Impact of Energy on a Measurement of Resilience in the Management of Tipping Points for Complex Natural and Engineered Systems

Abstract

Because of societies’ dependence on systems that have increasing interconnectedness, governments and industries have increasing interest in managing the resilience of these systems and the risks associated with their disruption or failure. The identification and localization of tipping points in complex systems is essential in predicting system collapse but exceedingly difficult to estimate. At critical tipping-point thresholds, systems may transition from stable to unstable and potentially collapse. The energy content of a system, or the effective system energy, should influence the location and dynamics of tipping-point thresholds, similar to the effects of binding energy in molecular phase changes or chemical reactions. Herein, an equation is derived that relates tipping points with the effective system energy in complex systems using molecular orbital theory and a universal resilience index. This relationship is tested in case studies involving ecosystem collapse, supply-chain sustainability, and disruptive technology. The results show that the location of tipping points shift with effective system energy following the derived theory. These results provide a new method for accurately predicting the location of tipping points in all systems that can be modeled as networks. Finally, this research shows that the concept of binding energy can scale from molecular dynamics to the behavior of complex systems.