Network Synchronization & Master Stability Function

Coupled oscillators · Laplacian spectrum · Synchronizability ratio λ_N/λ_2

Network topology — colored by oscillator phase

Master Stability Function Λ(α) — sync iff Λ<0 for α∈[ε·λ₂, ε·λ_N]

Oscillator phases over time

Laplacian eigenvalue spectrum

Parameters

λ₂ (algebraic conn.):
λ_N (max eigenval):
Ratio λ_N/λ_2:
Sync criterion:
Order param R:
Synchrony:
Pecora–Carroll MSF: Network synchronizes iff Master Stability Function Λ(αλ_k)<0 for all k=2..N. Ratio λ_N/λ_2 measures synchronizability — smaller is easier to sync.