A Computationally Bounded Test of Periodic and Aperiodic Forcing in the Forced Kuramoto–Sivashinsky Equation

Paper 14 in The Geometry of the Critical Line programme. We test the conjecture from Paper 13 that deterministic aperiodic spatial forcing suppresses steep-gradient formation in the forced Kuramoto–Sivashinsky (KS) equation, analogous to lock-in suppression in forced Kuramoto networks (Paper 11). Using pseudospectral simulations across nine forcing families and amplitudes F ∈ [0.5, 8.0], we obtain a robust negative result: periodic sinusoidal forcing produces the lowest time-averaged gradients, while aperiodic and random forcing preserve stronger steep-gradient activity. The contrast strengthens monotonically with forcing amplitude. Diagnostics reveal the mechanism. Periodic forcing imposes a coherent…