Social dynamics models with time-varying influence
Social dynamics models with time-varying influence
复制标题
具有时变影响的社会动力学模型
DOI：
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发表时间：
2019
影响因子：
3.5
通讯作者：
N. Duteil
中科院分区：
文献类型：
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作者：
Sean T. McQuade;B. Piccoli;N. Duteil
本文介绍了一阶意见动态的增强模型，其中将影响力权重分配给每个代理。每个代理人对另一个代理人的意见的影响不仅与经典的相互作用函数成正比，而且与其权重成正比。权重随时间演变，其方程与意见的演变相耦合。我们发现，众所周知的条件收敛到共识，可以推广到这个框架。在有界支持的相互作用函数的情况下，我们表明，恒定的权重导致聚类的条件类似于经典模型。通过设定一个特定的权重动态，设计了四个具体的模型，然后研究了每个模型的意见收敛性和权重的演化。我们证明了不同的长期行为的存在，如出现一个单一的领导人和出现两个共同领导人。然后，我们通过数值模拟来说明它们。最后，提供了一个统计分析的速度收敛到共识和聚类行为的每个模型，连同比较与经典的意见动态与恒定的等权重。
This paper introduces an augmented model for first-order opinion dynamics, in which a weight of influence is attributed to each agent. Each agent’s influence on another agent’s opinion is then proportional not only to the classical interaction function, but also to its weight. The weights evolve in time and their equations are coupled with the opinions’ evolution. We show that the well-known conditions for convergence to consensus can be generalized to this framework. In the case of interaction functions with bounded support, we show that constant weights lead to clustering with conditions similar to those of the classical model. Four specific models are designed by prescribing a specific weight dynamics, then the convergence of the opinions and the evolution of the weights for each of them are studied. We prove the existence of different long-term behaviors, such as emergence of a single leader and emergence of two co-leaders. Then we illustrate them via numerical simulations. Last, a statistical analysis is provided for the speed of convergence to consensus and for the clustering behavior of each model, together with a comparison to the classical opinion dynamics with constant equal weights.