Opinion dynamics with the increasing peer pressure and prejudice on the signed graph

  • Guang HeEmail author
  • Wenbing Zhang
  • Jing Liu
  • Haoyue Ruan
Original paper


In this paper, we propose the opinion dynamics model with the increasing peer pressure and the stubborn agents. Cooperation and competition between individuals are considered simultaneously in a social network. Similar to the signed DeGroot model, we adopt a weighted average update rule in our model. We derive conditions under which opinions converge to a fixed opinion distribution. In particular, we find conditions under which opinions reach consensus or polarization (bipartite consensus). Two examples are provided to illustrate the effectiveness of the obtained results.


Opinion dynamics Peer pressure Prejudice Bipartite consensus Signed graph 



This work was supported in part by the National Natural Science Foundation of China under grant 61703003, 61873294, 61873230, in part by the Research Fund for Distinguished Young Scholars of Anhui Province under grant 1908085J04, in part by the National Natural Science Foundation of Anhui under grant 1708085QA16, in part by the Top Talent Project of Department of Anhui Education under grant gxgwfx2018038, in part by the Top Talent Project of Anhui Polytechnic University under grant 2017BJRC012, 2018JQ01, 2016BJRC009.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment, Ministry of Education and School of Mathematics and PhysicsAnhui Polytechnic UniversityWuhuPeople’s Republic of China
  2. 2.Department of MathematicsYangzhou UniversityYangzhouPeople’s Republic of China
  3. 3.College of Information Science and TechnologyDonghua UniversityShanghaiPeople’s Republic of China
  4. 4.School of Mathematics and PhysicsAnhui Polytechnic UniversityWuhuPeople’s Republic of China

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