A Continuous Threshold Model of Cascade Dynamics
A Continuous Threshold Model of Cascade Dynamics
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DOI：
10.1109/cdc40024.2019.9029844
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Yaofeng Desmond Zhong;Naomi Ehrich Leonard
中科院分区：
文献类型：
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作者：
Yaofeng Desmond Zhong;Naomi Ehrich Leonard
我们提出了一个连续阈值模型（CTM）的级联动态的网络与实时值的活动水平，不断变化的代理。该模型概括了文献中的线性阈值模型（LTM），其中代理变得活跃（采用创新），如果其活跃的邻居的分数高于阈值。与CTM，我们研究的影响级联的异质性阈值的网络组成的一个链的三个集群的代理，每个区分不同的阈值。当动力学通过分叉点时，系统对变化最敏感：如果分叉是超临界的，则响应将被包含，而如果分叉是亚临界的，则响应将是级联的。我们发现，有一个亚临界分岔，从而级联，在响应创新，如果有足够大的差距之间的阈值足够大的集群链的两端，否则的响应将被包含。
We present a continuous threshold model (CTM) of cascade dynamics for a network of agents with real-valued activity levels that change continuously in time. The model generalizes the linear threshold model (LTM) from the literature, where an agent becomes active (adopts an innovation) if the fraction of its neighbors that are active is above a threshold. With the CTM we study the influence on cascades of heterogeneity in thresholds for a network comprised of a chain of three clusters of agents, each distinguished by a different threshold. The system is most sensitive to change as the dynamics pass through a bifurcation point: if the bifurcation is supercritical the response will be contained, while if the bifurcation is subcritical the response will be a cascade. We show that there is a subcritical bifurcation, thus a cascade, in response to an innovation if there is a large enough disparity between the thresholds of sufficiently large clusters on either end of the chain; otherwise the response will be contained.