Emergent Behaviors Over Signed Random Dynamical Networks: State-Flipping Model
Emergent Behaviors Over Signed Random Dynamical Networks: State-Flipping Model
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DOI：
10.1109/tcns.2014.2378915
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发表时间：
2014-10
影响因子：
4.2
通讯作者：
Guodong Shi;A. Proutière;M. Johansson;J. Baras;K. Johansson
中科院分区：
文献类型：
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作者：
Guodong Shi;A. Proutière;M. Johansson;J. Baras;K. Johansson
最近来自社会、生物和工程网络系统的研究引起了人们对签名网络上的动态的关注，其中每个链接都与表示信任/不信任、激活剂/抑制剂或安全/恶意交互的正/负符号相关联。我们研究的渐近动态模式，出现在一组节点之间的互动，在一个动态发展的签署随机网络。节点交互在一系列确定性符号图上随机发生。每个节点根据交互弧的符号从其邻居接收肯定或否定的建议，并相应地更新其状态。建议沿着一个积极的弧线遵循标准的共识更新。正如Altafini的工作一样，负面推荐使用邻居状态的符号翻转的更新。节点可以不同地加权积极和消极的建议，并引入随机过程来模拟节点对这些建议的时变注意力。建立了节点状态几乎处处收敛和发散的条件。我们表明，在这种所谓的状态翻转模型下，所有的链接有助于达成共识的绝对值的节点，即使在切换符号模式和动态变化的环境。一个无幸存者的性质，表明每个节点的状态几乎肯定发散，如果最大的网络状态发散。
Recent studies from social, biological, and engineering network systems have drawn attention to the dynamics over signed networks, where each link is associated with a positive/negative sign indicating trustful/mistrustful, activator/inhibitor, or secure/malicious interactions. We study asymptotic dynamical patterns that emerge among a set of nodes that interact in a dynamically evolving signed random network. Node interactions take place at random on a sequence of deterministic signed graphs. Each node receives positive or negative recommendations from its neighbors depending on the sign of the interaction arcs, and updates its state accordingly. Recommendations along a positive arc follow the standard consensus update. As in the work by Altafini, negative recommendations use an update where the sign of the neighbor state is flipped. Nodes may weight positive and negative recommendations differently, and random processes are introduced to model the time-varying attention that nodes pay to these recommendations. Conditions for almost sure convergence and divergence of the node states are established. We show that under this so-called state-flipping model, all links contribute to a consensus of the absolute values of the nodes, even under switching sign patterns and a dynamically changing environment. A no-survivor property is established, indicating that every node state diverges almost surely if the maximum network state diverges.