Reaction-diffusion fronts and the butterfly set

Jaime Cisternas*, Kevin Rohe, Stefan Wehner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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
Issue number11
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).


  • butterfly
  • Competition
  • Motion
  • Nonhuman
  • Reaction diffusion model
  • Steady state


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