Pair approximation for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-voter model with independence on complex networks

Jędrzejewski, Arkadiusz

doi:10.1103/physreve.95.012307

Cited by 81 publications

(157 citation statements)

References 33 publications

Supporting

Mentioning

146

Contrasting

Order By: Relevance

“…Additionally, they allow for analytical treatment based on the mean-field approach, and are therefore often incorporated into analyses [3,5,8]. More complex structures are also investigated as underlying frameworks for the q-voter dynamics [10,42], but for simplicity, we consider only a fully connected graph. Interactions in the system are driven by three factors interpreted as different social responses: conformity, independence, and anticonformity [43].…”

Section: Model Descriptionmentioning

confidence: 99%

See 1 more Smart Citation

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

Jędrzejewski

Sznajd-Weron

2017

Entropy

Self Cite

View full text Add to dashboard Cite

Abstract:We study the q-voter model driven by stochastic noise arising from one out of two types of nonconformity: anticonformity or independence. We compare two approaches that were inspired by the famous psychological controversy known as the person-situation debate. We relate the person approach with the quenched disorder and the situation approach with the annealed disorder, and investigate how these two approaches influence order-disorder phase transitions observed in the q-voter model with noise. We show that under a quenched disorder, differences between models with independence and anticonformity are weaker and only quantitative. In contrast, annealing has a much more profound impact on the system and leads to qualitative differences between models on a macroscopic level. Furthermore, only under an annealed disorder may the discontinuous phase transitions appear. It seems that freezing the agents' behavior at the beginning of simulation-introducing quenched disorder-supports second-order phase transitions, whereas allowing agents to reverse their attitude in time-incorporating annealed disorder-supports discontinuous ones. We show that anticonformity is insensitive to the type of disorder, and in all cases it gives the same result. We precede our study with a short insight from statistical physics into annealed vs. quenched disorder and a brief review of these two approaches in models of opinion dynamics.

show abstract

Section: Model Descriptionmentioning

confidence: 99%

“…As a prime example of an opinion formation model, the q-voter dynamics has gained a great deal of attention in recent studies [5][6][7][8][9][10][11]. As a spreading mechanism, it finds many applications not only 1.…”

Section: Introductionmentioning

confidence: 99%

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

Jędrzejewski

Sznajd-Weron

2017

Entropy

Self Cite

View full text Add to dashboard Cite

show abstract

“…Second, the nonlinearity parameterq measures the effect of local group interactions. Nonlinearity is mathematically implemented as a k q i i ( ) [36,[38][39][40][41]. When q=1, our model becomes the ordinary coevolving linear voter model [34].…”

Section: Modelmentioning

confidence: 99%

“…Specifically, a coevolving nonlinear voter model (CNVM) has been studied in order to incorporate collective interactions and coevolution dynamics at the same time [36]. The nonlinearity in the CNVM takes into account that the state of an agent is affected by the state of all of their neighbors as a whole, and not by a pairwise interaction [38][39][40][41]. The nonlinear interaction gives rise to diverse phases, with different mechanisms for fragmentation transitions.…”

Section: Introductionmentioning

confidence: 99%

Multilayer coevolution dynamics of the nonlinear voter model

Min

Miguel

2019

New J. Phys.

View full text Add to dashboard Cite

We study a coevolving nonlinear voter model (CNVM) on a two-layer network. Coevolution stands for coupled dynamics of the state of the nodes and of the topology of the network in each layer. The plasticity parameter p measures the relative time scale of the evolution of the states of the nodes and the evolution of the network by link rewiring. Nonlinearity of the interactions is taken into account through a parameterq that describes the nonlinear effect of local majorities being q=1 the marginal situation of the ordinary voter model. Finally the connection between the two layers is measured by a degree of multiplexing ℓ. In terms of these three parameters,p, q and ℓ we find a rich phase diagram with different phases and transitions. When the two layers have the same plasticity p, the fragmentation transition observed in a single layer is shifted to larger values of p plasticity, so that multiplexing avoids fragmentation. Different plasticities for the two layers lead to new phases that do not exist in a CNVM in a single layer, namely an asymmetric fragmented phase for q>1 and an active shattered phase for q<1. Coupling layers with different types of nonlinearity, q 1 <1 and q 2 >1, we can find two different transitions by increasing the plasticity parameter, a first absorbing transition with no fragmentation and a subsequent fragmentation transition.

show abstract

“…The model we investigate here is not a social model, but it could be treated as such Nyczka and Sznajd-Weron [11]. In fact, the qneighbor Ising model Jȩdrzejewski et al [3], reformulated later in terms of the kinetic Ising model on random regular graph, has been inspired by the q-voter model of opinion dynamics [12][13][14][15]. This is not entirely clear what it the scale of opinion changes and definitely exploring how opinion dynamics will be influenced by the dynamics of a network is an interesting task.…”

Section: Introductionmentioning

confidence: 99%

Phase Transitions in the Kinetic Ising Model on the Temporal Directed Random Regular Graph

Marcjasz

Sznajd-Weron

2017

Front. Phys.

View full text Add to dashboard Cite

We investigate a kinetic Ising model with the Metropolis algorithm on the temporal directed random q-regular graph. We introduce a rewiring time τ as a parameter of the model and show that there is a critical τ = τ * above which the model exhibits continuous order-disorder phase transition and below which the transition is discontinuous. We discuss our findings in a light of the very recent results obtained for a generalized kinetic Ising model on quenched and annealed networks.

show abstract

Pair approximation for theq-voter model with independence on complex networks

Cited by 81 publications

References 33 publications

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

Person-Situation Debate Revisited: Phase Transitions with Quenched and Annealed Disorders

Multilayer coevolution dynamics of the nonlinear voter model

Phase Transitions in the Kinetic Ising Model on the Temporal Directed Random Regular Graph

Contact Info

Product

Resources

About