Consider the Lorenz Equations
Here, A, T, D are the variables (loosely related to atmospheric flow,
namely the amplitude of convective motion, the temperature difference between
ascending and descending currents, and the deviation
of vertical temperature from a linear profile),
and k, r, b are parameters. Consider the values
(1) For the parameter values above, what are the equilibria (analytic)?
(2) With initial data A=T=D=1, write a code to solve this system. Your method should be at least second order. What timesteps are reasonable? How does the choice effect the flow? You should plot A vs time, T vs time, D vs time, and also the phase planes T vs A and D vs A.
You should hand in a small write-up, including plots, by February 18.