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arXiv · 2403.12442

Oscillatory and chaotic pattern dynamics driven by surface curvature

Ryosuke Nishide·Shuji Ishihara
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Abstract

Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a new mechanism of pattern propagation in which a static pattern on a flat plane becomes a propagating pattern on a curved surface [Nishide and Ishihara, Phys. Rev. Lett. 2022]. Here, we address whether surface curvature can drive more complex pattern dynamics beyond propagation. By employing a combination of weakly nonlinear analysis and numerical simulation, we show that oscillatory and chaotic pattern dynamics can emerge by controlling the surface shapes. These findings highlight a new role of surface topography in pattern formation and dynamics.

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Ryosuke Nishide, Shuji Ishihara. 2024-03-19. Oscillatory and chaotic pattern dynamics driven by surface curvature. https://doi.org/10.1103/physreve.111.l022202

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