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We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find…
We search for conditions under which a characteristic time scale for ordering dynamics towards either of two absorbing states in a finite complex network of interactions does not exist. With this aim, we study random networks and networks…
We consider a modification of the voter model in which a set of interacting elements (agents) can be in either of two equivalent states (A or B) or in a third additional mixed AB state. The model is motivated by studies of language…
We consider the voter model dynamics in random networks with an arbitrary distribution of the degree of the nodes. We find that for the usual node-update dynamics the average magnetization is not conserved, while an average magnetization…
We investigate how the topology of small-world networks affects the dynamics of the voter model for opinion formation. We show that, contrary to what occurs on regular topologies with local interactions, the voter model on small-world…
We introduce a model for random-walking nodes on a periodic lattice, where the dynamic interaction network is defined from local interactions and E randomly-added long-range links. With periodic states for nodes and an interaction rule of…
In many real-world complex systems, the time-evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here, we study opinion formation and imitation on an adaptive complex network which is dependent on…
Non-reciprocal couplings are frequently found in systems out-of-equilibrium such as neuronal networks. We consider generalized Kuramoto models with non-reciprocal adaptive couplings. The non-reciprocity refers to the type of couplings…
We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state of the agent, so that the update…
We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model,…
The voter model rules are simple, with agents copying the state of a random neighbor, but they lead to non-trivial dynamics. Besides opinion processes, the model has also applications for catalysis and species competition. Inspired by the…
We consider two social consensus models, the AB-model and the Naming Game restricted to two conventions, which describe a population of interacting agents that can be in either of two equivalent states (A or B) or in a third mixed (AB)…
The dynamics of competing opinions in social network play an important role in society, with many applications in diverse social contexts as consensus, elections, morality and so on. Here we study a model of interacting agents connected in…
For the voter model, we study the effect of a memory-dependent transition rate. We assume that the transition of a spin into the opposite state decreases with the time it has been in its current state. Counter-intuitively, we find that the…
The voter model is a paradigm of ordering dynamics. At each time step, a random node is selected and copies the state of one of its neighbors. Traditionally, this state has been considered as a binary variable. Here, we relax this…
We study numerically the ordering process of two very simple dynamical models for a two-state variable on several topologies with increasing levels of heterogeneity in the degree distribution. We find that the zero-temperature Glauber…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
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…
We study the behavior of a generalized consensus dynamics on a temporal network of interactions, the activity driven network with attractiveness. In this temporal network model, agents are endowed with an intrinsic activity $a$, ruling the…
We study a binary dynamical process that is a representation of the voter model with opinion makers. The process models an election with two candidates but can also describe the frequencies of a biallelic gene in a population or atoms with…