Ordering dynamics in the voter model with aging

We study theoretically and numerically the voter model with memory-dependent dynamics at the mean-field level. The “internal age”, related to the time an individual spends holding the same state, is added to the set of binary states of the population, such that the activation probability p_i for attempting a change of state has an explicit dependence on the internal age i. We derive a closed set of integro-differential equations describing the time evolution of the fraction of individuals with a given state and internal age, and from it we obtain analytical results characterizing the behavior of the system close to the absorbing states. In general, different internal age-dependent activation probabilities p_i have different effects on the dynamics. In the case of “aging”, i.e. p_i being a decreasing function of its argument i, either the system reaches consensus or it gets trapped in a frozen state, depending on whether the limiting value p_∞ is zero or positive, and on the rate at which p_i approaches p_∞. Moreover, when the system reaches consensus, the fraction x(t) of nodes not holding the consensus state may decay exponentially with time or as a power-law, depending again on the specific details of the functional form of p_i. https://www.sciencedirect.com/science/article/pii/S0378437119314219