Abstract
In this paper, we propose a Space Fractional Reaction-Diffusion model for growth of corals in a tank. We analyse spatial temporal pattern formation behavior of the model through Turing type instabi...
Highlights
In this research paper we propose a mathematical model for pattern formation in coral reefs, applying physical phenomena called fractional diffusion
The purpose of this investigation is to explore the suitability of space fractional diffusion phenomena in modelling coral reefs pattern formations
Some other possible numerical methods Discretising in space, a fractional reaction diffusion equation can be approximated to a system of ODEs using Matrix Transfer Technique
Summary
The purpose of this investigation is to explore the suitability of space fractional diffusion phenomena in modelling coral reefs pattern formations. Let A and B denote the dissolved nutrients and dissolved solid material (calcium carbonate), respectively, and u and v denote their respective biomasses In this case, nutrient and solid material concentrations at a point is controlled by two processes, reaction and anomalous diffusion. It is reasonable to assume that the time rate change of the dissolved solid material concentration is controlled by fractional diffusion, reactive production and loss due to aggregation on existing coral reefs. This process can be represented in the form: Time rate change of dissolved calcium carbonate ions concentration v = Anomalous diffusion of v − Loss of v due to deposition + Reactive production of v which gives v t. In order to reduce the number of parameters, we use nondimensionalisation techniques
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