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dd2 : Fixed Points of a Discrete Dynamical System.

This demo illustrates the computation of a solution family and its bifurcating families for a discrete dynamical system. Also illustrated is the continuation of Naimark-Sacker (or Hopf) bifurcations The equations, a discrete predator-prey system, are

\begin{displaymath}\begin{array}{cl} u_1^{k+1} &=p_1 u_1^{k}(1-u_1^{k})-p_2u_1^{...
...},\\ u_2^{k+1}&=(1-p_3)u_2^{k}+p_2u_1^{k}u_2^{k}.\\ \end{array}\end{displaymath} (13.2)

In the first run $ p_1$ is free. In the second run, both $ p_1$ and $ p_2$ are free. The remaining equation parameter, $ p_3$, is fixed in both runs.


Table 13.2: Commands for running demo dd2.
AUTO -COMMAND ACTION
! mkdir dd2 create an empty work directory
cd dd2 change directory
demo('dd2') copy the demo files to the work directory
ld('dd2') load the problem definition
run(c='dd2.1') 1st run; fixed point solution branches
sv('dd2') save output-files as b.dd2, s.dd2, d.dd2
run(c='dd2.2',s='dd2') 2nd run; a locus of Naimark-Sacker bifurcations. Constants changed : IRS, ISW
sv('ns') save output-files as b.ns, s.ns, d.ns



next up previous contents
Next: AUTO Demos : Periodic Up: AUTO Demos : Fixed points. Previous: enz : Stationary Solutions   Contents
Gabriel Lord 2007-11-19