To describe and understand global cascades, a network-based threshold model has been proposed by Duncan J. Watts in 2002.
(see Global Cascades Condition) A phase transition phenomenon has been observed: when the network of interpersonal influences is sparse, the size of the cascades exhibits a power law distribution, the most highly connected nodes are critical in triggering cascades, and if the network is relatively dense, the distribution shows a bimodal form, in which nodes with average degree show more importance by serving as triggers.
[8] To derive the precise cascade condition in the original model, a generating function method could be applied.
The Global cascades occur when the average vulnerable cluster size ⟨n⟩ diverges[1] The equation could be interpreted as: When
, the clusters in the network is small and global cascades will not happen since the early adopters are isolated in the system, thus no enough momentum could be generated.
The Model considers a change of state of individuals in different systems which belongs to a larger class of contagion problems.