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Convergence rate of the asymmetric Deffuant-Weisbuch dynamics

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Abstract

This paper considers the convergence rate of an asymmetric Deffuant-Weisbuch model.The model is composed by finite n interacting agents. In this model, agent i’s opinion is updated ateach time, by first selecting one randomly from n agents, and then combining the selected agent j’s opinion if the distance between j’s opinion and i’s opinion is not larger than the confidence radius ɛ0. This yields the endogenously changing inter-agent topologies. Based on the previous result that all agents opinions will converge almost surely for any initial states, the authors prove that the expected potential function of the convergence rate is upper bounded by a negative exponential function of time t when opinions reach consensus finally and is upper bounded by a negative power function of time t when opinions converge to several different limits.

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Authors and Affiliations

  1. The Faculty of Science, Southwest Petroleum University, Chengdu, 610500, China

    Jiangbo Zhang

  2. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ge Chen

Authors
  1. Jiangbo Zhang
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  2. Ge Chen
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Additional information

This research was supported by the Young Scholars Development Fund of Southwest Petroleum University(SWPU) under Grant No. 201499010050, the Scientific Research Starting Project of SWPU under Grant No.2014QHZ032, the National Natural Science Foundation of China under Grant No. 61203141, and the NationalKey Basic Research Program of China (973 Program) under Grant No. 2014CB845301/2/3.

This paper was recommended for publication by Editor HAN Jing.

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Zhang, J., Chen, G. Convergence rate of the asymmetric Deffuant-Weisbuch dynamics. J Syst Sci Complex 28, 773–787 (2015). https://doi.org/10.1007/s11424-015-3240-z

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  • DOI: https://doi.org/10.1007/s11424-015-3240-z

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