Research Article Percolation Theories for Multipartite Networked Systems under Random Failures Qing Cai , 1 Sameer Alam , 1 Mahardhika Pratama , 2 and Zhen Wang 3 1 School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 2 School of Computer Science and Engineering, Nanyang Technological University, Singapore 3 School of Mechanical Engineering and Center for Optical Imagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi’an, China Correspondence should be addressed to Sameer Alam; sameeralam@ntu.edu.sg, Mahardhika Pratama; pratama@ieee.org, and Zhen Wang; w-zhen@nwpu.edu.cn Received 26 November 2019; Accepted 26 March 2020; Published 20 May 2020 Academic Editor: Chittaranjan Hens Copyright © 2020 Qing Cai et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Real-world complex systems inevitably suffer from perturbations. When some system components break down and trigger cascading failures on a system, the system will be out of control. In order to assess the tolerance of complex systems to per- turbations, an effective way is to model a system as a network composed of nodes and edges and then carry out network robustness analysis. Percolation theories have proven as one of the most effective ways for assessing the robustness of complex systems. However, existing percolation theories are mainly for multilayer or interdependent networked systems, while little attention is paid to complex systems that are modeled as multipartite networks. is paper fills this void by establishing the percolation theories for multipartite networked systems under random failures. To achieve this goal, this paper first establishes two network models to describe how cascading failures propagate on multipartite networks subject to random node failures. Afterward, this paper adopts the largest connected component concept to quantify the networks’ robustness. Finally, this paper develops the corresponding percolation theories based on the developed network models. Simulations on computer-generated multipartite networks demonstrate that the proposed percolation theories coincide quite well with the simulations. 1.Introduction It is universally acknowledged that complex systems are ubiquitous in our lives [1]. Complex systems like city transportation systems [2] and power supplier systems [3] are indispensable infrastructures to human life. In order to better understand complex systems so as to facilitate better service providing, an effective way is to model a complex system as a complex network composed of nodes and edges with the nodes denoting the system components and the edges representing the interactions between system com- ponents [4]. For example, a power grid system can be represented by a network in which a node denotes a power station and an edge denotes the transmission line between two stations. Complex network modeling and analysis have proven as a potent instrument for system control [5–7] and have received great popularity in the last two decades [8, 9]. Note that complex systems in reality will inevitably suffer from external and/or internal unpredictable perturbations which can trigger cascading failures wreaking havoc on system structures and functionalities [5, 10]. A dramatic event in history was the Italian blackout that happened in 2003 [11]. It had been reported that the blackout was triggered by the breakdown of several power lines caused by a storm. It was until the seminal work done in [11] that the science underlying the event had been disclosed from the perspective of network robustness analysis. Network ro- bustness analysis now has proven to be an effective approach to evaluating the robustness of complex systems so as to help prevent unseen system disasters [12–14]. Due to its Hindawi Complexity Volume 2020, Article ID 3974503, 12 pages https://doi.org/10.1155/2020/3974503