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  • Letter
  • Open Access

Oscillatory and chaotic pattern dynamics driven by surface curvature

Ryosuke Nishide1,*,† and Shuji Ishihara1,2

  • *Contact author: ryosuke.nishide@nbi.ku.dk
  • †Present address: Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100, Denmark.
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Phys. Rev. E 111, L022202 – Published 18 February, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.L022202

Abstract

Patterns on curved surfaces are ubiquitous, yet the influence of surface geometry on pattern dynamics remains elusive. We recently reported a mechanism of pattern propagation in which a static pattern on a flat plane becomes a propagating pattern on a curved surface [Phys. Rev. Lett. 128, 224101 (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 theoretically determine the condition for the emergence of pattern dynamics on curved surfaces and show that oscillatory and chaotic pattern dynamics can emerge by controlling the surface shapes. These findings highlight a role of surface topography in pattern formation and dynamics.

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Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces

Ryosuke Nishide and Shuji Ishihara
Phys. Rev. E 111, 024208 (2025)

Article Text

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Outline

Information

Phys. Rev. E 111, L022202– Published 18 February, 2025
  • Received 4 March 2024
  • Revised 25 November 2024
  • Accepted 21 January 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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