Pattern Selection In A Diffusion-Reaction System With Global Or Long-Range Interaction
We review recent results on pattern selection in the one- or two-dimensional reaction-diffusion system xt - Δx = f(x, y, λ), y t = εg(x, y), subject to global (〈x〉 = x 0) or long-range interaction; the source functions may be realistic kinetic functions or simple cubic or quintic f(x) functions for which the system admits inversion symmetry. This review discusses: (i) physical sources of such interactions and experimental observations in catalytic and electrochemical systems; (ii) the main emerging patterns and their classification according to their symmetry; (iii) the bifurcation between patterns; (iv) patterns when f(x) = 0 is tristable and can sustain several fronts.
The rich class of patterns simulated in a ribbon can be classified as stationary-front solutions (including oscillating fronts and antiphase oscillations) and moving pulse solutions (unidirectional, back-and-forth and source-points). Patterns on a disk may be classified as circular (including oscillatory or moving target patterns), rotating (stationary or moving spiral wave) and other patterns.
KeywordsPattern Selection Spiral Wave Inversion Symmetry Target Pattern Bistable System
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