"By looking at Lyapunov functions and comparing it to some of our other models, like Markov processes and the Langton model, we begin to see how having multiple models in our heads enables us to understand some of the richness we see
"when you think about a model, when you think about a process like the Lyapunov process, right? Lyapunov functions. What you've got is, you can say, hey, there some cases like the case of chairs, a pure exchange market, this thing works
"We've got that, without externalities, or with only positive externalities in the case of finding a maximum, what you're gonna get is that, it's easy to construct a Lyapunov function, and boom, you get there. The system's gonna stop. But if there's
"What we learn is that it's at least possible to put a Lyapunov function on a process and have it stop at somewhere less than the optimal point. Doesn't have to stop at the optimal point, it could stop below. That's what
"Simple model is, there's a min, if the process moves, it goes down by some amount each time, therefore the process has to stop. We use that model to say, let's think about how a city organizes itself. " -Transcript from Scott
"In the theory of ordinary differential equations (ODEs), Lyapunov functions are scalar functions that may be used to prove the stability of an equilibrium of an ODE. Named after the Russian mathematician Aleksandr Mikhailovich Lyapunov, Lyapunov functions (also called the Lyapunov’s second