Contagion in simplicial complexes

The propagation of information in social, biological and technological systems represents a crucial component their dynamic behavior. When limited to pairwise interactions, rather firm grip is available on the relevant parameters critical transitions these spreading processes, most notably pandemic transition, which indicates conditions for spread cover large fraction network. challenge that, many applications, driven by higher order relationships, several components undergo group interaction. To address this, we analyze dynamics simplicial complex environment, designed capture coexistence interactions different orders. We find while play key role initial stages spread, once it gains coverage, simplices take over drive contagion dynamics. result distinctive phase diagram, exhibiting discontinuous hence offering qualitative departure from traditional network