Resilience of dynamical systems

Abstract Stability is among the most important concepts in dynamical systems. Local stability well-studied, whereas determining ‘global stability’ of a nonlinear system very challenging. Over last few decades, many different ideas have been developed to address this issue, primarily driven by concrete applications. In particular, several disciplines suggested web under headline ‘resilience’. Unfortunately, there are variants and explanations resilience, often, definitions left relatively vague, sometimes even deliberately. Yet, allow for structural development mathematical theory resilience that can be used across areas, one has ensure precise starting provide comparison measures. work, we systematic review relevant indicators context continuous systems, grouped according their features. The also generalised applicable any attractor. These steps more reliable, quantitatively comparable reproducible study Furthermore, develop new concept against certain nonautonomous perturbations demonstrate how naturally extend our framework. All finally compared via analysis classic scalar model from population dynamics show direct quantitative application-based comparisons an immediate consequence detailed analysis.