Network resilience

Many systems on our planet shift abruptly and irreversibly from the desired state to an undesired state when forced across a “tipping point”. Some examples are mass extinctions within ecosystems, cascading failures in infrastructure systems, and changes in human and animal social networks. The ability to avoid such regime shifts or to recover quickly from such a non-resilient state demonstrates a system's resilience; system resilience is a quality that enables a system to adjust its activities to retain its basic functionality when errors and failures occur. In the past 50 years, attention has been paid almost exclusively to low-dimensional systems; scholars have focused on the calibration of the resilience functions of such systems and the identification of indicators of early warning signals based on two to three connected components. In recent years, taking advantage of network theory and the availability of lavish real datasets, network scientists have begun to explore real-world complex networked multidimensional systems, as well as their resilience functions and early warning indicators. This report presents a comprehensive review of resilience functions and regime shifts in complex systems in domains such as ecology, biology, society, and infrastructure. The research approach includes empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also review the definitions of some ambiguous terms, including robustness, resilience, and stability.