Nonlinear Dynamics and Bifurcation in the Hoff Model of Oscillations of a Microbubble Contrast Agent

Student: Tyuteva Anastasiya

Supervisor: Dmitry Sinelshchikov

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2021

The main object of the study is a microbubble contrast agent that is injected into the circulatory system. For extended use in medicine, it is necessary to have an understanding of the behavior of nonlinear dynamics and emerging states. In the course of the work, the model of a microbubble contrast agent in the Hoff's model was considered, which had not been studied earlier. To study the dynamics, programs were developed that allow one to build phase portraits, Poincaré sections and bifurcation diagrams; the senior Lyapunov exponent is also calculated. A study on the emergence of a state of multistability in the system was carried out. The results of this work can be useful in medicine for ultrasound diagnostics and in other applications.

Student Theses at HSE must be completed in accordance with the University Rules and regulations specified by each educational programme.

Summaries of all theses must be published and made freely available on the HSE website.

The full text of a thesis can be published in open access on the HSE website only if the authoring student (copyright holder) agrees, or, if the thesis was written by a team of students, if all the co-authors (copyright holders) agree. After a thesis is published on the HSE website, it obtains the status of an online publication.

Student theses are objects of copyright and their use is subject to limitations in accordance with the Russian Federation’s law on intellectual property.

In the event that a thesis is quoted or otherwise used, reference to the author’s name and the source of quotation is required.

Search all student theses