plp : Fold Continuation for Periodic Solutions.

This demo, which corresponds to computations in DoKeKe:91a DoKeKe:91a, shows how one can continue a fold on a family of periodic solution in two parameters. The calculation of a locus of Hopf bifurcations is also included. The equations, that model a one-compartment activator-inhibitor system (JPK:80 JPK:80), are given by

$$\begin{array}{cl} s' &= (s_{0} - s) - \rho R (s,a), \\ a' &=\alpha (a_{0} - a) - \rho R (s,a), \\ \end{array}$$ (14.8)

where

$$R(s,a)=\frac{s a}{1+s+ \kappa s^{2} }, \qquad \kappa > 0.$$

The free parameter is $\rho$. In the fold continuation $s_0$ is also free.

Table 14.14: Commands for running demo plp.

AUTO -COMMAND	ACTION
! mkdir plp	create an empty work directory
cd plp	change directory
demo('plp')	copy the demo files to the work directory
ld('plp')	load the problem definition
run(c='plp.1')	1st run; compute a stationary solution family and locate HBs
sv('plp')	save output-files as b.plp, s.plp, d.plp
run(c='plp.2',s='plp')	compute a family of periodic solutions and locate a fold. Constants changed : IPS, IRS, NMX
ap('plp')	append output-files to b.plp, s.plp, d.plp
run(c='plp.3',s='plp')	Compute a locus of Hopf bifurcation points. Constants changed : IPS, ICP, ISW, NMX, RL1
sv('2p')	save output-files as b.2p, s.2p, d.2p
run(c='plp.4',s='plp')	generate starting data for the fold continuation. Constants changed : IPS, IRS, ICP, NMX
sv('tmp')	save output-files as b.tmp, s.tmp, d.tmp
run(c='plp.5',s='tmp')	fold continuation; restart data from s.tmp. Constants changed : IRS, NUZR
ap('2p')	append output-files to b.2p, s.2p, d.2p
run(c='plp.6',s='2p')	compute an isola of periodic solutions; restart data from s.2p. Constants changed : IRS, ISW, NMX, NUZR
sv('iso')	save output-files as b.iso, s.iso, d.iso