A bit of a soft question: When talking to beginning students in dynamics, I often use some intuitive examples to illustrate the idea of stable vs unstable equilibria. The classics are a pendulum hanging downwards vs balancing upwards, or a rock sitting in a valley vs a rock sitting on top of a hill. However recently a student asked me for an example that didn't involve the gravitational force, and I wasn't able to come up with a compelling intuitive example off the top of my head. Does anybody have any examples they could recommend? I think for teaching purposes, an example would be especially useful if it contained both a stable and an unstable equilibrium point, like in the pendulum example, but this isn't strictly necessary.
Thank you in advance!
Thanks for all of the responses - the examples from population biology (logistic model, SIR model) are perfect for my purposes.