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 language | English |
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Pages (from-to) | 4255-4281 |
Number of pages | 27 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 41 |
Issue number | 9 |
DOIs | |
State | Published - 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