Using AUTO-Commands.

  Next, with the commands in Table 8.5, we execute the first two runs of demo ab again, but now using the commands that one would normally use in an actual application. We still use the demo constants-files that were prepared in advance.

 

COMMAND ACTION

make clean reset the work directory

cp r.ab.1 r.ab get the first constants-file

@r ab compute a stationary solution branch with folds and Hopf bifurcation

@sv ab save output-files as p.ab, q.ab, d.ab

cp r.ab.2 r.ab get the second constants-file

@r ab compute a branch of periodic solutions from the Hopf point

@ap ab append the output-files to p.ab, q.ab, d.ab

 

It is instructive to look at the constants-files r.ab.1 and r.ab.2 used in the two runs above. The significance of each AUTO-constant set in these files can be found in Chapter 6. Note in particular the AUTO-constants that were changed between the two runs; see Table 8.6.

 

Constant Run 1 Run 2 Reason for Change

IPS 1 2 To compute periodic solutions in Run 2

IRS 0 4 To specify the Hopf bifurcation restart label

NICP 1 2 The second run has two free parameters

ICP 1 1, 11 To use and print PAR(1) and PAR(11) in Run 2

NMX 100 150 To allow more continuation steps in Run 2

NPR 100 30 To print output every 30 steps in Run 2

 

Actually, for periodic solutions, AUTO automatically adds PAR(11) (the period) as second parameter. However, for the period to be printed, one must specify the index 11 in the ICP list, as shown in Table 8.6.