Abstract：To investigate the evolutionary patterns of expressed and private opinions among individuals in social networks where cooperative and competitive relationships coexist, and to analyze the convergence properties of opinions, we establish a multi-leader opinion dynamics model under cooperative-competitive relationships to describe the evolution of both individuals' expressed and private opinions. By employing the randomness and aperiodicity of the influence matrix, we provide a sufficient condition for the convergence of individual expressed and private opinions, assuming the signed network satisfies specific connectivity conditions. The results demonstrate that in a balanced network structure, followers' expressed opinions are influenced by leaders' opinions, while private opinions ultimately guide the expressed opinions toward an equilibrium point. Simulation experiments further validate the effectiveness of the proposed model.
蔡丹妮, 张文兵, 吴光磊. 多领导影响下个体表达与隐私意见的动态分析[J]. 复杂系统与复杂性科学, 2026, 23(3): 73-79.
CAI Danni, ZHANG Wenbing, WU Guanglei. Dynamic Analysis of Individuals' Expressed and Private Opinions Under the Influence of Multi-leaders[J]. Complex Systems and Complexity Science, 2026, 23(3): 73-79.
[1] DONG Y C, ZHAN M, KOU G, et al. A survey on the fusion process in opinion dynamics[J]. Information Fusion, 2018, 43: 57-65. [2] 董艳萍, 任晓涛, 赵文虓. French-DeGroot社会网络模型的结构辨识与参数估计[J]. 控制理论与应用, 2019, 36(11): 1905-1911. DONG Y P, REN X T, ZHAO W X. Structure inference and parameter identification for French-DeGroot type of social networks[J]. Control Theory & Applications, 2019, 36(11): 1905-1911. [3] CHEN G, DUAN X M, FRIEDKIN N E, et al. Social power dynamics over switching and stochastic influence networks[J]. IEEE Transactions on Automatic Control, 2019, 64(2): 582-597. [4] 刘琪, 肖人彬. 观点动力学视角下基于意见领袖的网络舆情反转研究[J]. 复杂系统与复杂性科学, 2019, 16(1): 1-13. LIU Q, XIAO R B. An opinion dynamic approach to public opinion reversion with the guidance of opinion leaders[J]. Complex Systems and Complexity Science, 2019, 16(1): 1-13. [5] 闫晓雪, 纪志坚. 社交网络中多领导者观点的博弈建模分析[J]. 复杂系统与复杂性科学, 2023, 19(1): 20-26. YAN X X, JI Z J. Game modeling analysis of multi-leaders opinion in social network[J]. Complex Systems and Complexity Science, 2023, 19(1): 20-26. [6] DEGROOT M H. Reaching a consensus[J]. Journal of the American Statistical Association, 1974, 69(345): 118-121. [7] FRIEDKIN N E, JOHNSEN E C. Social influence networks and opinion change[J]. Advances in Group Processes, 1999, 16(1): 1-29. [8] HE G, SHEN Z W, HUANG T W, et al. Opinion dynamics with heterogeneous multiple interdependent topics on the signed social networks[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2023, 53(10): 6181-6193. [9] MENG D Y. Bipartite containment tracking of signed networks[J]. Automatica, 2017, 79: 282-289. [10] YE M B, LIU J, ANDERSON B. On the analysis of the DeGroot-Friedkin model with dynamic relative interaction matrices[J]. IFAC Papers Online, 2017, 50(1): 11902-11907. [11] TIAN Y, WANG L. Opinion dynamics in social networks with stubborn agents: An issue-based perspective[J]. Automatic, 2018, 96: 213-223. [12] YE M B, QIN Y Z, Govaert A, et al. An influence network model to study discrepancies in expressed and private opinions[J]. Automatica, 2019, 107: 371-381. [13] KURAN T. Private Truths, Public Lies: the Social Consequences of Preference Falsification[M]. Cambridge, USA: Harvard University Press, 1997. [14] HEGSELMANN R. Opinion dynamics and bounded confidence: models, analysis and simulation[J]. Journal of Artificial Societies and Social Simulation, 2002, 5(3): 34-38. [15] SHI L, CHENG Y H, SHAO J L, et al. Leader-follower opinion dynamics of signed social networks with asynchronous trust/distrust level evolution[J]. IEEE Transactions on Network Science and Engineering, 2022, 9(2): 495-509. [16] CAO L, LIU G P, ZHANG D L. A leader-follower formation strategy for networked multi-agent systems based on the PI predictive control method[C]. Proceedings of the 40th Chinese Control Conference. Shanghai, China: CAA, 2021. [17] ZACHARY WW. An information flow model for conflict and fission in small groups[J]. Journal of Anthropological Research, 1977, 33(4): 452-473. [18] DEFFUANT G, NEAU D, AMBLARD F, et al. Mixing beliefs among interaction agents[J]. Advances in Complex Systems, 2000, 3: 87-89. [19] MOTSCHO S, TAFMOR E. Heterophilious dynamics enhances consensus[J]. SIAM Review, 2014, 56(4): 577-612. [20] ALTAFINI C. Consensus problems on networkswith antagonistic interactions[J]. IEEE Transactions on Automatic Control, 2013, 58(4): 935-946. [21] SHAO J L, ZHENG W X, HUANG T Z, et al. On leader-follower consensus with switching topologies: an analysis inspired by pigeon hierarchies[J]. IEEE Transaction on Automatic Control, 2018, 63(10): 3588-3593. [22] 刘青松, 李明鹏, 柴利. 具有遗忘个体的社会网络多维观点动力学分析与应用[J]. 自动化学报, 2023, 49(10): 2201-2210. LIU Q S, LI M P, CHAI L. Analysis and application of multidimensional opinion dynamics on social networks with oblivion individuals[J]. Acta Automatica Sinica, 2023, 49(10): 2201-2210.
