Folds and period-doublings.

The continuation of folds, for periodic orbits and rotations, and the continuation of period-doubling bifurcations require two free problem parameters plus the free period. Thus, one would normally set NICP=3. For example, in Run 6 of demo pen, where a locus of period-doubling bifurcations is computed for rotations, we have NICP=3, with PAR(2), PAR(3), and PAR(11) specified as free parameters. Note that one must set ISW=2 for computing such loci of special solutions. Also note that in the continuation of folds the principal continuation parameter must be the one with respect to which the fold was located.

Actually, one may set NICP=2, and only specify the problem parameters, as AUTO will automatically add the period. For example, in Run 3 of demo plp, where a locus of folds is computed for periodic orbits, we have NICP=2, with PAR(4) and PAR(1) specified as free parameters. However, in this case the period will not appear in the screen output and in the fort.7 output-file.

To continue a locus of folds or period-doublings with fixed period, simply set NICP=3 and specify three problem parameters, not including PAR(11).