ABSTRACT
Pattern formation is a common phenomenon, which appears in biological systems, especially in cell differentiation processes. The proper level for understanding the creation of patterns seems to be a physicochemical description. The most fundamental models should be based on systems, in which only chemical reactions and diffusion transport occur (reaction-diffusion systems). In order to present a richness of patterns, we show here the asymptotic patterns in the form of capital letters obtained in two-dimensional reaction-diffusion systems with zero-flux boundary conditions. All capital letters are obtained in the same model, but initial conditions and sizes of the systems are different for each letter. The chemical model consists of elementary reactions and is realistic. It can be realized experimentally in continuous-flow unstirred reactor with an enzymatic reaction allosterically inhibited by an excess of its reactant and product.
ABSTRACT
The two-variable reaction-diffusion model of a chemical system describing the spatiotemporal evolution to large amplitude stationary periodical structures in a one-dimensional open, continuous-flow, unstirred reactor is investigated. Numerical solutions show that the structures are generated by divisions of the traveling impulse and its stopping at the boundary of the system. Analyses of projections of numerical solutions on the phase plane of two variables elaborated in the present paper allow qualitative explanation of the results. The coexistence of the large amplitude stationary periodical structures is shown. A number of coexisting structures grows strongly with increasing length of the reactor and may be as large as one wishes. The relationship of these results to biological systems is stressed.
