Jolien Kamphuis | Searcharxiv

arXiv2026

Microscopic Variability Alters Macroscopic Rotation Speed in Stochastic Spiral Waves

We present a general theory for noise-induced corrections to the angular velocity of spiral waves. Stochasticity produces two second-order effects: an instantaneous term from heterogeneity that always slows rotation, and an orbital-drift term from temporal fluctuations that can either accelerate or decelerate it. For our parameters, orbital drift is weaker, producing a net slowdown. Analytical predictions match Barkley-model simulations with temporal noise. Examination of additional noise types in silico confirms angular velocity slowing. This mechanism provides a robust route by which stochasticity reshapes spiral dynamics in excitable media, with direct implications for arrhythmias and neural wave propagation.

nlin.PS↗

arXiv2025

Pattern formation in a Swift-Hohenberg equation with spatially periodic coefficients

We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns whose leading order form is a Bloch wave modulated by solutions of a Ginzburg-Landau type equation. Since the interplay between forcing wavenumber and intrinsic wavenumber crucially shapes the spectrum and emerging patterns, we distinguish between resonant and non-resonant regimes. Extending earlier work that assumed asymptotically small coefficients, we tackle the more involved onset analysis produced by O(1) forcing and work directly in Bloch space, where the richer structure of the bifurcating solutions becomes apparent. This abstract framework is readily transferable to more complex systems, such as reaction-diffusion equations arising as dryland vegetation models, where topography induces spatial heterogeneity.

nlin.PS↗