapsulated into a viscoelastic shell. Such bubbles are used for enhancing ultrasound visualization of blood flow and have other promising applications like targeted drug delivery and noninvasive therapy. Here, we consider a model of two such bubbles interacting via the Bjerknes force and exposed to an external ultrasound field.