Three types of outflow dynamics on square and triangular lattices and universal scaling

Kondrat, Grzegorz; Sznajd-Weron, Katarzyna

doi:10.1103/physreve.77.021127

Cited by 7 publications

(5 citation statements)

References 26 publications

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“…Other studies focused on the dynamics of clusters of agents with regular opinion patterns, ferromagnetic and/or antiferromagnetic (Schneider and Hirtreiter, 2005b), damage spreading (Klietsch, 2005;Roehner et al, 2004), the combination of Sznajd with other convincing strategies (Sousa and Sánchez, 2006), contrarian behavior (de la Lama et al, 2005;Wio et al, 2006), the effect on the dynamics of agents biased towards the global majority and/or minority opinion (Schneider, 2004;Schneider and Hirtreiter, 2005a). Recently extensions of Sznajd B to higher dimensions have been considered as well (Kondrat and Sznajd-Weron, 2008). …”

Section: E Sznajd Modelmentioning

confidence: 99%

Statistical physics of social dynamics

2009

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Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Here we review the state of the art by focusing on a wide list of topics ranging from opinion, cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, social spreading. We highlight the connections between these problems and other, more traditional, topics of statistical physics. We also emphasize the comparison of model results with empirical data from social systems.

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Section: E Sznajd Modelmentioning

confidence: 99%

Statistical physics of social dynamics

2009

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“…However, already for the two-dimensional square lattice, several versions have been proposed, e.g. in the so-called Stauffer generalization, the group consists of four agents [19], but in Galam’s and Kondrat’s generalizations it consists always of two agents, no matter the structure of a graph [27].…”

Section: The Basis Of the Modelmentioning

confidence: 99%

Conformity in numbers—Does criticality in social responses exist?

et al. 2018

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Within this paper we explore the idea of a critical value representing the proportion of majority members within a group that affects dramatic changes in influence targets’ conformity. We consider the threshold q-voter model when the responses of the Willis-Nail model, a well-established two-dimensional model of social response, are used as a foundation. Specifically, we study a generalized threshold q-voter model when all basic types of social response described by Willis-Nail model are considered, i.e. conformity, anticonformity, independence, and uniformity/congruence. These responses occur in our model with complementary probabilities. We introduce independently two thresholds: one needed for conformity, as well as a second one for anticonformity. In the case of conformity, at least r individuals among q neighbors have to share the same opinion in order to persuade a voter to follow majority’s opinion, whereas in the case of anticonformity, at least w individuals among q neighbors have to share the same opinion in order to influence voters to take an opinion that goes against that of their own reference group. We solve the model on a complete graph and show that the threshold for conformity significantly influences the results. For example, there is a critical threshold for conformity above which the system behaves as in the case of unanimity, i.e. displays continuous and discontinuous phase transitions. On the other hand, the threshold for anticonformity is almost irrelevant. We discuss our results from the perspective of theories of social psychology, as well as the philosophy of agent-based modeling.

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“…In fact, all these companies are located now much more closely to the SZG vertex than earlier, i.e. during the nucleation process [45][46][47] 2007-01-25 (cf. also our earlier considerations given in Refs.…”

Section: B Dominant Role Of the Szg Companymentioning

confidence: 99%

Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution

et al. 2015

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Abstract. We fill a void in merging empirical and phenomenological characterisation of the dynamical phase transitions in complex networks by identifying and thoroughly characterising a triple sequence of such transitions on a real-life financial market. We extract and interpret the empirical, numerical, and analytical evidences for the existence of these dynamical phase transitions, by considering the medium size Frankfurt stock exchange (FSE), as a typical example of a financial market. By using the canonical object for the graph theory, i.e. the minimal spanning tree (MST) network, we observe: (i) the (initial) dynamical phase transition from equilibrium to non-equilibrium nucleation phase of the MST network, occurring at some critical time. Coalescence of edges on the FSE's transient leader (defined by its largest degree) is observed within the nucleation phase; (ii) subsequent acceleration of the process of nucleation and the emergence of the condensation phase (the second dynamical phase transition), forming a logarithmically diverging temporal λ-peak of the leader's degree at the second critical time; (iii) the third dynamical fragmentation phase transition (after passing the second critical time), where the λ-peak logarithmically relaxes over three quarters of the year, resulting in a few loosely connected sub-graphs. This λ-peak (comparable to that of the specific heat vs. temperature forming during the equilibrium continuous phase transition from the normal fluid I 4 He to the superfluid II 4 He) is considered as a prominent result of a non-equilibrium superstar-like superhub or a dragon-king's abrupt evolution over about two and a half year of market evolution. We capture and meticulously characterise a remarkable phenomenon in which a peripheral company becomes progressively promoted to become the dragon-king strongly dominating the complex network over an exceptionally long period of time containing the crash. Detailed analysis of the complete trio of the dynamical phase transitions constituting the λ-peak allows us to derive a generic nonlinear constitutive equation of the dragon-king dynamics describing the complexity of the MST network by the corresponding inherent nonlinearity of the underlying dynamical processes.

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Three types of outflow dynamics on square and triangular lattices and universal scaling

Cited by 7 publications

References 26 publications

Statistical physics of social dynamics

Statistical physics of social dynamics

Conformity in numbers—Does criticality in social responses exist?

Temporal condensation and dynamic λ-transition within the complex network: an application to real-life market evolution

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