Abstract:
À very simple mathematical model of blood coagulation is considered, consisting of à 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 à 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) à new type of excitation propagation in active media — stable multihumped peaks due to trigger wave bifurcation — predicted by the model.