ArticleBulletin of mathematical biology2022
Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems.
Article in Bulletin of mathematical biology, 2022. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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4 citing papers in PubMed.
- Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.Bulletin of mathematical biology · 2026Article
- Fundamental limits on symmetry breaking by Turing-like activator-inhibitor mechanisms.Development (Cambridge, England) · 2026Article
- Numerical bifurcation analysis of turing and symmetry broken patterns of a PDE model for vegetation dynamics.Journal of mathematical biology · 2026Article
- Dynamical systems of fate and form in development.Seminars in cell & developmental biology · 2025Review
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Abstract
Turing's theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux boundary conditions. However, under fixed boundary conditions, the Turing bifurcation becomes generically transcritical. We derive these algebraic results through weakly nonlinear analysis and apply them to the Schnakenberg kinetics. We observe that the combination of kinetics and boundary conditions produce their own uncommon boundary complexities that we explore numerically. Overall, this work demonstrates that it is not enough to only consider parameter perturbations in a sensitivity analysis of a specific application. Variations in boundary conditions should also be considered.
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