International Journal of Mathematical Sciences and Computing (IJMSC)
IJMSC Vol. 5, No. 3, 8 Jul. 2019
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Periodic Pattern Formation Analysis Numerically in a Chemical Reaction-Diffusion System
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Author(s)
Index Terms
Reaction Diffusion System, Periodic Traveling wave, Pattern Formation, Brusselator Model
Abstract
In this paper, we analyze the pattern formation in a chemical reaction-diffusion Brusselator model. Twocomponent Brusselator model in two spatial dimensions is studied numerically through direct partial differential equation simulation and we find a periodic pattern. In order to understand the periodic pattern, it is important to investigate our model in one-dimensional space. However, direct partial differential equation simulation in one dimension of the model is performed and we get periodic traveling wave solutions of the model. Then, the local dynamics of the model is investigated to show the existence of the limit cycle solutions. After that, we establish the existence of periodic traveling wave solutions of the model through the continuation method and finally, we get a good consistency among the results.
Cite This Paper
A. K. M. Nazimuddin, Md. Showkat Ali, "Periodic Pattern Formation Analysis Numerically in a Chemical Reaction-Diffusion System ", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.5, No.3, pp.17-26, 2019. DOI:10.5815/ijmsc.2019.03.02
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