Parametric Pattern Selection in a Reaction-Diffusion Model

Parametric Pattern Selection in a Reaction-Diffusion Model

We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate) where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to ...

A numerical treatment of a reaction-diffusion model of spatial pattern in the embryo

In this work the mathematical model of a spatial pattern in chemical and biological systems is investigated numerically. The proposed model considered as a nonlinear reaction-diffusion equation. A computational approach based on finite difference and RBF-collocation methods is conducted to solve the equation with respect to the appropriate initial and boundary conditions. The ability and robust...

a numerical treatment of a reaction-diffusion model of spatial pattern in the embryo

in this work the mathematical model of a spatial pattern inchemical and biological systems is investigated numerically. theproposed model considered as a nonlinear reaction-diffusionequation. a computational approach based on finite difference andrbf-collocation methods is conducted to solve the equation withrespect to the appropriate initial and boundary conditions. theability and robustness o...

Pattern formation in reaction diffusion systems: a Galerkin model

Reaction diffusion systems are extremely useful for studying pattern formation in biological systems. We carry out a Lorenz like few mode truncation of a reaction diffusion system and show that it not only gives the same qualitative behaviour as the more complicated systems but also indicates of the existence of a Hopf-bifurcation in the turing region. PACS. 87.10.+e General theory and mathemat...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems