Analysis of pattern formation using numerical continuation

Vladimír Janovský

Applications of Mathematics (2022)

  • Volume: 67, Issue: 6, page 705-726
  • ISSN: 0862-7940

Abstract

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The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter L , which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries. We define and classify them. Our goal is to calculate a global bifurcation diagram.

How to cite

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Janovský, Vladimír. "Analysis of pattern formation using numerical continuation." Applications of Mathematics 67.6 (2022): 705-726. <http://eudml.org/doc/298511>.

@article{Janovský2022,
abstract = {The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter $L$, which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries. We define and classify them. Our goal is to calculate a global bifurcation diagram.},
author = {Janovský, Vladimír},
journal = {Applications of Mathematics},
keywords = {pattern formation; reaction-diffusion model; Turing instability; diffusion-driven instability; bifurcation},
language = {eng},
number = {6},
pages = {705-726},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Analysis of pattern formation using numerical continuation},
url = {http://eudml.org/doc/298511},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Janovský, Vladimír
TI - Analysis of pattern formation using numerical continuation
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 6
SP - 705
EP - 726
AB - The paper deals with the issue of self-organization in applied sciences. It is particularly related to the emergence of Turing patterns. The goal is to analyze the domain size driven instability: We introduce the parameter $L$, which scales the size of the domain. We investigate a particular reaction-diffusion model in 1-D for two species. We consider and analyze the steady-state solution. We want to compute the solution branches by numerical continuation. The model in question has certain symmetries. We define and classify them. Our goal is to calculate a global bifurcation diagram.
LA - eng
KW - pattern formation; reaction-diffusion model; Turing instability; diffusion-driven instability; bifurcation
UR - http://eudml.org/doc/298511
ER -

References

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