Threshold cascade dynamics on coevolving networks

We study the coevolutionary dynamics of network topology and social complex contagion using
a threshold cascade model. Our coevolving threshold model incorporates two mechanisms: the
threshold mechanism for the spreading of a minority state such as a new opinion, idea, or innovation
and the network plasticity implemented as rewiring of links to cut the connections between nodes in
different states. Using numerical simulations and a mean-field theoretical analysis, we demonstrate
that the coevolutionary dynamics can significantly affect the cascades dynamics. The domain of
parameters, i.e., threshold and network mean degree, for which global cascades occur shrinks with
increasing network plasticity, indicating that the rewiring process suppresses the onset of global
cascades. We also found that during evolution, non-adopted nodes form denser connections, resulting
in a wider degree distribution and a non-monotonous dependence of cascades sizes with plasticity.