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Regul. Chaotic Dyn., 2018, Volume 23, Issue 3, Pages 257–272 (Mi rcd322)  

Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall

Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Nikolay A. Kudryashov

National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia

Abstract: Contrast agent microbubbles, which are encapsulated gas bubbles, are widely used to enhance ultrasound imaging. There are also several new promising applications of the contrast agents such as targeted drug delivery and noninvasive therapy. Here we study three models of the microbubble dynamics: a nonencapsulated bubble oscillating close to an elastic wall, a simple coated bubble and a coated bubble near an elastic wall.We demonstrate that complex dynamics can occur in these models. We are particularly interested in the multistability phenomenon of bubble dynamics. We show that coexisting attractors appear in all of these models, but for higher acoustic pressures for the models of an encapsulated bubble.We demonstrate how several tools can be used to localize the coexisting attractors. We provide some considerations why the multistability can be undesirable for applications.

Keywords: contrast agent, dynamical system, nonlinear dynamics, dynamical chaos, multistability, coexisting attractors

Funding Agency Grant Number
Russian Science Foundation 17-71-10241


DOI: https://doi.org/10.1134/S1560354718030036

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 37N10, 34A34, 37N25
Received: 05.02.2018
Language: English

Citation: Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Nikolay A. Kudryashov, “Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall”, Regul. Chaotic Dyn., 23:3 (2018), 257–272

Citation in format AMSBIB
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\by Ivan R. Garashchuk, Dmitry I. Sinelshchikov, Nikolay A. Kudryashov
\paper Nonlinear Dynamics of a Bubble Contrast Agent Oscillating near an Elastic Wall
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 3
\pages 257--272
\mathnet{http://mi.mathnet.ru/rcd322}
\crossref{https://doi.org/10.1134/S1560354718030036}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3811818}
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