Network Synchronization — Master Stability Function

Coupling σ: 0.10
Network:
RingCompleteSmall-worldRandom Nodes N: 12
Rebuild Network λ₂: — | λₙ: — | Synced: —

The Master Stability Function (MSF) Λ_max(κ) gives the max Lyapunov exponent for transverse perturbation modes. A network synchronizes when σ·λₖ falls in the stable region (Λ_max < 0) for ALL non-zero Laplacian eigenvalues λₖ. The MSF has a stability window [α₁,α₂]; synchronization requires α₁ < σ·λ₂ and σ·λₙ < α₂.