Convergence rate of the asymmetric Deffuant-Weisbuch dynamics

Zhang, Jiangbo; Chen, Ge

doi:10.1007/s11424-015-3240-z

Cited by 17 publications

(11 citation statements)

References 25 publications

(35 reference statements)

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“…Whereas with d = 0.5, as shown in Figure 2a, all individuals could interact with each other, smaller d values result in a decreased interaction behavior which influences the steady state. It was also observed that the number of the forming opinion clusters c for uniformly distributed initial opinion can be approximated as [2,12] c ≈ 1 2d (10) which is in good agreement with our simulation results. The shown qualitative as well as the quantitative results are well in agreement with the original publications of the DW model [5,6] as well as with the further model uses cited above.…”

Section: Uniform Initial Distributionsupporting

confidence: 90%

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Population Balance Modeling and Opinion Dynamics -- A Mutually Beneficial Liaison?

Kühn¹,

Kirse²,

Briesen³

2018

Preprint

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In this contribution, we aim to show that opinion dynamics and population balance modeling can benefit from an exchange of problems and methods. To support this claim, the Deffuant-Weisbuch model, a classical approach in opinion dynamics, is formulated as a population balance model. This new formulation is subsequently analyzed in terms of moment equations, and conservation of the first and second order moment is shown. Exemplary results obtained by our formulation are presented and agreement with the original model is found. Also the influence of the initial distribution is studied. Additionally, the Deffuant-Weisbuch model is transferred to engineering and interpreted as mass transfer between liquid droplets which results in a more flexible formulation compared to alternatives from the literature. On the one hand, it is concluded that the transfer of opinion-dynamics problems to the domain of population balance modeling offers some interesting insights as well as stimulating challenges for the population-balance community. On the other hand, it is inferred that population-balance methods can contribute to the solution of problems in opinion dynamics. In a broad outlook, some further possibilities of how the two fields can possibly benefit from a close interaction are outlined.

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Section: Uniform Initial Distributionsupporting

confidence: 90%

“…For example, the DW model was used and analyzed by Urbig et al [7]. Convergence analyses of different model variants were shown by Zhang and Hong [8], Zhang and Hong [9], and Zhang and Chen [10]. The DW model was even used as a basis for such unconventional applications as image segmentation [11].…”

Section: Introductionmentioning

confidence: 99%

Population Balance Modeling and Opinion Dynamics -- A Mutually Beneficial Liaison?

Kühn¹,

Kirse²,

Briesen³

2018

Preprint

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“…Current analysis results focus on the homogeneous case in which all the agents have the same confidence bound. The convergence of the homogeneous DW model has been proved in (Lorenz, 2005) and its convergence rate is established in (Zhang and Chen, 2015). Some research has considered also modified DW models.…”

Section: Introductionmentioning

confidence: 99%

Convergence properties of the heterogeneous Deffuant–Weisbuch model

Chen

Mei

et al. 2020

Automatica

Self Cite

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The Deffuant-Weisbuch (DW) model is a bounded-confidence opinion dynamics model that has attracted much recent interest. Despite its simplicity and appeal, the DW model has proved technically hard to analyze and its most basic convergence properties, easy to observe numerically, are only conjectures. This paper solves the convergence problem for the heterogeneous DW model. We establish that, for any positive confidence bounds and initial values, the opinion of each agent will converge to a limit value almost surely. Additionally, we show that the limiting opinions of any two agents either are the same or have a distance larger than the confidence bounds of the two agents. Moreover, we provide some sufficient conditions for the heterogeneous DW model to reach consensus. Finally, we show the mean-square convergence rate of the heterogeneous DW model is exponential.

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“…More complicated are "multi-choice" [216] extensions of (51), allowing an "active" agent i to interact with several neighbors. Lyapunov techniques allow to obtain some explicit estimates for the convergence rate of (50) and its asymmetric counterparts [217].…”

Section: The Deffuant-weisbuch Modelmentioning

confidence: 99%

A tutorial on modeling and analysis of dynamic social networks. Part II

Proskurnikov

Tempo

2018

Annual Reviews in Control

255

135

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Recent years have witnessed a significant trend towards filling the gap between Social Network Analysis (SNA) and control theory. This trend was enabled by the introduction of new mathematical models describing dynamics of social groups, the development of algorithms and software for data analysis and the tremendous progress in understanding complex networks and multi-agent systems (MAS) dynamics. The aim of this tutorial is to highlight a novel chapter of control theory, dealing with dynamic models of social networks and processes over them, to the attention of the broad research community. In its first part [1], we have considered the most classical models of social dynamics, which have anticipated and to a great extent inspired the recent extensive studies on MAS and complex networks. This paper is the second part of the tutorial, and it is focused on more recent models of social processes that have been developed concurrently with MAS theory. Future perspectives of control in social and techno-social systems are also discussed.touched by control theory, despite the long-term studies on social group dynamics [24][25][26] and "sociocybernetics" [27][28][29][30]. This gap between SNA and control can be explained, to a great extent, by the lack of dynamic models of social processes and mathematical armamentarium for their analysis. Focusing on topological properties of networks, SNA and network science have paid much less attention to dynamics over them, except for some special processes such as e.g. random walks, branching and queueing processes, percolation and contagion dynamics [19,20].The recent years have witnessed an important tendency towards filling the gap between SNA and control theory, enabled by the rapid progress in multiagent systems and dynamic networks. The emerging branch of control theory, studying social processes, is very young and even has no name yet. However, the interest of sociologists to this new area and understanding that "coordination and control of social systems is the foundational problem of sociology" [31] leaves no doubt that it should become a key instrument to examine social networks and dynamics over them. Without aiming to provide a exhaustive survey of "social control theory" at its dawn, this tutorial fo-

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Convergence rate of the asymmetric Deffuant-Weisbuch dynamics

Cited by 17 publications

References 25 publications

Population Balance Modeling and Opinion Dynamics -- A Mutually Beneficial Liaison?

Population Balance Modeling and Opinion Dynamics -- A Mutually Beneficial Liaison?

Convergence properties of the heterogeneous Deffuant–Weisbuch model

A tutorial on modeling and analysis of dynamic social networks. Part II

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