Complex dynamics of the formation of spatially localized standing structures in the vicinity of saddle-node bifurcations of waves in the reaction-diffusion model of blood clotting.

Local activation in a one-dimensional three-component reaction-diffusion model of blood clotting may lead to a formation of spatially localized standing structures (peaks) via several complex scenarios. In the first scenario, two concentration pulses first propagate from the site of activation, then stop and transform into peaks [Zarnitsina et al., Chaos 11, 57 (2001)]. Here, we examine this scenario, and also describe a different scenario of peak formation. In this scenario, two trigger waves propagate initially in opposite directions away from the site of activation. Then they stop and change direction of propagation toward each other to the activation site, where they interact and form a peak. Both of these scenarios of stable peak formation are observed in the vicinity of saddle-node bifurcation and may be viewed as a memory of the extinct wave modes.

Running pulses of complex shape in a reaction-diffusion model.

In a one-dimensional reaction-diffusion model of an active medium, stable steady-state wave pulses of a new type are described. They are called multihumped because their waveforms contain several maxima of similar size. Presumably, the multihumped pulses arise via a bifurcation at which an unstable trigger wave disappears. The parameter governing this bifurcation is the diffusion coefficient for the model inhibitor. The model is analyzed by varying this parameter to determine the conditions for the emergence of multihumped pulses. The results of this analysis show how their waveform and dynamics of excitation depend on the inhibitor diffusion coefficient.

[From nonequilibrium thermodynamics to nonlinear dynamics]. / Ot neravnovesnoi termodinamiki k nelineinoi dinamike.

Differences between the thermodynamic and kinetic approaches were discussed by using a system with two or more different steady states as an example. It was shown that the behavior of such systems can be described adequately by the kinetic approach only.

Unstable trigger waves induce various intricate dynamic regimes in a reaction-diffusion system of blood clotting.

In this work we demonstrate that the unstable trigger waves, connecting stable and unstable spatially uniform steady states, can create intricate dynamic regimes in one-dimensional three-component reaction-diffusion model describing blood clotting. Among the most interesting regimes are the composite and replicating waves running at a constant velocity. The front part of the running composite wave remains constant, while its rear part oscillates in a complex manner. The rear part of the running replicating wave periodically gives rise to new daughter waves, which propagate in the direction opposite the parent wave. The domain of these intricate regimes in parameter space lies in the region of monostability near the region of bistability.