Formal Measures of Dynamical Properties: Robustness and Sustainability

Robustness and its many related concepts (stability, resilience, reliability, sustainability, etc.) are essential to understanding and maintaining systems of all kinds: engineered systems, ecologies, political regimes, computer algorithms, economies, homeostatic organisms, and decision procedures to name a few. However the concepts in this family have not been generally and formally defined and, as a result, the terms' uses across these various applications are inconsistent and sometimes contradictory. As part of a larger research project encompassing several categories of dynamical properties this paper distinguishes among several different robustness-related concepts using formal and general definitions of each. In addition to providing conceptual clarity through rigorous mathematical definitions, the techniques can also be used as domain-agnostic measures of the included properties. To help realize the potential of complex systems models we need such measures to capture features of processes that exhibit feedback, nonlinearity, heterogeneity, and emergence. The paper finishes with several branches of future work involving applications of these measures, more new measures for complex systems, and establishing of equivalence classes for the dynamics of complex systems for behavior-based categorization.