Competing local and global interactions in social dynamics: How important is the friendship network?

Jędrzejewski, Arkadiusz; Nowak, B.; Abramiuk, Angelika; Sznajd-Weron, Katarzyna

doi:10.1063/5.0004797

Cited by 10 publications

(24 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, recently it was proposed that the size of the source needed for conformity may not be the same as the size needed for anticonformity 7 . Such a generalization led to discontinuous phase transitions, which were not observed before within the q -voter model with anticonformity, neither on the complete graph 28 , 41 , nor on the random graph 29 .…”

Section: Modelmentioning

confidence: 69%

“…In the original model, the source of influence consists of q agents for both types of social response 19 , 29 , 41 . However, recently it was proposed that the size of the source needed for conformity may not be the same as the size needed for anticonformity 7 .…”

Section: Modelmentioning

confidence: 99%

“…In our case, an opinion change happens only if neighbors with opposite opinions are drawn in case of conformity or neighbors with matching opinions are selected in case of anticonformity. Therefore, as the total number of neighbors with opposite opinions is equal to the number of active links i of a given voter and the group of influence is chosen without repetition, the flipping probability takes the following form Thus, in the limit of an infinite graph, the time evolution of this model is defined by a system of differential equations: As always for the q -voter model, evolution equations ( 4 ) does not depend on the degree distribution P ( k ) but only on the average degree 26 , 29 . Hence, from now on we denote by k for brevity.…”

Section: Pair Approximationmentioning

confidence: 99%

“…Until recently, it seemed that in models of opinion dynamics, a type of nonconformity could also be a factor influencing the type of the phase transition. For example, in the case of the q -voter model 27 , the presence of independence (noise) was needed to induce discontinuous phase transitions and the anticonformity itself was not sufficient 26 , 28 , 29 . Analogous observation was done for the symmetrical threshold model 30 .…”

Section: Introductionmentioning

confidence: 99%

“…We decided on such a simple structure because in such a case the pair approximation (PA) should be more valid than for networks with a higher clustering coefficient 26 , 34 – 37 . However, to validate the analytical results, we conduct also Monte Carlo simulations, because it was reported recently that PA can give invalid results even on ER graphs if the mean degree of nodes is small and comparable with the size of the influence group q 10 , 29 , 38 . In such a case, the results can be wrong not only quantitatively, but even qualitatively, indicating discontinuous phase transitions, which are not observed in the computer simulations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Abramiuk-Szurlej

Lipiecki

Pawłowski

et al. 2021

Sci Rep

Self Cite

View full text Add to dashboard Cite

We study the binary q-voter model with generalized anticonformity on random Erdős–Rényi graphs. In such a model, two types of social responses, conformity and anticonformity, occur with complementary probabilities and the size of the source of influence $$q_c$$ q c in case of conformity is independent from the size of the source of influence $$q_a$$ q a in case of anticonformity. For $$q_c=q_a=q$$ q c = q a = q the model reduces to the original q-voter model with anticonformity. Previously, such a generalized model was studied only on the complete graph, which corresponds to the mean-field approach. It was shown that it can display discontinuous phase transitions for $$q_c \ge q_a + \Delta q$$ q c ≥ q a + Δ q , where $$\Delta q=4$$ Δ q = 4 for $$q_a \le 3$$ q a ≤ 3 and $$\Delta q=3$$ Δ q = 3 for $$q_a>3$$ q a > 3 . In this paper, we pose the question if discontinuous phase transitions survive on random graphs with an average node degree $$\langle k\rangle \le 150$$ ⟨ k ⟩ ≤ 150 observed empirically in social networks. Using the pair approximation, as well as Monte Carlo simulations, we show that discontinuous phase transitions indeed can survive, even for relatively small values of $$\langle k\rangle$$ ⟨ k ⟩ . Moreover, we show that for $$q_a < q_c - 1$$ q a < q c - 1 pair approximation results overlap the Monte Carlo ones. On the other hand, for $$q_a \ge q_c - 1$$ q a ≥ q c - 1 pair approximation gives qualitatively wrong results indicating discontinuous phase transitions neither observed in the simulations nor within the mean-field approach. Finally, we report an intriguing result showing that the difference between the spinodals obtained within the pair approximation and the mean-field approach follows a power law with respect to $$\langle k\rangle$$ ⟨ k ⟩ , as long as the pair approximation indicates correctly the type of the phase transition.

show abstract

Section: Modelmentioning

confidence: 69%

Section: Modelmentioning

confidence: 99%

Section: Pair Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Abramiuk-Szurlej

Lipiecki

Pawłowski

et al. 2021

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

Introduction to the chaos focus issue on the dynamics of social systems

Miguel

Toral

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

Nonlinear dynamical social and political prediction algorithm for city planning and public participation using the impulse pattern formulation

Bader,

Linke,

Gernert

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

A nonlinear-dynamical algorithm for city planning is proposed as an impulse pattern formulation (IPF) for predicting relevant parameters such as health, artistic freedom, or financial developments of different social or political stakeholders over the cause of a planning process. The IPF has already shown high predictive precision at low computational cost in musical instrument simulations, brain dynamics, and human–human interactions. The social and political IPF consists of three basic equations of system state developments, self-adaptation of stakeholders, two adaptive interactions, and external impact terms suitable for respective planning situations. Typical scenarios of stakeholder interactions and developments are modeled by adjusting a set of system parameters. These include stakeholder reaction to external input, enhanced system stability through self-adaptation, stakeholder convergence due to adaptive interaction, as well as complex dynamics in terms of fixed stakeholder impacts. A workflow for implementing the algorithm in real city planning scenarios is outlined. This workflow includes machine learning of a suitable set of parameters suggesting best-practice planning to aim at the desired development of the planning process and its output.

show abstract

Competing local and global interactions in social dynamics: How important is the friendship network?

Cited by 10 publications

References 43 publications

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Discontinuous phase transitions in the q-voter model with generalized anticonformity on random graphs

Introduction to the chaos focus issue on the dynamics of social systems

Nonlinear dynamical social and political prediction algorithm for city planning and public participation using the impulse pattern formulation

Contact Info

Product

Resources

About