Dynamics of social balance on networks: The emergence of multipolar societies

Pouya Manshour and Afshin Montakhab
Phys. Rev. E 104, 034303 – Published 9 September 2021

Abstract

Within the context of social balance theory, much attention has been paid to the attainment and stability of unipolar or bipolar societies. However, multipolar societies are commonplace in the real world, despite the fact that the mechanism of their emergence is much less explored. Here, we investigate the evolution of a society of interacting agents with friendly (positive) and enmity (negative) relations into a final stable multipolar state. Triads are assigned energy according to the degree of tension they impose on the network. Agents update their connections to decrease the total energy (tension) of the system, on average. Our approach is to consider a variable energy ε[0,1] for triads which are entirely made of negative relations. We show that the final state of the system depends on the initial density of the friendly links ρ0. For initial densities greater than an ε-dependent threshold ρ0c(ε), a unipolar (paradise) state is reached. However, for ρ0ρ0c(ε), multipolar and bipolar states can emerge. We observe that the number of stable final poles increases with decreasing ε where the first transition from bipolar to multipolar society occurs at ε*0.67. We end the paper by providing a mean-field calculation that provides an estimate for the critical (ε dependent) initial positive link density, which is consistent with our simulations.

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  • Received 7 July 2021
  • Accepted 31 August 2021

DOI:https://doi.org/10.1103/PhysRevE.104.034303

©2021 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsStatistical Physics & ThermodynamicsNetworks

Authors & Affiliations

Pouya Manshour1,2,* and Afshin Montakhab3

  • 1Physics Department, Persian Gulf University, Bushehr 75169, Iran
  • 2Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic
  • 3Physics Department, Shiraz University, Shiraz 71454, Iran

  • *manshour@pgu.ac.ir

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Vol. 104, Iss. 3 — September 2021

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