Turing instability and attractor bifurcation for the general Brusselator model
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| Title: | Turing instability and attractor bifurcation for the general Brusselator model |
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| Authors: | Choi, Yuncherl, Ha, Taeyoung, Han, Jongmin, Kim, Young Rock, Lee, Doo Seok |
| Source: | Communications on Pure and Applied Analysis. 23:718-735 |
| Publisher Information: | American Institute of Mathematical Sciences (AIMS), 2024. |
| Publication Year: | 2024 |
| Subject Terms: | center manifold funct, SYSTEMS, Turing instability, WAVES, s. general Brusselator model, PATTERNS, attractor bifurcation |
| Description: | In this paper, we analyze the dynamic bifurcation of the general Brusselator model when the order of reaction is p ∈ (1, ∞). We verify that the Turing instability occurs above the critical control number and obtain a rigorous formula for the bifurcated stable patterns. We define a constant sN that gives a criterion for the continuous transition. We obtain continuous transitions for sN > 0, but jump transitions for sN < 0. By using this criterion, we prove mathematically that higher-molecular reactions are rarely observed. We also provide some numerical results that illustrate the main results. © 2024 American Institute of Mathematical Sciences. All rights reserved. ; FALSE ; scie ; scopus |
| Document Type: | Article |
| ISSN: | 1553-5258 1534-0392 |
| DOI: | 10.3934/cpaa.2024032 |
| Accession Number: | edsair.doi.dedup.....24c01a5225a5375a3944fde9aca1427e |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | In this paper, we analyze the dynamic bifurcation of the general Brusselator model when the order of reaction is p ∈ (1, ∞). We verify that the Turing instability occurs above the critical control number and obtain a rigorous formula for the bifurcated stable patterns. We define a constant sN that gives a criterion for the continuous transition. We obtain continuous transitions for sN > 0, but jump transitions for sN < 0. By using this criterion, we prove mathematically that higher-molecular reactions are rarely observed. We also provide some numerical results that illustrate the main results. © 2024 American Institute of Mathematical Sciences. All rights reserved. ; FALSE ; scie ; scopus |
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| ISSN: | 15535258 15340392 |
| DOI: | 10.3934/cpaa.2024032 |