BCAM Scientific Seminar: Nonlinear dynamics of interacting microbubble contrast agents: bifurcations, multistability and synchronization

Location: BCAM Seminar room and online

Abstract
In this talk we study nonlinear dynamics of two interacting microbubble contrast agents in a liquid. Contrast agents are micro-meter size gas-filled bubbles, which are encapsulated into a viscoelastic shell. Such bubbles can be used for various biomedical applications, for example, for enhancing ultrasound visualization of blood flow and targeted drug delivery. It is known that contrast agents can demonstrate complex dynamics and its type is important for applications. However, the dynamics of coupled bubbles has not been thoroughly considered. Therefore, the main goal of this talk is to study typical bifurcation scenarios in the considered model of two coupled bubbles and demonstrate that their dynamics can be multistable. We also investigate synchronization of microbubbles and the processes of its destruction.
We demonstrate that the dynamics of two coupled microbubbles can be of four types. Namely, they can exhibit periodic, quasi-periodic, chaotic and hyperchaotic oscillations. We describe typical bifurcation scenarios for the appearance of chaotic attractors. For the onset of hyperchaotic oscillations we propose a new universal bifurcation scenario. This scenario is based on the appearance of a homoclinic chaotic attractor containing a saddle-focus periodic orbit with its two-dimensional unstable manifold. Moreover, our scenario is typical for other multidimensional dynamical systems, where hyperchaos emerge through the invariant torus destruction. Furthermore, we demonstrate that the dynamics of bubbles is essentially multistable, i.e. all of the above mentioned types of attractors can mutually co-exist.
Finally, we consider synchronous oscillations of microbubbles and demonstrate that there are two typical ways that are responsible for the loss of synchronization. The first and more obvious one is the destruction of the synchronization manifold. The second one is based on the bubbling transition scenario and is possible without the destruction of the synchronization manifold. We study the impact of both mechanisms on bubbles´ dynamics in details.

Link to the seminar: 
https://us06web.zoom.us/j/87265727973?pwd=angyWU1KUFZSbXNEVTVpdzg2clhKQT09