In real-world systems, one random failure or targeted attack may lead to the cascading destruction within a system, and even create the systemic collapse among multiple correlated ones. With the help of network science, modeling the cascade failure on complex networks has become a challenging topic. In this paper, we put forward an improved cascading model on two interdependent networks to further explore the impact of the specific detachment logic on the system collapse, where the distinct condition to leave the system for a pair of nodes exists on the two-layered networks. Meanwhile, once the detachment logic is satisfied, two different criteria are adopted to determine whether this pair of nodes will leave the interdependent networks. Through extensive numerical simulations, we analyze the effects of detachment logic, network topology, departure criteria and nodal coupling relationship between layers in detail. It is found that in our detachment logic, both criteria will render the whole system to exhibit the phenomenon of pseudo-steady state and sudden collapse. In particular, two critical thresholds to characterize the evolution of system crashing emerge, which is different from previous findings under other detachment logic conditions on two-layered networks. Current results are conducive to further understanding the crashing behaviors of interdependent networks and designing the more robust networked systems in practice.

中文翻译：

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两个相互依赖网络的碰撞行为建模与分析

在现实世界的系统中，一次随机故障或有针对性的攻击可能导致系统内部的级联破坏，甚至在多个相关系统之间造成系统崩溃。在网络科学的帮助下，对复杂网络上的级联故障进行建模已成为一个具有挑战性的课题。在本文中，我们在两个相互依赖的网络上提出了一种改进的级联模型，以进一步探索特定分离逻辑对系统崩溃的影响，其中两层网络上存在一对节点离开系统的不同条件. 同时，一旦满足分离逻辑，则采用两个不同的标准来确定这对节点是否会离开相互依赖的网络。通过广泛的数值模拟，我们分析了分离逻辑、网络拓扑、层间离开准则和节点耦合关系的详细说明。发现在我们的脱离逻辑中，这两个标准都会使整个系统呈现出伪稳态和突然崩溃的现象。特别是，出现了表征系统崩溃演变的两个关键阈值，这与之前在两层网络上的其他分离逻辑条件下的发现不同。目前的结果有利于进一步理解相互依赖的网络的崩溃行为，并在实践中设计出更健壮的网络系统。出现了两个表征系统崩溃演变的关键阈值，这与之前在两层网络上的其他分离逻辑条件下的发现不同。目前的结果有利于进一步理解相互依赖的网络的崩溃行为，并在实践中设计出更健壮的网络系统。出现了两个表征系统崩溃演变的关键阈值，这与之前在两层网络上的其他分离逻辑条件下的发现不同。目前的结果有利于进一步理解相互依赖的网络的崩溃行为，并在实践中设计出更健壮的网络系统。