为了研究合作与竞争关系共存下的社交网络中的个体的表达意见与隐私意见的演化规律,并分析意见的收敛性情况,建立了合作-竞争关系下具有多领导者的观点动力学模型来描述个体表达意见和隐私意见的演化过程。在符号网络满足一定连通性的条件下,基于影响矩阵的随机性和非周期性,给出了个体表达意见与隐私意见收敛的充分条件。结果显示,当所考虑的网络结构平衡时,跟随者表达意见的演化受领导者意见的影响,且个体表达意见被隐私意见主导,最终趋于平衡点。最后,通过仿真实验,验证了所提模型的有效性。
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.
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