2019/03/10 by Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Alexey O. Kazakov +1 · 41 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Attractor #Bifurcation #Chaotic #Contrast (vision) #Dynamics (music) #Homoclinic bifurcation #Homoclinic orbit #Micro and Nano Robotics #Multistability #Nonlinear system #Ultrasound and Cavitation Phenomena #Ultrasound and Hyperthermia Applications #math.DS #nlin.CD
paper · pdf · doi:10.1063/1.5098329
published in Chaos An Interdisciplinary Journal of Nonlinear Science 29(6), 063131 (American Institute of Physics) · 22 pages, 13 figures
arxiv created 2019/03/10 · openalex publication_date 2019/06/01 · openalex created_date 2019/07/12 · arxiv updated 2019/07/24 · openalex updated_date 2026/08/05
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. We demonstrate that in this five-dimensional nonlinear dynamical system, various types of complex dynamics can occur, namely, we observe periodic, quasiperiodic, chaotic, and hypechaotic oscillations of bubbles. We study the bifurcation scenarios leading to the onset of both chaotic and hyperchaotic oscillations. We show that chaotic attractors in the considered system can appear via either the Feigenbaum cascade of period-doubling bifurcations or the Afraimovich-Shilnikov scenario of torus destruction. For the onset of hyperchaotic dynamics, we propose a new bifurcation scenario, which is based on the appearance of a homoclinic chaotic attractor containing a saddle-focus periodic orbit with its two-dimensional unstable manifold. Finally, we demonstrate that the dynamics of two bubbles can be essentially multistable, i.e., various combinations of the coexistence of the above mentioned attractors are possible in this model. These cases include the coexistence of a hyperchaotic regime with an attractor of any other remaining type. Thus, the model of two coupled gas bubbles provides a new example of physically relevant system with multistable hyperchaos.