Scale-invariance in reaction-diffusion models of spatial pattern formation.

Scale-invariance in reaction-diffusion models of spatial pattern formation.

We propose a reaction-diffusion model of spatial pattern formation whose solutions can exhibit scale-invariance over any desired range for suitable choices of parameters in the model. The model does not invoke preset polarity or any other ad hoc distinction between cells and provides a solution to the French flag problem without sources at the boundary. Furthermore, patterns other than the pola...

Reaction-diffusion Models for Biological Pattern Formation

We consider the use of reaction-diffusion equations to model biological pattern formation and describe the derivation of the reaction terms for several illustrative examples. After a brief discussion of the Turing instability in such systems we extend the model formulation to incorporate domain growth. Comparisons are drawn between solution behaviour on growing domains and recent results on sel...

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...

Pattern formation in spatially heterogeneous Turing reaction–diffusion models

The Turing reaction–diffusion model [Phil. Trans. R. Soc. 237 (1952) 37–72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially homogeneous parameters. The case of parameters which vary spatially has received less attention. Here, we show that a simple step function heterogeneity in a kinetic parameter can lead to spatial pattern ...

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