Media Summary: Perhaps the most iconic model of chaotic dynamics is the eponymous system of Lorenz, who, in trying to model simple convection ... Let's simulate and see what happens. Oh dear. The Lorenz system is the classic model of continuous-time chaos. Let's briefly go over the model and where it comes from.
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Perhaps the most iconic model of chaotic dynamics is the eponymous system of Lorenz, who, in trying to model simple convection ... Let's simulate and see what happens. Oh dear. The Lorenz system is the classic model of continuous-time chaos. Let's briefly go over the model and where it comes from. The logistic map is a great example of how one transitions from simple to chaotic dynamics. In this case, there's a curious pattern ... Where do we go from here? Let's summarize what we know about the Lorenz system. We observe that the Lorenz system is chaotic... but what does that mean?
Let's build a language for chaotic dynamics by importing a key idea from Computer Science -- DFAs or deterministic finite ... By converting second order linear dynamics into first order planar systems, we can put all our linear algebraic tools to good use. Since we are looking for oscillatory phenomena in convection, I wonder if there isn't a Hopf bifurcation somewhere in the Lorenz ... Let's think about the challenges of raising livestock. Some people get very excited (perhaps a bit too much so) at the existence of deterministic chaotic dynamics. Let's avoid the hype ... Here's a classic -- the Henon map! It's chaotic! What's it good for? Hey, it's chaotic!
Let's bump things up a dimension and consider how chaotic dynamics are manifested in discrete-time
