The previous chapter presents different views of resilience, starting from Holling’s conceptual definition of “ecological resilience”: the capacity of a system to absorb “disturbance and reorganize while undergoing change so as to still retain essentially the same function, structure, identity, and feedbacks” (Walker et al. 2004). In this chapter, we focus on operational, mathematically precise definitions of resilience. In the literature, the main mathematical definitions of resilience are based on dynamical systems theory, and more specifically on attractors and attraction basins (also related to ‘regime shifts’ presented in the previous chapter). We present these definitions in detail, and illustrate their utility on a relatively simple rangeland management model. Furthermore, we use the rangeland example to highlight some key limitations of attractor based definitions of resilience.