Watts threshold model (2002): Each node i has threshold τ_i (fraction of neighbors that must be active to trigger node i).
Complex contagion differs from simple: exposure frequency matters, not just any exposure.
Phase diagram: Cascades are possible only in a "vulnerable window" — neither too sparse (no clusters) nor too dense (nodes too hard to tip). Watts-Dodds (2007): heterogeneous thresholds collapse cascade window.