Brain Spiral Waves and Cortical Curvature

Recent evidence points to the role of spiral waves and geometry in brain function such as cognition. To probe this interplay, we employ analytical theory and numerical simulations of the complex Ginzburg-Landau equation. Our results reveal that surface curvature fundamentally alters spiral behavior: while spirals remain stationary on uniformly curved surfaces, spatially varying curvature drives rich dynamics including orbital motion, ballistic trajectories, and localization. We analyze the geometric mechanisms underlying these effects and discuss implications for spiral-wave dynamics on complex biological surfaces such as brain tissue, where surface geometry could act as a mechanism for localizing and clustering defects.