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

F.I. Ataullakhanov^a, E.S. Lobanova^a, O.L. Morozova^b, E.E. Shnol’^c, E.A. Ermakova^d, A.A. Butylin^e, A.N. Zaikin^f
^aResearch Center for Hematology, Russan Academy of Medical Sciences, Novozykovskii proezd 4a, Moscow, 125167, Russian Federation
^bInstitute of Control Sciences, Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997, Russian Federation
^cInstitute of Mathematical Problems of Biology, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Prof. Vitkevich str. 1, Pushchino, Moscow Region, 142290, Russian Federation
^dSemenov Federal Research Center for Chemical Physics, Russian Academy of Sciences, ul. Kosygina, 4, Moscow, 119991, Russian Federation
^eLomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
^fInstitute 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.

PACS: 05.45.−a, 82.39.−k, 87.19.Uv (all)
DOI: 10.1070/PU2007v050n01ABEH006156
URL: https://ufn.ru/en/articles/2007/1/d/
Web of Science

000246449500004
Scopus

2-s2.0-34249703618
ADS NASA

2007PhyU...50...79A
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