TURING INSTABILITY AND ATTRACTOR BIFURCATION FOR THE GENERAL BRUSSELATOR MODEL

Yuncherl Choi; Taeyoung Ha; Jongmin Han; Young Rock Kim; Doo Seok Lee

doi:10.3934/cpaa.2024032

TURING INSTABILITY AND ATTRACTOR BIFURCATION FOR THE GENERAL BRUSSELATOR MODEL

Yuncherl Choi, Taeyoung Ha, Jongmin Han, Young Rock Kim, Doo Seok Lee

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 s_N that gives a criterion for the continuous transition. We obtain continuous transitions for s_N > 0, but jump transitions for s_N < 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.

Original language	English
Pages (from-to)	718-735
Number of pages	18
Journal	Communications on Pure and Applied Analysis
Volume	23
Issue number	5
DOIs	https://doi.org/10.3934/cpaa.2024032
Publication status	Published - May 2024

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© 2024 American Institute of Mathematical Sciences. All rights reserved.

Keywords

Turing instability
attractor bifurcation
center manifold function
general Brusselator model

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10.3934/cpaa.2024032

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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.",

keywords = "Turing instability, attractor bifurcation, center manifold function, general Brusselator model",

author = "Yuncherl Choi and Taeyoung Ha and Jongmin Han and Kim, {Young Rock} and Lee, {Doo Seok}",

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AU - Choi, Yuncherl

AU - Ha, Taeyoung

AU - Han, Jongmin

AU - Kim, Young Rock

AU - Lee, Doo Seok

PY - 2024/5

Y1 - 2024/5

N2 - 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.

AB - 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.

KW - Turing instability

KW - attractor bifurcation

KW - center manifold function

KW - general Brusselator model

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SP - 718

EP - 735

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 5

ER -

TURING INSTABILITY AND ATTRACTOR BIFURCATION FOR THE GENERAL BRUSSELATOR MODEL

Abstract

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