lrz : The Lorenz Equations.

This demo computes two symmetric homoclinic orbits in the Lorenz equations

$$\begin{array}{cl} u_1' &= p_3 (u_2 - u_1), \\ u_2' &= p_1 u_1 - u_2 - u_1 u_3, \\ u_3' &= u_1 u_2 - p_2 u_3. \\ \end{array}$$ (14.1)

Here $p_1$ is the free parameter, and $p_2=8/3$, $p_3=10$. The two homoclinic orbits correspond to the final, large period orbits on the two periodic solution families.

Table 14.1: Commands for running demo lrz.

AUTO -COMMAND	ACTION
! mkdir lrz	create an empty work directory
cd lrz	change directory
demo('lrz')	copy the demo files to the work directory
ld('lrz')	load the problem definition
run(c='lrz.1')	compute stationary solutions
sv('lrz')	save output-files as b.lrz, s.lrz, d.lrz
run(c='lrz.2',s='lrz')	compute periodic solutions; the final orbit is near-homoclinic. Constants changed : IPS, IRS, NICP, ICP, NMX, NPR, DS
ap('lrz')	append the output-files to b.lrz, s.lrz, d.lrz
run(c='lrz.3',s='lrz')	compute the symmetric periodic solution family. Constants changed : IRS
ap('lrz')	append the output-files to b.lrz, s.lrz, d.lrz