The dog at the Burrow has a suspiciously regular patrol, during which he looks for food. If you give him food, he will lick your hand and wag his tail gratefully, before returning to the patrol.
If someone took him away in a car, he would not return to the route.
When I move my mouse, my monitor activates. If I do nothing for a while, it will go dark again.
If I set up a robot which constantly twitched the mouse, the monitor would not go dark, no matter how long I waited.
An elastic object, such as a rubber band, will hang such that the force of tension equals the force of gravity.
If I snap the band, it will not return to its original equilibrium.
The first one highlights a useful sub-frame of stable equilibrium: stable cycles (aka limit cycles). The equilibrium isn’t just one state, it’s a cycle of states. Perturb it, and eventually it goes back to the same cycle.
The dog at the Burrow has a suspiciously regular patrol, during which he looks for food. If you give him food, he will lick your hand and wag his tail gratefully, before returning to the patrol.
If someone took him away in a car, he would not return to the route.
When I move my mouse, my monitor activates. If I do nothing for a while, it will go dark again.
If I set up a robot which constantly twitched the mouse, the monitor would not go dark, no matter how long I waited.
An elastic object, such as a rubber band, will hang such that the force of tension equals the force of gravity.
If I snap the band, it will not return to its original equilibrium.
The first one highlights a useful sub-frame of stable equilibrium: stable cycles (aka limit cycles). The equilibrium isn’t just one state, it’s a cycle of states. Perturb it, and eventually it goes back to the same cycle.