On the Interplay of Geometrical Shapes and the Analysis of a Dispersal Model for Pattern Formations

Main Article Content

Zakir Hossine
Md. Kamrujjaman

Abstract

A reaction-diffusion model is put forward which is capable of generating chemical maps whose concentration contours are similar to the patterns seen on the flanks of zebras, leopards and other mammals. Initially, this type of reaction diffusion kinetics model was introduced by Turing and later Murray applied it to animal coat patterns. Among many chemical reaction mechanism, we consider Schnackenberg reaction mechanism in details and show that the geometry and scale of the domain, the relevant part of the integument, during the time of laying down plays a crucial role in the structural patterns which result. Patterns which exhibit a limited randomness are obtained for a selection of geometries. Finally the system was solved numerically using finite difference method.

Keywords:
Pattern formation, Turing pattern, reaction-diffusion, numerical analysis

Article Details

How to Cite
Hossine, Z., & Kamrujjaman, M. (2019). On the Interplay of Geometrical Shapes and the Analysis of a Dispersal Model for Pattern Formations. Journal of Advances in Mathematics and Computer Science, 34(4), 1-10. https://doi.org/10.9734/jamcs/2019/v34i430219
Section
Original Research Article

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