Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization
Opinion Dynamics in Social Networks With Hostile Camps: Consensus vs. Polarization
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DOI：
10.1109/tac.2015.2471655
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发表时间：
2015-08
影响因子：
6.8
通讯作者：
A. Proskurnikov;A. Matveev;M. Cao
中科院分区：
文献类型：
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作者：
A. Proskurnikov;A. Matveev;M. Cao
大多数分布式多智能体协商协议都假定智能体之间是相互协作和信任的，因此智能体之间的耦合使它们的状态值更接近。然而，由于某些主体之间普遍存在的竞争和不信任，社会群体中的意见动力学需要超越这些传统模型，这种竞争和不信任通常具有排斥耦合的特征，并可能导致意见的聚集。最近，C.Altafini研究了静态符号图上的一阶共识算法，提出了一个既有吸引力又有排斥耦合的观点动力学模型。该协议建立模数共识，其中意见在模数上变得相同，但在符号上可能不同。本文将模一致性模型推广到网络拓扑为任意时变符号图的情况，并证明了在图的一致连通性的温和充分条件下达到模一致性。对于割平衡图，不仅给出了模一致的充分条件，而且给出了模一致的必要条件。
Most of the distributed protocols for multi-agent consensus assume that the agents are mutually cooperative and “trustful,” and so the couplings among the agents bring the values of their states closer. Opinion dynamics in social groups, however, require beyond these conventional models due to ubiquitous competition and distrust between some pairs of agents, which are usually characterized by repulsive couplings and may lead to clustering of the opinions. A simple yet insightful model of opinion dynamics with both attractive and repulsive couplings was proposed recently by C. Altafini, who examined first-order consensus algorithms over static signed graphs. This protocol establishes modulus consensus, where the opinions become the same in modulus but may differ in signs. In this paper, we extend the modulus consensus model to the case where the network topology is an arbitrary time-varying signed graph and prove reaching modulus consensus under mild sufficient conditions of uniform connectivity of the graph. For cut-balanced graphs, not only sufficient, but also necessary conditions for modulus consensus are given.