Reducibility of triadic percolation

Determine whether the triadic percolation process, in which a node activates or suppresses the link between two other nodes according to group-dependent dynamics, can be reproduced by an appropriate lower-order pairwise percolation model, particularly with respect to its time-dependent giant component, period doubling, and chaotic behavior.

Background

Triadic percolation differs from ordinary fixed-edge pairwise percolation because group interactions control whether edges exist, producing a time-dependent giant component and potentially period doubling and chaos. Fixed-edge pairwise percolation cannot generate a time-dependent giant component in the same way.

However, period doubling and chaos are generic nonlinear phenomena and therefore do not uniquely diagnose a higher-order mechanism. The review states that a definitive lower-order comparison is still lacking, especially because the triadic update depends on the global giant component rather than a local interaction rule.