dx/dt = 10*(y - x)
dy/dt = r*x - y - x*z
dz/dt = -8*z/3 + x*y
where, r>0 is a parameter. Use MATLAB or some other program to
discuss the behavior of this system. (In MATLAB, you will need to use
ode23 to solve the system and plot3 to
display the results in a three dimensional phase plot.) Include in
your discussion the equilibrium (constant) solutions, and also the
bifurcation that occurs at r = 1. Make three dimensional
plots of the solutions, each for different initial values and for
r=0.5, r=1, r=10, r=30. The object that you see at about r=25 is the
Lorenz attractor. Keep the report to about three typed pages of prose,
and an additional two or three pages of plots. In your discussion,
think of writing a paper to be presented to people who know something
about differential equations, but who are not interested in all of the
technical details.
Due date: Tuesday, 1 May