Global stability, it basically means, this is a simple, you've seen the Duffing equation, let me get the generally noxious. We wrote the stuff and got till make a double Dotson there. And we have this Duffing's equations and basically here, you've got three equilibriums of these dynamical system. One of them here is stable so if you have small departures, you're good. But if you give really large departures and your state and rates exceed some neighborhood, you're going to go off and drive yourself to infinity, just mathematics. So that's a classic Duffing equation also used throughout in chaos dynamics, [INAUDIBLE], structural analysis as well. But that's an illustration. So here the area where you have stability would actually be this eyelid looking region around plus/minus one and everything within it. When we do arguments of stability though, you saw our definitions. We used an L2 bound. So very often we come up with the somewhat conservative thing. The best you would have is kind of this circle that just touches these lower and upper sides. But a missing these outer lobes essentially, right? So if you use an L2 norms to [INAUDIBLE] proof, you come up with a region that guarantees within this ball, I am going to converge. But the opposite doesn't is necessarily true. If you're outside the ball, you haven't proven that you will diverge. You just don't know, right? And that's a lot of these math arguments are one way but not both ways. One doesn't imply the other. So we have to kind of be very careful in how we do that. So if it's global stability, which is really what we hope for, then of course it doesn't matter, because then anything goes. Any arbitrary large error and this system within the mathematical assumptions will converge perfectly. So those are some of the key things we have. Linear, if you're stable, you're stable. You converge, you're globally converging. Non linear systems. There's layers of that. And the LAgrange stability is somewhat like marginal stability. So that's kind of a corollary if you want to think of it that way if that helps you. And we'll go from there. Maurice. >> So that is an example of not- >> This is not globally stable, this is only locally stable. Yes, so I'm showing the opposite example of what I'm labeling.