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تسجيل مستخدم جديدSeparate or perish - the coevolving voter model
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Recent generalization of the coevolving voter model (J. Toruniewska et al, PRE 96 (2017) 042306) is further generalized here, including spin-dependent probability of rewiring. Mean field results indicate that either the system splits into two separate networks with different spins, or one of spin orientation goes extinct. In both cases, the density of active links is equal to zero. The results are discussed in terms of homophily in social contacts.
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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
nk to another node of the same state with probability $p$. That exhibits an absorbing transition to a frozen phase above a critical value of rewiring probability. Our analytical and numerical studies show that in the active phase mean values of magnetization of nodes $n$ and links $m$ tend to the same value that depends on initial conditions. In a similar way mean degrees of spins up and spins down become equal. The system obeys a special statistical conservation law since a linear combination of both types magnetizations averaged over many realizations starting from the same initial conditions is a constant of motion: $Lambdaequiv (1-p)mu m(t)+pn(t) = const$, where $mu$ is the mean node degree. The final mean magnetization of nodes and links in the active phase is proportional to $Lambda$ while the final density of active links is a square function of $Lambda$. If the rewiring probability is above a critical value and the system separates into disconnected domains, then the values of nodes and links magnetizations are not the same and final mean degrees of spins up and spins down can be different.
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 unan
imous 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.
The voter model has been studied extensively as a paradigmatic opinion dynamics model. However, its ability for modeling real opinion dynamics has not been addressed. We introduce a noisy voter model (accounting for social influence) with agents recu
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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
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