DOI: 10.5281/zenodo.7619195
Gierer-Meinhardt nonlinear system for pattern formation: An analytical and
computational approach
Zakir Hossine 1, Afia Farzana
2, Md. Abdur Rafe 3, and Md. Kamrujjaman 4*
1,2,3Department of
Applied Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
4Department of
Mathematics, University of Dhaka, Dhaka 1000, Bangladesh
*Corresponding author Email :
kamrujjaman@du.ac.bd
Abstract:
In the universe, an infinite number of patterns are visible, which is the
premier beauty of nature. Mathematical modeling is a powerful tool to decorate
the patterns in scientific computation. This paper studied the Gierer-Meinhardt
reaction-diffusion model of pattern formation to visualize a class of patterns
for different animals and plants. It is also noted that many biological and
chemical phenomena can be explained using the Gierer-Meinhardt model. We have
analyzed the linear stability to get the stability and instability conditions of
a system of reaction-diffusion equations with diffusion and in the absence of
diffusion. Finally, as an application, a series of different types of patterns
are presented using numerical simulation of the model.
Keywords:
Gierer-Meinhardt Model; stability analysis; Turing pattern; reaction-diffusion;
numerical analysis.
International Journal of Ground Sediment & Water
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