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Preferential positioning and positional transitions of localized Turing patterns on curved surfaces
1Gandhi Institute of Technology and Management (GITAM) University, Department of Physics, Bengaluru campus, Bengaluru 561203, India.
Physical Review. E
|October 21, 2025
Summary
Localized Turing patterns exhibit unique behaviors on curved surfaces, influenced by shape and reaction-diffusion parameters. This study reveals how surface geometry dictates pattern positioning and transitions, offering insights into cellular processes.
Area of Science:
- Mathematical Biology
- Chemical Kinetics
- Pattern Formation
Background:
- Turing patterns are fundamental to understanding natural phenomena.
- Curved surfaces introduce unique pattern behaviors not seen on flat surfaces.
- Reaction-diffusion systems are key to modeling these patterns.
Purpose of the Study:
- To analyze the positioning and transitions of localized Turing patterns on curved surfaces.
- To investigate the interplay between surface geometry and reaction-diffusion parameters.
- To understand how non-axisymmetric shapes influence pattern formation.
Main Methods:
- Analytical and numerical examination of Turing patterns.
- Utilizing the Schnakenberg kinetics model.
- Simulations on non-axisymmetric ellipsoids.
Main Results:
- Demonstrated the significant effect of surface shape on pattern positioning.
- Showcased how reaction-diffusion parameters tune pattern transitions.
- Identified specific behaviors of single-spot Turing patterns on curved geometries.
Conclusions:
- Surface geometry plays a critical role in localized Turing pattern formation and dynamics.
- Provides a generic understanding of reaction-diffusion models interacting with system geometry.
- Offers insights into cellular surface shape's influence on symmetry-breaking mechanisms.
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