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Model Fibrillation as an Analogue of the Hyperbolic the Smale-Williams Attractorстатья
- Авторы: Белякин С.Т., Шутеев С.А.
- Журнал: American Jornal of Biomedical Science & Research
- Том: 2
- Номер: 5
- Год издания: 2019
- Первая страница: 197
- Последняя страница: 201
- DOI: 10.34297/AJBSR.2019.02.000606
- Аннотация: Currently, active media form a very promising area of research, because they include a variety of physical, chemical, biological, etc. objects: electronic solid-state systems, a number of chemical solutions and gels (including the Belousov reaction), nerve and muscle tissue, microbial colonies, ecological systems, etc. Representation of active media through ensembles linked excitable or self-oscillating elements is quite useful method of analysis, because the active media allows you to deeply understand the basic dynamic processes occurring in such environments. As is known, this approach goes back to the Wiener and rosenbluth Model [1], according to which the excitable medium consists of a set of interacting elements in one of three possible States: excitation, refractoriness or rest. Later, models such as limit-cycle oscillators and chaotic maps [2-3] also began to play an important role not only in a fairly realistic description of active media, but also in understanding the possible behavior of systems far from equilibrium. Many useful concepts, such as phase captures, synchronization, and space-time chaos, have become popular due to detailed studies of similar nonlinear models [4-6]. Analysis of systems of interacting elements allows us to determine a number of patterns of behavior of active environments, often hidden and implicit. For example, it becomes possible to describe complex (including chaotic) dynamic regimes at a qualitatively different level, to calculate a number of invariant characteristics of the process dynamics and to give a visual representation of the obtained solution. The development of the theory of dynamic systems and computer methods allowed a new approach to the study of such a complex active medium as heart tissue. The combined use of these two approaches, as well as the consideration of cardiac tissue as a system consisting of self-oscillating and excitable elements, makes it possible to deeply understand the processes underlying the functioning of the heart and describe the various cardiac pathologies (arrhythmias). One of the very relevant and practically important directions here is the task of stabilizing the work of the heart muscle in some types of deep arrhythmias [7-8]. Stabilization of unstable or chaotic behavior of a dynamic system, creation of artificial in the studied system of stable periodic oscillations, by means of external multiplicative or additive influences. To stabilize, it is necessary to find such external disturbances that would bring the system out of the chaotic regime on a regular one. To solve these problems, there is, at present, sufficient scientific interest. The relevance of this problem in the application to active environments is obvious. For example, for cardiac tissue, the removal of the system to the desired dynamic mode makes it possible to control the rhythm and thus restore the required dynamics. This approach to the stabilization of dangerous arrhythmias allows us to hope for the creation of new effective rhythm drivers. At the same time, it is important to minimize energy costs, since the application of pulses of large amplitude to biological tissues is unacceptable.
- Добавил в систему: Белякин Сергей Тихонович
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | Model Fibrillation as an Analogue of the Hyperbolic the Smale-Williams Attractor | AJBSR.MS.ID.000606.pdf | 1,4 МБ | 1 мая 2019 [Sergey111] |
| 2. | Полный текст | Model Fibrillation as an Analogue of the Hyperbolic the Smale-Williams Attractor | MODEL_FIBRILLATION_AS_AN_ANALOGUE_OF_THE_HYPERBOLIC_THE_SMA… | 1,3 МБ | 1 мая 2019 [Sergey111] |