Localized patterns and semi-strong interaction, a unifying framework for reaction–diffusion systems

• Published in: IMA journal of applied mathematics Vol. 86; no. 5; pp. 1031 - 1065
• Main Authors: Al Saadi, Fahad, Champneys, Alan, Verschueren, Nicolas
• Format: Journal Article
• Language: English
• Published: Oxford University Press 19.10.2021
• Subjects: Schnakenberg; reaction–diffusion; homoclinic snaking; localized patterns; Brusselator; Turing instability

Abstract Systems of activator–inhibitor reaction–diffusion equations posed on an infinite line are studied using a variety of analytical and numerical methods. A canonical form is considered, which contains all known models with simple cubic autocatalytic nonlinearity and arbitrary constant and line...