Contents
clear all; close all; format compact; clear classes;
init
ndim=2; dir='hom2d';
p=[]; lx=pi; nx=25; par=[0.75; 1; 0.1; -1; 1];
p=cGLinit(p,lx,nx,par,ndim); p=setfn(p,dir); p.nc.mu1=1;
p.sw.bifcheck=2; p.nc.neig=10; p.sol.ds=0.1; p.sol.dsmax=0.2; p=cont(p,20);
first res=0
Problem directory name: hom2d
step lambda y-axis residual iter meth ds #-EV
0 got first point with lam=0.75, res=0
- now lam=0.76
1 got second point with lam=0.76, res=0
2 0.86004 0.000e+00 0.00e+00 0 nat 0.10000 0
3 1.00000 0.000e+00 0.00e+00 0 nat -0.06009 0
4 1.06011 0.000e+00 0.00e+00 0 nat 0.20000 0
- 1 possible bif between 1.06011 and 1.46026, om=0
mu_r=0.000103888, mu_i=-1
5 1.26136e+00 (HP, saved to hom2d/hpt1.mat) bisection steps 10, last ds 0.000195313
6 1.46026 0.000e+00 0.00e+00 0 nat 0.40000 0
- 1 possible bif between 1.46026 and 1.86041, om=0
mu_r=-0.199189, mu_i=-1 - no convergence
7 1.86041 0.000e+00 0.00e+00 0 nat 0.40000 2
- 1 possible bif between 1.86041 and 2.6607, om=0
mu_r=-0.000267582, mu_i=-1
8 2.03313e+00 (HP, saved to hom2d/hpt2.mat) bisection steps 10, last ds -0.000390625
9 2.66070 0.000e+00 0.00e+00 0 nat 0.80000 4
...
first 2 branches
para=4; ds=0.1; aux=[]; aux.tl=11; figure(2); clf;
for bnr=1:2
switch bnr
case 1; p=hoswibra('hom2d','hpt1',ds,para,'2db1',aux); nsteps=15;
case 2; p=hoswibra('hom2d','hpt2',ds,para,'2db2',aux); nsteps=10;
end
p.hopf.jac=1; p.nc.dsmax=0.4; p.hopf.xi=1e-3;
p.fuha.blss=@mbel; p.nc.mbw=2; p.hopf.ilss=0;
tic; p=cont(p,nsteps); toc
end
Problem directory name: 2db1
real(mu)=0.000103888, imag(mu)=1
lam=1.26136, om=1, NF-coeffis: dlam=-1, alpha=6.9282
arc.parametr, lambda-guess=1.26119
max|y-u0|=0.704542, res=0.00131438
step lambda y-axis res iter ds T nT
poor solve in mbel, |r|=0.0115898, b(end)=1, iterating ...it=1, |r|=3.27938e-09
1 1.25239 0.06336 2.535e-13 3 0.20000 6.50437 11 0.10251 -0.15369
2 1.20003 0.17034 3.535e-09 2 0.20000 6.54242 11 0.27423 -0.34411
3 1.12562 0.27235 6.045e-10 2 0.20000 6.61411 11 0.44019 -0.36455
poor solve in mbel, |r|=0.00179215, b(end)=1, iterating ...it=1, |r|=6.27654e-12
4 1.06865 0.37198 3.685e-10 2 0.20000 6.71828 11 0.58974 -0.16405
poor solve in mbel, |r|=26.5507, b(end)=1, iterating ...it=3, |r|=5.73646e-05
5 1.07177 0.47034 1.592e-13 3 0.20000 6.84675 11 0.65870 0.20657
poor solve in mbel, |r|=0.146009, b(end)=1, iterating ...it=1, |r|=1.06393e-05
6 1.14953 0.56193 8.976e-13 3 0.20000 6.97896 11 0.63635 0.54256
...
BD, L^2
bpcmp=9; figure(3); clf;
plotbraf('2db1','pt17',3,bpcmp,'cl','k');
plotbraf('2db2','pt11',3,bpcmp,'lab',10,'cl','b');
axis([1 2.6 0 1]); xlabel('r'); ylabel('||u||_*');
BD, T
bpcmp=6; figure(3); clf;
plotbraf('2db1','pt17',3,bpcmp,'cl','k');
plotbraf('2db2','pt11',3,bpcmp,'lab',10,'cl','b');
axis([1 2.3 6.33 7.5]); xlabel('r'); ylabel('T');
soln plot
aux=[]; aux.pstyle=3; aux.xtics=[-2 2]; aux.ytics=[-1 1];
hoplotf('2db2','pt10',1,1,aux);
lam=2.28492
stab-cmds
p=loadp('2db2','pt10'); hoplot(p,1,1); dir='stab2d';
p.u(1:p.nu)=p.hopf.y(1:p.nu,1); u0=p.u(1:p.nu); p=setfn(p,dir);
ts=[]; t0=0; npp=40; pmod=50; smod=5; tsmod=1; nc=0;
Problem directory name: stab2d
repeat if necessary ...
nt=400;
[p,t0,ts,nc]=hotintxs(p,u0,t0,ts,npp,nt,nc,tsmod,pmod,smod,@nodalf,1);
figure(4); clf; plot(ts(1,:), ts(2,:));
figure(5); clf; plot(ts(1,:), ts(3,:));
set(gca,'FontSize',p.plot.fs); axis tight; axis([0 10*p.hopf.T 0 3]);
xlabel('t'); ylabel('||u(t)-u_0||_{\infty}');
soln plot
dir='stab2d'; si=0; incr=80; nt=1*npp/smod; wnr=2; cmp=1; pstyle=2;
ind=si:incr:5*incr; lay=[2 3]; notic=1;
tintplot2d(dir,ind,wnr,cmp,pstyle,lay,notic);
movie
p=loadp('2db2','pt11'); aux.xtics=[-2 2]; aux.ytics=[-1 1];
mov=homov2d(p,1,1,aux); movie2avi(mov,'mcGL2d.avi');
