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This article is cited in 22 scientific papers (total in 23 papers)
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Intricate regimes of propagation of an excitation and self-organization in the blood clotting model
F. I. Ataullakhanovabc, E. S. Lobanovab, O. L. Morozovad, È. È. Shnol'e, E. A. Ermakovaf, A. A. Butylina, A. N. Zaikinc a Physics Department, M. V. Lomonosov Moscow State University
b Hematologic Centre, Russian Academy of Medical Sciences
c Institute for Theoretical and Experimental Biophysics, Russian Academy of Sciences
d Institute of Control Sciences, Russian Academy of Sciences
e Institute of Mathematical Problems of Biology, Russian Academy of Sciences
f N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences
Abstract:
А very simple mathematical model of blood coagulation is considered, consisting of а 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 а 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) а new type of excitation propagation in active media — stable multihumped peaks due to trigger wave bifurcation — predicted by the model.
Received: June 26, 2006 Revised: July 26, 2006
Citation:
F. I. Ataullakhanov, E. S. Lobanova, O. L. Morozova, È. È. Shnol', E. A. Ermakova, A. A. Butylin, A. N. Zaikin, “Intricate regimes of propagation of an excitation and self-organization in the blood clotting model”, UFN, 177:1 (2007), 87–104; Phys. Usp., 50:1 (2007), 79–94
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https://www.mathnet.ru/eng/ufn422 https://www.mathnet.ru/eng/ufn/v177/i1/p87
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