ab : A Programmed Demo.

This demo illustrates the computation of stationary solutions, Hopf bifurcations and periodic solutions. The equations, that model an A $\to$ B reaction, are those from URP:74 URP:74, namely

$$\begin{array}{cl} u_1 ' &= -u_1 + p_1 (1-u_1) e^{u_2}, \\ u_2 ' &= -u_2 + p_1 p_2 ( 1-u_1) e^{u_2} - p_3 u_2.\\ \end{array}$$ (12.2)

This demo is full scripted, see Table 12.6.

Table 12.6: Commands for running demo ab.

AUTO -COMMAND	ACTION
! mkdir ab	create an empty work directory
cd ab	change directory
demo('ab')	copy the demo files to the work directory
execfile('ab.auto')	run the demo

If you look at the file ab.auto you see that the script computes a stationary solution family for certain values of $p_2$, and that a periodic orbit family is computed for each Hopf bifurcation that was found in the stationary solution families.