Emergent and divergent resilience behavior in catastrophic shift systems

Resilience in dynamic ecological systems has been intuitively associated with the ability to withstand disturbances in system drivers represented as shocks. Typically shocks are characterized as instantaneous, and isolated non-interacting events with the system dynamics corresponding to a fixed potential well. However, ecological systems are subject to continuous variation in environmental drivers such as rainfall, temperature, etc. and these interact with the ecosystem dynamics to alter the potential well. These variations are typically represented as a stochastic process. Furthermore, with climate change, the stochastic characteristics of the environmental drivers also change, thereby impacting the well dynamics. To characterize the resilience behavior under continuous variation in system drivers, and contrast it with that subject to instantaneous shock in system drivers, we employ the canonical catastrophic shift system as an example, and demonstrate emergent and contrasting divergent resilience behavior of the measures as the properties of the system-driver couple change. These behaviors include variability induced stabilization or enhancement of dynamic regimes, regions of sensitivity to dynamic regime transitions and existence of trap or escape regions. Furthermore, we introduce the concept of iso-resilience curves which are employed to design travel paths in resilience landscapes. These results provide valuable insights for managing resilience attributes associated with dynamic regime transitions in catastrophic shift systems under instantaneous shock and continuous variability in system drivers.