Network Synchronization & Master Stability

The Master Stability Function (Pecora-Carroll 1998) links network topology to synchronization: stability requires σλ₂ > α₁ and σλₙ < α₂. The eigenratio Q = λₙ/λ₂ measures synchronizability — smaller Q is better.

L = D - A | 0=λ₁≤λ₂≤...≤λₙ | Sync if σλ₂ > α₁ and σλₙ < α₂ | Q = λₙ/λ₂