Title: Oscillatory and chaotic pattern dynamics driven by surface curvature

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.