Abstract:
In this informal talk we will consider the concept of resilience and how to address it mathematically. In general, resilience means the ability of a system to recover function after a disturbance, and is associated with other concepts as stability, resistance, and tolerance. It applies to natural, biological, social and engineered systems. Modeling resilience is both urgent and challenging, specially in the presence of uncertainty. We will review some of the existing approaches both conceptually and technically and introduce a new technique for modeling and computing Resilience Through Adaptation. This approach uses linear response theory and applies to systems modeled by stochastic differential equations. Our aim is to quantify the process of resilience through adaptation after a structural disturbance to the parameters governing the dynamics of the system. We will discuss how this approach can be combined with efforts to make systems more resilient to risk.