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Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces.
Ryosuke Nishide1, Shuji Ishihara1,2
1The University of Tokyo, Graduate School of Arts and Sciences, Komaba 3-8-1, Meguro-ku, Tokyo 153-8902, Japan.
Physical Review. E
|March 19, 2025
Summary
Surface curvature can drive pattern propagation and lead to complex dynamics like periodic and chaotic behaviors. This research offers insights into controlling pattern formation on curved surfaces.
Area of Science:
- Mathematical modeling
- Theoretical physics
- Chemical kinetics
Background:
- Pattern dynamics are common on curved surfaces, but the influence of geometry and topology is not fully understood.
- Previous studies showed static patterns can propagate on curved surfaces under specific conditions.
Purpose of the Study:
- To investigate pattern propagation driven by surface curvature using a more comprehensive approach.
- To explore the influence of surface geometry on pattern dynamics beyond constant-speed propagation.
Main Methods:
- Weakly nonlinear analysis of reaction-diffusion equations on curved surfaces.
- Examination of pattern dynamics on axisymmetric surfaces.
Main Results:
- Confirmed conditions for pattern propagation driven by surface curvature.
- Predicted diverse dynamics, including periodic and chaotic behaviors, based on surface geometry.
Conclusions:
- Surface geometry significantly influences pattern dynamics, enabling propagation and complex behaviors.
- Provides a framework for understanding and controlling pattern formation on curved surfaces.
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