Geodesic
Analysis of pattern formation using numerical continuation
Applications of Mathematics, Tome 67 (2022) no. 6, pp. 705-726.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.2022.0126-21
Classification : 34B24, 35B36, 35K57, 92C15
Keywords: pattern formation; reaction-diffusion model; Turing instability; diffusion-driven instability; bifurcation 
@article{10_21136_AM_2022_0126_21,
     author = {Janovsk\'y, Vladim{\'\i}r},
     title = {Analysis of pattern formation using numerical continuation},
     journal = {Applications of Mathematics},
     pages = {705--726},
     publisher = {mathdoc},
     volume = {67},
     number = {6},
     year = {2022},
     doi = {10.21136/AM.2022.0126-21},
     mrnumber = {4505701},
     zbl = {07613020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0126-21/}
}
TY  - JOUR
AU  - Janovský, Vladimír
TI  - Analysis of pattern formation using numerical continuation
JO  - Applications of Mathematics
PY  - 2022
SP  - 705
EP  - 726
VL  - 67
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0126-21/
DO  - 10.21136/AM.2022.0126-21
LA  - en
ID  - 10_21136_AM_2022_0126_21
ER  - 
%0 Journal Article
%A Janovský, Vladimír
%T Analysis of pattern formation using numerical continuation
%J Applications of Mathematics
%D 2022
%P 705-726
%V 67
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0126-21/
%R 10.21136/AM.2022.0126-21
%G en
%F 10_21136_AM_2022_0126_21
Janovský, Vladimír. Analysis of pattern formation using numerical continuation. Applications of Mathematics, Tome 67 (2022) no. 6, pp. 705-726. doi : 10.21136/AM.2022.0126-21. http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0126-21/

Cité par Sources :