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Intricate regimes of propagation of an excitation and self-organization in the blood clotting model

 a,  a,  b,  c,  d,  e,  f
a Research Center for Hematology, Russan Academy of Medical Sciences, Novozykovskii proezd 4a, Moscow, 125167, Russian Federation
b Institute of Control Sciences, Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997, Russian Federation
c Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region, Russian Federation
d Semenov Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina, 4, Moscow, 119991, Russian Federation
e Lomonosov Moscow State University, Department of Physics, Vorobevy gory, Moscow, 119992, Russian Federation
f Institute for Theoretical and Experimental Biophysics, Russian Academy of Sciences, Institutskaya str. 3, Pushchino, Moscow Region, 142290, Russian Federation

A very simple mathematical model of blood coagulation is considered, consisting of a set of three partial differential equations that treat blood as an active (excitable) medium. Many well-known phenomena (running pulses, trigger waves, and dissipative structures) can be observed in such a medium. Recent analytic and numerical results obtained by the authors using this model are presented. The following aspects of the formation of dynamic and static structures in this medium are discussed: (1) three scenarios of the formation of spatially localized standing structures (peaks) observed in the model, (2) complex dynamical modes induced by unstable trigger waves, some of the modes leading to unattenuated activity (dynamical chaos) in the entire space, and (3) a new type of excitation propagation in active media — stable multihumped peaks due to trigger wave bifurcation — predicted by the model.

Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 05.45.−a, 82.39.−k, 87.19.Uv (all)
DOI: 10.1070/PU2007v050n01ABEH006156
URL: https://ufn.ru/en/articles/2007/1/d/
Citation: Ataullakhanov F I, Lobanova E S, Morozova O L, Shnol’ E E, Ermakova E A, Butylin A A, Zaikin A N "Intricate regimes of propagation of an excitation and self-organization in the blood clotting model" Phys. Usp. 50 79–94 (2007)
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Оригинал: Атауллаханов Ф И, Лобанова Е С, Морозова О Л, Шноль Э Э, Ермакова Е А, Бутылин А А, Заикин А Н «Сложные режимы распространения возбуждения и самоорганизация в модели свертывания крови» УФН 177 87–104 (2007); DOI: 10.3367/UFNr.0177.200701d.0087

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