On the Stability of a Mathematical Model for Coral growth in a Tank

Somathilake, L. W.; Wedagedera, J. R.

doi:10.9734/bjmcs/2012/1387

Cited by 7 publications

(7 citation statements)

References 9 publications

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“…Symbiodinium, a group of simbiotic microalgae in polyp of coral reef, may has ability to adapt with photon flux densities and UV in shalow coral reef system as indicated in coral growth model (Somathilake and Wedagedera, 2012). The adaptation mechanisms may involved photolyasemediated photo reactivation that repairs UV damaged DNA, UV screening along membrane, and turn over of repair cycle (Muhaemin 2011).…”

Section: Introductionmentioning

confidence: 99%

Glutathione (GSH) Production as Protective Adaptation Against Light Regime Radiation of Symbiodinium Natural Population

et al. 2017

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Section: Introductionmentioning

confidence: 99%

Glutathione (GSH) Production as Protective Adaptation Against Light Regime Radiation of Symbiodinium Natural Population

et al. 2017

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“…The stability of ), S 2 depends on the parameters = 0, and for α > and 2λ, (Somathilake & Wedagedera, 2012). Therefore, Turing type instability may occur only at ), S 2 .…”

Section: Introductionmentioning

confidence: 99%

“…However, various modelling approaches on coral morphogenesis processes have been previously reported (Kaandorp et al, 1996;2005;2008;Mistr & Bercovici, 2003;Merks, 2003a; b; c; 2010; Chindapol et al, 2013). A reaction diffusion type mathematical model for the growth of corals in a tank has been previously proposed by Somathilake and Wedagedera (2012;2014) considering the nutrient polyps interaction. This model has been derived based on the model proposed by Mistr and Bercovici (2003).…”

Section: Introductionmentioning

confidence: 99%

“…... (2) The local and global stability of the solutions of the system of ordinary differential equations (2) have been discussed in a previous study (Somathilake & Wedagedera, 2012). Instability analysis and pattern formation behaviour in the Turing sense of the model (1), subject to the following boundary conditions have been discussed previously (Somathilake & Wedagedera, 2014).…”

Section: Introductionmentioning

confidence: 99%

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

Somathilake¹,

Wedagedera²

2016

J. Natn. Sci. Foundation Sri Lanka

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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 conditions and it is shown that the numerical results agree with the analytically derived properties of the solutions.Dispersion relation, reaction-diffusion equations, spatial temporal pattern formation, Turing instability.

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“…A reaction diffusion type mathematical model for growth of corals in a tank is proposed in [11] [12] considering the nutrient polyps interaction. This model is derived based on the model appear in [8].…”

Section: Introductionmentioning

confidence: 99%

Stationary Solutions of a Mathematical Model for Formation of Coral Patterns

Somathilake

Wedagedera²

2015

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A reaction-diffusion type mathematical model for growth of corals in a tank is considered. In this paper, we study stationary problem of the model subject to the homogeneous Neumann boundary conditions. We derive some existence results of the non-constant solutions of the stationary problem based on Priori estimations and Topological Degree theory. The existence of non-constant stationary solutions implies the existence of spatially variant time invariant solutions for the model.

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On the Stability of a Mathematical Model for Coral growth in a Tank

Cited by 7 publications

References 9 publications

Glutathione (GSH) Production as Protective Adaptation Against Light Regime Radiation of Symbiodinium Natural Population

Glutathione (GSH) Production as Protective Adaptation Against Light Regime Radiation of Symbiodinium Natural Population

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

Stationary Solutions of a Mathematical Model for Formation of Coral Patterns

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