Many websites about stability and resilience offer very confusing descriptions, and quite often, mix up the two concepts. In this blogpost, I want to give you a metaphor that will help you decide when to use the concept of stability and when to add resilience. Spoiler: it is not either or!

Stability tells you whether a system can recover from a perturbation. If it can, it is stable, if not, it is unstable.

Resilience tells you about the capacity of a system to recover from perturbations. If it can withstand large perturbations, it is more resilient, if it can withstand small perturbations, it is less resilient.

To illustrate, think of a ball dropped into a bowl (Figure, ball A). The ball will roll down the bowl and come to rest at the bottom of the bowl where it remains steady. To test for stability, we can perturb the system by shaking the bowl. Due to gravity, the ball will recover and return to the bottom of the bowl. Hence, the bottom of the bowl is stable.

Now think of a ball carefull balanced on top of a hill (Figure, ball B). Again, the ball will rest at the top of the hill and remain steady. To test for stability, we can perturb the system by shaking the bowl. This time, however, due to gravity, the ball will not recover and roll away from the top of the hill. Hence, the top of the hill is unstable.

To test for resilience, we can check how strongly we can shake the system before the balls do not return to their original positions. The stable position of ball A (bottom of the bowl) is obviously also resilient. This is inherent to every stable position, they are all resilient. However, they are not all equally resilient. Some bowls are deeper, requiring more shaking until the ball does not return to its equilibrium, and some bowls are flatter, requiring less shaking until the ball does not return to its equilibrium.

Contrary, the unstable position of ball B (top of the hill) is not resilient at all. This is inherent to every unstable position. In rare cases, it could make sense to ask how much "none-resilient" an unstable position is, but this is practically irrelvant and, perhaps, more a philosophical exercise.

In summary, resilience is a concept that can be added on top of the concept of stability. And, we typically only ask "how resilient" a stable position is, and not how "none-resilient" an unstable one is.

As a final example, let us look at the double-bowl system on the right of the figure above. The system has three steady ball positions (C, D, and E) at which the ball can remain if completely uninfluenced. Two of those steady positions are stable and also resilient (C and E), and one of those steady positions is unstable and not resilient (D). To verify this, we can shake the whole system, and find that the ball in position C requiers heavier shaking (stable and more resilient) than the ball in position E (stable and less resilient) until it cannot return to its original position (or stable state). In contrast, ball D is immediatly leaving its position after even the smallest amount of shaking (unstable and not resilient).