Biomedical subjects

Marcin Leda

Publications and source records attributed to Marcin Leda.

3 recordsLinked to original sources

PubMed2006

On the variety of traveling fronts in one-variable multistable reaction-diffusion systems.

The still-open problem of the variety of asymptotic solutions to one-variable, one-dimensional infinite multistable reaction-diffusion systems is solved. We show that in such systems, besides monotonic traveling fronts, nonmonotonic traveling fronts can exist for appropriate initial conditions. The dependence of numbers of various types of traveling fronts on the number of stable stationary states also is given. Examples of traveling fronts for the chemical model describing two enzymatic (catalytic) reactions inhibited by an excess of their reactant is presented.

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PubMed2006

Periodic spatiotemporal patterns in a two-dimensional two-variable reaction-diffusion model.

Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable thermochemical (reaction-diffusion) system are shown. In a one-dimensional system the traveling impulse which reflects from impermeable boundaries is a stable asymptotic solution if the diffusion coefficient of the reactant is greater than the thermal diffusivity of the system. Periodic patterns of two symmetries are presented in the 2D system: the impulse of excitation propagating along the diagonal of a square spatial domain and a structure consisting of curved impulses which propagate in the direction perpendicular to one side of a rectangular domain.

Journal Article↗

PubMed2006

Breaking of translational symmetry of a traveling planar impulse in a two-dimensional two-variable reaction-diffusion model.

The stability of a planar impulse in rectangular spatial domains for a two-variable excitable reaction-diffusion system is numerically studied. The dependence of the stability on the size of the domain perpendicular to the direction of the propagation of the impulse is shown. The instability results in asymptotic stable curved impulses or an asymptotic spatiotemporal structure, which is generated similarly to the one-dimensional backfiring phenomenon.

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