ppp : Continuation of Hopf Bifurcations.

This demo illustrates the continuation of Hopf bifurcations in a 3-dimensional predator prey model (Do:84 Do:84). This curve contain branch points, where one locus of Hopf points bifurcates from another locus of Hopf points. The equations are

$$\begin{array}{cl} u_1 ' &= u_1(1-u_1) - p_4 u_1 u_2 , \\ u_2 ... ...{-p_6 u_2}) \\ u_3 ' &= -p_3 u_3 + p_5 u_2 u_3 . \\ \end{array}$$ (14.7)

Here $p_2=1/4$, $p_3=1/2$, $p_4=3$, $p_5=3$, $p_6=5$, and $p_1$ is the free parameter. In the continuation of Hopf points the parameter $p_4$ is also free.

Table 14.13: Commands for running demo ppp.

AUTO -COMMAND	ACTION
! mkdir ppp	create an empty work directory
cd ppp	change directory
demo('ppp')	copy the demo files to the work directory
ld('ppp')	load the problem definition
run(c='ppp.1')	compute stationary solutions; detect Hopf bifurcations
sv('ppp')	save output-files as b.ppp, s.ppp, d.ppp
run(c='ppp.2',s='ppp')	compute a family of periodic solutions. Constants changed : IPS, IRS, ICP
ap('ppp')	append the output-files to b.ppp, s.ppp, d.ppp
run(c='ppp.3',s='ppp')	compute Hopf bifurcation curves
sv('hb')	save the output-files as b.hb, s.hb, d.hb