Numerical bifurcation analysis of a 3D turing-type reaction–diffusion model

Weiyan Song*, Fred Wubs, Jonas Thies, Sven Baars

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)


We perform a numerical study of a two-component reaction–diffusion model. By using numerical continuation methods, combined with state-of-the-art sparse linear and eigenvalue solvers, we systematically compute steady state solutions and analyze their stability and relations in both two and three space dimensions. The approach gives a more reliable and complete picture than previous efforts based on time integration schemes and is also typically much more efficient in terms of computing time. We are therefore able to produce a rich bifurcation diagram showing a variety of solution patterns and transitions.

Original languageEnglish
Pages (from-to)145-164
Number of pages20
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusPublished - 2018
Externally publishedYes


  • Bifurcation diagram
  • Continuation
  • Pattern formation
  • Stability


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