网络上的布尔延迟方程：在经济损失传播中的应用
Boolean delay equations on networks: An application to economic damage propagation
摘要：
我们介绍了基于布尔延迟方程的经济模型：这种形式主义更容易考虑到企业之间的相互作用的复杂性，特别适合于研究由于灾难造成的初始损害的传播。在这里，我们集中在简单的情况下，允许了解多个并发生产路径的影响，以及存在的随机性的路径时间长度或网络结构。在缺乏灵活性的情况下，具有多个连接的孤立网络中单个企业的生产缩短通常最终会获得有限部分的企业或整个经济，而与外部的相互作用允许活动的部分恢复，从而产生周期性的解决方案，其中损坏波在整个结构中传播。损伤扩展速度强烈依赖于拓扑结构。多个并发生产路径的存在并不一定意味着传播的减慢，传播可以像最短路径一样快。
英文摘要：
We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for studying the propagation of an initial damage due to a catastrophe. Here we concentrate on simple cases, which allow to understand the effects of multiple concurrent production paths as well as the presence of stochasticity in the path time lengths or in the network structure. In absence of flexibility, the shortening of production of a single firm in an isolated network with multiple connections usually ends up by attaining a finite fraction of the firms or the whole economy, whereas the interactions with the outside allow a partial recovering of the activity, giving rise to periodic solutions with waves of damage which propagate across the structure. The damage propagation speed is strongly dependent upon the topology. The existence of multiple concurrent production paths does not necessarily imply a slowing down of the propagation, which can be as fast as the shortest path.
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