Resilience

If a system has alternative stable states, slowly changing conditions can make it increasingly vulnerable to collapse into the alternative state.
This typically happens in an invisible way, that is, without apparent effects on the state of the system. Such loss of resilience arises if the basin of attraction around the present
state shrinks, making it increasingly likely that some stochastic event will tip the system into an alternative basin of attraction. As an intuitive example, consider being in a canoe and leaning over to one side to see something under water. Leaning over too much may cause the canoe to capsize and end up in an alternative stable state, upside down. It is difficult to see the tipping point coming, as the position of the boat may change relatively little up until the critical point. Moreover, close to the tipping point, small disturbances such as waves can tip the balance.

Obviously, the ability to absorb perturbations without being pushed into an alternative basin of attraction is an important measure of the stability of a system. For this concept, Holling (1973) suggested using the term “resilience.” Unfortunately, this term is often also
used for another aspect of stability, namely, the return rate to equilibrium after a small perturbation, an aspect sometimes referred to as “engineering resilience”. We usually use the term “resilience” for the width of the basin of attraction and the term “recovery rate” for the return rate after a disturbance to equilibrium.