Home assignment for the MINI-course by
E. Doedel (deadline: June 9, 2010)

The work below is based on the "r3b" demo, as distributed during the course.

1. Run the r3b.auto script and investigate the stability properties

of the families L1, H1, and V1, that are computed by this script.

(The Floquet multipliers can be found in the diagnostic files

d.L1, d.H1, and d.V1 .) Note that mu=0.063 in this demo.

Also compute the A1 family that connects the L1 and V1 families,

and investigate its stability properties. (See Page 222 of the

Lecture Notes for a basic bifurcation diagram.)

Compute a selection of other periodic solution families with mu=0.063.

For example, the V2 family can be computed as follows:

cp c.r3b.V1 c.r3b.V2

[ In c.r3b.V2 change the value of IRS from 2 to 4, and

look at the README file to see what is in s.start. ]

@R r3b V2 start

Note that various AUTO constants may need to be adjusted in such

new runs.

2. Compute some other unstable manifolds than those already computed by

H1a.auto, H1b.auto, L1a.auto, V1a.auto, and V1a.auto.

For example, after running H1a.auto, change the value of IRS from 4

to 6 in c.man.H1a.1 , and then run

@R man H1a.1 startH1a

The starting orbits in s.startH1a have different length, as can be seen

by plotting these orbits with the command

@r3b startH1a

The length of the starting orbits saved in s.startH1a can be set by making

appropriate changes in the last line of c.man.H1a.0 .

Various AUTO constants may need to be adjusted in such new runs. For example,

the value of NMX may need to be increased, and possibly NTST as well.

From your numerical experiments select the most interesting cases and present

these in detail with appropriate Figures and accompanying detailed descriptions.