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We introduce a non-linear variant of the voter model, the q-voter model, in which q neighbors (with possible repetition) are consulted for a voter to change opinion. If the q neighbors agree, the voter takes their opinion; if they do not have an unanimous opinion, still a voter can flip its state with probability $epsilon$. We solve the model on a fully connected network (i.e. in mean-field) and compute the exit probability as well as the average time to reach consensus. We analyze the results in the perspective of a recently proposed Langevin equation aimed at describing generic phase transitions in systems with two ($Z_2$ symmetric) absorbing states. We find that in mean-field the q-voter model exhibits a disordered phase for high $epsilon$ and an ordered one for low $epsilon$ with three possible ways to go from one to the other: (i) a unique (generalized voter-like) transition, (ii) a series of two consecutive Ising-like and directed percolation transition, and (iii) a series of two transitions, including an intermediate regime in which the final state depends on initial conditions. This third (so far unexplored) scenario, in which a new type of ordering dynamics emerges, is rationalized and found to be specific of mean-field, i.e. fluctuations are explicitly shown to wash it out in spatially extended systems.
We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the
The voter model with memory-dependent dynamics is theoretically and numerically studied at the mean-field level. The `internal age, or time an individual spends holding the same state, is added to the set of binary states of the population, such that
We study memory dependent binary-state dynamics, focusing on the noisy-voter model. This is a non-Markovian process if we consider the set of binary states of the population as the description variables, or Markovian if we incorporate age, related to
We consider the process of reaching the final state in the coevolving voter model. There is a coevolution of state dynamics, where a node can copy a state from a random neighbor with probabilty $1-p$ and link dynamics, where a node can re-wire its li
We propose a generalized framework for the study of voter models in complex networks at the the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of furthe