Resilience, Tipping Points, and Hysteresis

In the essay we introduce present-day systems concepts, such as resilience, tipping points, and hysteresis effects, via the concept of fast–slow dynamical systems (whether explicit in the models or implicit through bifurcation and stability behaviours). These lead naturally to ideas first propagated within catastrophe theory, fifty years ago. We discuss the historical catastrophe (the backlash) that befell such an abstract yet mathematically grounded (and thus inescapable) theory within economics and also its subsequent re-appraisal and re-adoption. Finally, we discuss some of the challenges inherent in anticipating tipping points from live systems data (observations), within systems-theoretic interpretations, and whether methods from topological data analysis might respond to them. While it is fashionable for national, governmental and policy institutions to speak of “resilience” in all manner of national systems contexts, we aver that it is foolishly inadequate to do so without an understanding and consideration of tipping points and hysteresis (sometimes termed “path dependence”), giving rise to “lock-in”.