Aging in binary-state models: The Threshold model for complex contagion

We study the non-Markovian effects associated with aging for binary-state dynamics in complex networks. Aging is considered as the property of the agents to be less prone to change their state the longer they have been in the current state, which gives rise to heterogeneous activity patterns. In particular, we analyze aging in the Threshold model, which has been proposed to explain the process of adoption of new technologies. Our analytical approximations give a good description of extensive Monte Carlo simulations in Erdos-Renyi, random-regular and Barabasi-Albert networks. While aging does not modify the cascade condition, it slows down the cascade dynamics towards the full-adoption state: the exponential increase of adopters in time from the original model is replaced by a stretched exponential or power law, depending on the aging mechanism. Under several approximations, we give analytical expressions for the cascade condition and for the exponents of the adopters' density growth laws. Beyond random networks, we also describe by Monte Carlo simulations the effects of aging for the Threshold model in a two-dimensional lattice.

Automated summary

We investigated the non-Markovian effects of aging on binary-state dynamics in complex networks. Aging is defined as the tendency of agents to be less likely to change their state the longer they have been in the current state, resulting in heterogeneous activity patterns. We focused on the aging effects in the Threshold model, which is used to explain the adoption process of new technologies. Through analytical approximations and Monte Carlo simulations, we found that aging slows down the cascade dynamics towards the full-adoption state and alters the growth laws of adopters' density.