  Rising interest in the resilience of ecological systems has spawned diverse
interpretations of the term's precise meaning. This paper classifies and
explores definitions of resilience from the ecological literature using a
dynamical systems framework. A model consisting of ordinary differential
equations is assumed to represent the ecological system. The question
"resilience of what to what?" posed by Carpenter et al. [2001] informs two
broad categories of definitions, based on resilience to state variable
perturbations and to parameter changes, respectively. Definitions of resilience
to state variable perturbations include measures of basin size (relevant to
one-time perturbations) and of basin steepness (relevant to repeated
perturbations). Resilience to parameter changes can be quantified by viewing
parameters as state variables, but could also take into account reversibility.
The dynamical systems viewpoint yields the following key insights: (i) system
properties that confer resistance to state variable perturbations can differ
from those that promote recovery from them, (ii) recovery rates, oft deemed the
purview of "engineering resilience," do matter for ecological resilience, and
(iii) resilience to repeated state variable perturbations correlates with
resilience to parameter changes due to the critical slowing down phenomenon.
