Reaction-diffusion fronts and the butterfly set

Jaime Cisternas, Kevin Rohe, Stefan Wehner

Research output: Contribution to journalArticlepeer-review

Abstract

A single-species reaction-diffusion model is used for studying the coexistence of multiple stable steady states. In these systems, one can define a potential-like functional that contains the stability properties of the states, and the essentials of the motion of wave fronts in one-and two-dimensional space. Using a quintic polynomial for the reaction term and taking advantage of the well-known butterfly bifurcation, we analyze the different scenarios involving the competition of two and three stable steady states, based on equipotential curves and points in parameter space. The predicted behaviors, including a front splitting instability, are contrasted to numerical integrations of reaction fronts in two dimensions.

Original languageEnglish
Article number113138
JournalChaos
Volume30
Issue number11
DOIs
StatePublished - 1 Nov 2020

Bibliographical note

Funding Information:
K.R., J.C., and S.W. are grateful for the financial support of the Erasmus+ mobility programme of the European Union. The authors are grateful for the general support of Dr. Christian Fischer.

Publisher Copyright:
© 2020 Author(s).

Fingerprint Dive into the research topics of 'Reaction-diffusion fronts and the butterfly set'. Together they form a unique fingerprint.

Cite this