1. Meteors. This one isn’t exactly right since the equilibrium point either happens or gets skipped over entirely but nonetheless...imagine a meteoroid flying through the solar system towards Earth. If it crosses into the atmosphere, it becomes a meteor. And then depending on the composition of the meteor and its size, it may burn up in the atmosphere or it may make it to the surface (at that point, it’s a meteorite).
   
   In this case, you can think of the “zone of attraction” as the entire journey to the atmosphere. Once it hits the atmosphere, it quickly is decelerated by air resistance. And if the meteor burns up, then its velocity “stabilizes” at 0. So “burned up in the atmosphere” is sort of like an equilibrium point. If it doesn’t burn up (e.g. because it’s larger), then it plummets to the surface. In this case, the other side of the equilibrium point is not really repulsive. Rather, it’s just a continuation of the pre-equilibrium point. And then when it hits the Earth the entire system is changed.
    
2. Nuclear Weapon Acquisition. You could argue the initial development of nuclear weapons triggered an “attractive force” for major world powers to stock up on warheads (e.g. an arms race). Eventually, the development and acquisition slowed down and even regressed (as in nuclear disarmament). But supplies were not totally eliminated. You could say an equilibrium point has been reached. The reasoning continues for the “repulsive force”: the equilibrium could be broken if any country were to deploy nuclear attacks on another. It would (probably?) lead to retaliatory strikes and the acquisition of warheads may accelerate drastically. (related: apparently the semistability of nuclear deterrence has a name! stability–instability paradox)
    
3. My Steam library on a weekend night. On weekend nights when I have nothing going on, I am attracted to my steam library. I often arrive at an equilibrium where I will sift through my games but don’t actually play anything. Then, I either decide against playing games, at which point I usually back away from the equilibrium point for the night. Or some “external force” nudges me into playing, in which case +4 hours of my night are gone.
   
   Unsurprisingly, friends-wanting-to-play-something-as-a-group is almost always enough to convince me to go past the point of no return. Similarly, I am also likely to break equilibrium if I am playing through a recently acquired game.

Again, I don’t think my first example is a true semistable equilibrium (neither the second example?) but maybe there’s something there. All in all, this was great. I just came across the Framing Practicum Sequences and love them! Thanks for the post AllAmericanBreakfast!

...now off to sift through some games :p