Dynamics of spatially nonuniform patterning in the model of blood coagulation

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Abstract
We propose a reaction-diffusion model that describes in detail the cascade of molecular events during blood coagulation. In a reduced form, this model contains three equations in three variables, two of which are self-accelerated. One of these variables, an activator, behaves in a threshold manner. An inhibitor is also produced autocatalytically, but there is no inhibitor threshold, because it is generated only in the presence of the activator. All model variables are set to have equal diffusion coefficients. The model has a stable stationary trivial state, which is spatially uniform and an excitation threshold. A pulse of excitation runs from the point where the excitation threshold has been exceeded. The regime of its propagation depends on the model parameters. In a one-dimensional problem, the pulse either stops running at a certain distance from the excitation point, or it reaches the boundaries as an autowave. However, there is a parameter range where the pulse does not disappear after stopping and exists stationarily. The resulting steady-state profiles of the model variables are symmetrical relative to the center of the structure formed.

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