Network resilience Xueming Liua, Daqing Lib, Manqing Mac, Boleslaw K. Szymanskid, H Eugene Stanleye, Jianxi Gaof aKey Laboratory of Image Information Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China bSchool of Reliability and Systems Engineering, Beihang University, Beijing 100191, China cDepartment of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180; Network Science and Technology Center, Rensselaer Polytechnic Institute, Troy, NY 12180 dDepartment of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180; Network Science and Technology Center, Rensselaer Polytechnic Institute, Troy, NY 12180 eCenter for Polymer Studies, Department of Physics, Boston University, Boston, MA 02215; fDepartment of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180; Network Science and Technology Center, Rensselaer Polytechnic Institute, Troy, NY 12180 (e-mail:
[email protected]) Abstract Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a “tipping point,” such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system’s resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators.