Target patterns in reaction-diffusion systems
نویسندگان
چکیده
منابع مشابه
Target Patterns and Spirals in Planar Reaction-Diffusion Systems
Solutions of reaction-diffusion equations on a circular domain are considered. With Robin boundary conditions, the primary instability may be a Hopf bifurcation with eigenfunctions exhibiting prominent spiral features. These eigenfunctions, defined by Bessel functions of complex argument, peak near the boundary and are called wall modes. In contrast, if the boundary conditions are Neumann or Di...
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We discuss a variety of experimental and theoretical studies of localized stationary spots, oscillons, and localized oscillatory clusters, moving and breathing spots, and localized waves in reaction-diffusion systems. We also suggest some promising directions for future research in this area.
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In this paper, bifurcations of stationary and time-periodic solutions to reactiondiffusion systems are studied. We develop a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns. In particular, we show the existence of localized pulses near saddle-nodes, critical Gibbs kernels in the cusp, focus patterns in Turing inst...
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The supercritical short-wave oscillatory bifurcation is studied in finite systems using the amplitude ~Ginzburg-Landau! equation. Numerical simulations show that a zero-flux boundary stabilizes sources of target patterns. As a result, stable sources attached to the boundary can exist at small overcriticality, under the condition of convective instability of the homogeneous steady state. Oscilla...
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Reaction-Diffusion systems are important in the field of non-equilibrium phenomena with relevance to biological and synthetic pattern formation. While homogenous distribution of chemicals was always believed to be a stable state, the symmetry-breaking treatment by Turing on such systems in 1951 showed pattern formation could be more stable in certain cases. This paper reviews the treatment by T...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1981
ISSN: 0196-8858
DOI: 10.1016/0196-8858(81)90042-7