Fisher–KPP traveling wave: invasion front spreading through space
The Fisher–KPP equation ∂u/∂t = D∂²u/∂x² + ru(1−u) models gene waves, invasive species, and neural activity spreading. It always develops into a traveling front with minimum wave speed c* = 2√(rD). The Allee effect (cooperativity) creates a threshold below which populations collapse.