Turing instability and dynamic phase transition for the brusselator model with multiple critical eigenvalues

Yuncherl Choi, Taeyoung Ha, Jongmin Han, Sewoong Kim, Doo Seok Lee

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In this paper, we study the dynamic phase transition for one dimensional Brusselator model. By the linear stability analysis, we define two critical numbers λ0 and λ1 for the control parameter λ in the equation. Motivated by [9], we assume that λ0 < λ1 and the linearized operator at the trivial solution has multiple critical eigenvalues β + N and β + N+1. Then, we show that as λ passes through λ0, the trivial solution bifurcates to an S 1-attractor AN . We verify that AN consists of eight steady state solutions and orbits connecting them. We compute the leading coefficients of each steady state solution via the center manifold analysis. We also give numerical results to explain the main theorem.

Original languageEnglish
Pages (from-to)4255-4281
Number of pages27
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume41
Issue number9
DOIs
StatePublished - Sep 2021

Bibliographical note

Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Attractor bifurcation
  • Brusselator model
  • Center manifold function
  • Dynamic phase transition

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