Related papers: Information cascade on networks and phase transiti…
In transportation networks, a spontaneous jamming transition is often observed, e.g in urban road networks and airport networks. Because of this instability, flow distribution is significantly imbalanced on a macroscopic level. To mitigate…
Studies have been made on the phase transition phenomena of an oscillator network model based on a standard Hebb learning rule like the Hopfield model. The relative phase informations---the in-phase and anti-phase, can be embedded in the…
The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyse the time to consensus for the voter model when the underlying graph is a subcritical scale-free random graph.…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
We introduce two models of consensus following a majority rule on time-evolving stochastic block models (SBM), in which the network evolution is Markovian or non-Markovian. Under the majority rule, in each round, each agent simultaneously…
The critical boundaries separating ordered from chaotic behavior in randomly wired S-state networks are calculated. These networks are a natural generalization of random Boolean nets and are proposed as on extended approach to genetic…
The Asymmetric BA model extends the Barab\'asi-Albert scale-free network model by introducing a parameter $\omega$. As $\omega$ varies, the model transitions through different network structures: an extended lattice at $\omega = -1$, a…
We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The…
The Watts-Strogatz algorithm of transferring the square lattice to a small world network is modified by introducing preferential rewiring constrained by connectivity demand. The evolution of the network is two-step: sequential preferential…
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…
Both quantum phase transitions and thermodynamic phase transitions are probably induced by fluctuations, yet the specific mechanism through which fluctuations cause phase transitions remains unclear in existing theories. This paper…
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…
A voting model (or a generalization of the Glauber model at zero temperature) on a multidimensional lattice is defined as a system composed of a lattice each site of which is either empty or occupied by a single particle. The reactions of…
Analytical results are presented for the structure of networks that evolve via a preferential-attachment-random-deletion (PARD) model in the regime of overall network growth and in the regime of overall contraction. The phase transition…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
We study simple interacting particle systems on heterogeneous networks, including the voter model and the invasion process. These are both two-state models in which in an update event an individual changes state to agree with a neighbor.…
Racism remains a persistent societal issue, increasingly amplified by the structure and dynamics of online social networks. In this work, we propose a three-state compartmental model to study the spreading and suppression of racist content,…
Social movements, neurons in the brain or even industrial suppliers are best described by agents evolving on networks with basic interaction rules. In these real systems, the connectivity between agents corresponds to the a critical state…
Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we…
The adaptive voter model is widely used to model opinion dynamics in social complex networks. However, existing adaptive voter models are limited to only pairwise interactions and fail to capture the intricate social dynamics that arises in…