ArticleBulletin of mathematical biology2024
Turing Instabilities are Not Enough to Ensure Pattern Formation.
Article in Bulletin of mathematical biology, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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10 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
- Revisiting Turing's Chemical Basis of Morphogenesis.Bulletin of mathematical biology · 2026Review
- Chase-and-Run and Chirality in Nonlocal Models of Pattern Formation.Bulletin of mathematical biology · 2025Article
- Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics.Bulletin of mathematical biology · 2025Article
- Designing reaction-cross-diffusion systems with Turing and wave instabilities.Journal of mathematical biology · 2025Article
- Pattern Formation as a Resilience Mechanism in Cancer Immunotherapy.Bulletin of mathematical biology · 2025Article
- Optimal network sizes for most robust Turing patterns.Scientific reports · 2025Article
- Widespread biochemical reaction networks enable Turing patterns without imposed feedback.Nature communications · 2024Article
- Turing Instabilities are Not Enough to Ensure Pattern Formation.Bulletin of mathematical biology · 2024Article
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Authors and funding
5 authors.
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Abstract
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.
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