Master Stability Function — Network Synchronization

The MSF λ_max(σ·λ_2,...,σ·λ_N) determines synchronizability: coupling σ times each Laplacian eigenvalue must lie in the stable region (MSF < 0). Different network topologies have different eigenvalue spectra — some synchronize, some don't.

Master Stability Function

Network Oscillators

Eigenvalue Spectra (σ·λ) for Each Network

Coupling σ

N nodes

MSF zero crossing α₁

MSF zero crossing α₂

Ring network

Random network

All-to-all

Star network