Previous studies have verified that the local-world mechanism can greatly affect the structural properties and dynamical processes occurring on isolated complex networks; however, the impact of local-world mechanism on structural vulnerability of interdependent systems is still not efficiently explored. Therefore, in this study, the joint influence of interdependence and local worlds on attack vulnerability of interdependent networks is addressed. First, a partially interdependent system model is proposed, consisting of two networks which are dependent on each other with different types of interdependence preference. In particular, each network evolves according to the local-world model with an adjustable parameter to control the size of local worlds during network evolution. Next, the cascading failure process induced by intentional attack on high-degree nodes is presented. Then, the responses of interdependent systems after cascading failures are investigated through large quantities of numerical simulations. The results show that the emergence of local worlds during network evolution plays an important role in the structural vulnerability of both single and interdependent networks; that is, networks with larger size of local worlds are found to be more vulnerable against attacks. Moreover, interdependent links make the entire system much more fragile, especially when the networks are with max–max assortative interdependence and the strength is enhanced. These results are beneficial to the deep understanding of the intrinsic connection between attack robustness and underlying structure of large-scale interdependent systems.

先前的研究已经证实，局部世界机制可以极大地影响孤立的复杂网络上发生的结构特性和动力学过程。然而，仍然没有有效地探索局部世界机制对相互依赖系统的结构脆弱性的影响。因此，在本研究中，研究了相互依存和局部世界对相互依存网络的攻击脆弱性的共同影响。首先，提出了一种部分相互依存的系统模型，该模型由两个相互依存，互不相同类型的网络组成。特别地，每个网络根据具有可调整参数的局部世界模型来演化，以在网络演化过程中控制局部世界的大小。下一个，提出了有意攻击高级节点导致的级联失效过程。然后，通过大量的数值模拟研究了级联故障后相互依赖的系统的响应。结果表明，网络演化过程中局部世界的出现在单个和相互依赖的网络的结构脆弱性中起着重要作用。也就是说，发现具有较大本地世界规模的网络更容易受到攻击。此外，相互依存的链接使整个系统更加脆弱，尤其是当网络具有最大-最大分类相互依存关系并且强度得到增强时。