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

$$\begin{array}{cl} x'(t) & = \bigr[ -(\beta+\nu)x + \beta y - ... ...(\beta + \gamma) y - z - b_3 (y-x)^3, \\ z'(t) &= y,\end{array}$$ (14.10)

where $\gamma=-0.6$, $r=0.6$, $a_3=0.328578$, and $b_3=0.933578$. Initially $\nu=-0.9$ and $\beta=0.5$.

Table 14.18: Commands for running demo tor.

AUTO -COMMAND	ACTION
! mkdir tor	create an empty work directory
cd tor	change directory
demo('tor')	copy the demo files to the work directory
ld('tor')	load the problem definition
run(c='tor.1')	1st run; compute a stationary solution family with Hopf bifurcation
sv('1')	save output-files as b.1, s.1, d.1
run(c='tor.2',s='1')	compute a family of periodic solutions; restart from s.1. Constants changed : IPS, IRS
ap('1')	append output-files to b.1, s.1, d.1
run(c='tor.3',s='1')	compute a bifurcating family of periodic solutions; restart from s.1. Constants changed : IRS, ISW, NMX
ap('1')	append output-files to b.1, s.1, d.1