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Investigation of branching structure formation by solutions of a mathematical model of pattern formation in coral reefs

Authors:

LW Somathilake ,

LK
About LW
Department of Mathematics, Faculty of Science, University of Ruhuna, Matara.
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JR Wedagedera

GB
About JR

Simcyp-CERTARA Limited, Blades Enterprise Centre, John Street, Sheffield S2 4SU, United Kingdom.

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Abstract

A reaction-diffusion type mathematical model for the growth of corals in a tank, describing the spatial time evolution of the biomass of dissolved nutrients (food of polyps) and dissolved solid materials (calcium carbonate) of the tank, is considered. Some properties of the spatial patterns when the model parameters lie in the Turing space are investigated based on dispersion relation and unstable wave numbers of the linearised system. Branching structure formation process in the model is explained analytically. The model is solved numerically in one dimension subject to no-flux boundary conditions and it is shown that the numerical results agree with the analytically derived properties of the solutions.   

How to Cite: Somathilake, L. & Wedagedera, J., (2016). Investigation of branching structure formation by solutions of a mathematical model of pattern formation in coral reefs. Journal of the National Science Foundation of Sri Lanka. 44(4), pp.427–436. DOI: http://doi.org/10.4038/jnsfsr.v44i4.8025
Published on 27 Dec 2016.
Peer Reviewed

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