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DYNAMIC TRANSITIONS AND TURING PATTERNS OF THE BRUSSELATOR MODEL
  • UMAR FARUK MUNTARI,
  • Taylan Sengul
UMAR FARUK MUNTARI
Marmara Universitesi - Goztepe Kampusu

Corresponding Author:[email protected]

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Taylan Sengul
Marmara University
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Abstract

The dynamic transitions of the Brusselator model has been recently analyzed in Y. Choi et’al (2021) and T. Ma, S. Wang (2011). Our aim in this paper is to address the relation between the pattern formation and dynamic transition results left open in those papers. We consider the problem in the setting of a 2D rectangular box where an instability of the homogeneous steady state occurs due to the perturbations in the direction of several modes becoming critical simultaneously. Our main results are two folds: (1) a rigorous characterization of the types and structure of the dynamic transitions of the model from basic homogeneous states and (2) the relation between the dynamic transitions and the pattern formations. We observe that the Brusselator model exhibits different transition types and patterns depending on the nonlinear interactions of the pattern of the critical modes.
03 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
04 Mar 2022Submission Checks Completed
04 Mar 2022Assigned to Editor
30 Mar 2022Editorial Decision: Accept
15 Nov 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 16 on pages 9130-9151. 10.1002/mma.8296