Fisher-KPP equation:
∂u/∂t = D∂²u/∂x² + f(u)
f(u) = ru(1−u) (logistic)
Minimum wave speed:
c* = 2√(Dr)
Selected for steep IC
Profile: exponential front
ξ > 0: u ~ e^(−λξ)
λ = (c − √(c²−4Dr)) / 2D
Extensions:
• Bistable: u(1−u)(u−a)
• Monostable: f(u) > 0
• Excitable: FitzHugh-Nagumo
∂u/∂t = D∂²u/∂x² + f(u)
f(u) = ru(1−u) (logistic)
Minimum wave speed:
c* = 2√(Dr)
Selected for steep IC
Profile: exponential front
ξ > 0: u ~ e^(−λξ)
λ = (c − √(c²−4Dr)) / 2D
Extensions:
• Bistable: u(1−u)(u−a)
• Monostable: f(u) > 0
• Excitable: FitzHugh-Nagumo
0.50
1.00
10
Fisher
8
c* = 0 | measured c = 0