tor : Detection of Torus Bifurcations.

  This demo uses a model in FrRLuGaPo:93 FrRLuGaPo:93 to illustrate the detection of a torus bifurcation. It also illustrates branch switching at a secondary periodic bifurcation with double Floquet multiplier at z=1. The computational results also include folds, homoclinic orbits, and period-doubling bifurcations. Their continuation is not illustrated here; see instead the demos plp, pp2, and pp3, respectively. The equations are

where , r=0.6, , and . Initially and .

 

COMMAND ACTION

mkdir tor create an empty work directory

cd tor change directory

@dm tor copy the demo files to the work directory

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

@r tor 1st run; compute a stationary solution branch with Hopf bifurcation

@sv 1 save output-files as p.1, q.1, d.1

cp r.tor.2 r.tor constants changed : IPS, IRS

@r tor 1 compute a branch of periodic solutions; restart from q.1

@ap 1 append output-files to p.1, q.1, d.1

cp r.tor.3 r.tor constants changed : IRS, ISW, NMX

@r tor 1 compute a bifurcating branch of periodic solutions; restart from q.1

@ap 1 append output-files to p.1, q.1, d.1