Threshold cascade dynamics on coevolving networks

Abstract: 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.