schnak22cmds

 command templates for Schnakenberg on a large domain; run cell-by-cell;

0001 % command templates for Schnakenberg on a large domain; run cell-by-cell;
0002 clear all;f2=[]; t1=cputime; 
0003 spx=2; spy=2; nx=100;%means 2 spots in x direction and 2 spots in y direction
0004 df=0.99; %deformation factor
0005 f2=schnakinit(f2,spx,spy,nx,df);
0006 f2.parasw=2;f2.bifchecksw=2;f2.ds=-0.1;f2.nsteps=1; f2.lammin=0.75;
0007 f2.dsmin=1E-10;f2.smod=5;f2=cont(f2); % 1 initial step
0008 f2=findbif(f2,1); % find 1st, 2nd and 3nd bifurcation from homogen.branch
0009 f2=findbif(f2,1);
0010 f2=findbif(f2,1);
0011 f2.ineg=50;
0012 % cold hexagons
0013 c2=swibra('f2','bp3','c2'); %bifurcation of to the cold hexagons
0014 % suitable parameters for first step
0015 c2.pmod=20;c2.ds=-0.01;c2.dsmin=0.01;c2.nsteps=1;c2.amod=1;c2=pmcont(c2);
0016 % suitable parameters for further steps
0017 c2.ds=-0.1;c2.nsteps=200;c2=pmcont(c2);
0018 % hot hexagons
0019 load('c2/p5');h2=p;h2=setfn(h2);h2.bifchecksw=0;h2.ds=-h2.ds;% load a cold hexagon point and flip direction
0020 h2.dsmin=abs(h2.ds);h2=pmcont(h2);
0021 % up-stripes
0022 s2=swibra('f2','bp2','s2',-0.01);
0023 s2.nsteps=1;s2.bifchecksw=2;s2=pmcont(s2);
0024 s2.nsteps=200;s2.ds=-0.1;s2.dsmin=0.1;s2=pmcont(s2);
0025 % cold beans
0026 b2=swibra('s2','bp4','b2');b2.ds=0.01;b2.dsmax=0.02;b2.dsmin=0.02;
0027 b2.mst=10;b2.nsteps=10;b2=pmcont(b2);
0028 % further continue the homogen branch
0029 f2.nsteps=1000;
0030 f2=cont(f2);
0031 % down stripes
0032 ss2=swibra('f2','bp2','ss2',0.01);ss2.bifchecksw=2;ss2.nsteps=2;
0033 ss2=pmcont(ss2);ss2.nsteps=5;ss2.ds=0.1;ss2.dsmin=0.1;ss2=pmcont(ss2);
0034 % find bif. point on down stripe branch
0035 load('ss2/p32'); ss2=p; ss2=findbif(ss2,1); ss2=pmcont(ss2);
0036 % hot beans
0037 bb2=swibra('bif','bp1','bb2',0.01);bb2.dsmin=0.01;bb2.dsmax=0.01;
0038 bb2.nsteps=10;bb2=pmcont(bb2);
0039 t2=cputime-t1; fprintf('\nTotal time=%g\n',t2);
0040 %% bifurcation diagram
0041 figure(5); clf;ms=10;
0042 load('s2/p30');plotbra(p,5,2,'ms',ms,'lw',3, 'cl',[0 0.4 0],'lab',30,'labo',0,0.1);
0043 load('b2/p31');plotbra(p,5,2,'ms',ms,'lw',3, 'cl',[0.7 0 0.3],'lab',5,'labo',-0.15,0);
0044 load('bb2/p82');plotbra(p,5,1,'ms',ms,'lw',3, 'cl',[0 0.3 0.7],'lp',76,'lab',60,'labo',-0.15,0);
0045 load('c2/p37');plotbra(p,5,2,'ms',ms,'lw',3, 'cl',[0 0 1],'lab',25,'labo',0,0.3);
0046 load('ss2/p46');plotbra(p,5,1,'ms',ms,'lw',3, 'cl',[0 0.3 0],'lab',30,'labo',0,-.3);
0047 load('h2/p34');plotbra(p,5,1,'ms',ms,'lw',3, 'cl',[0.7 0 0],'lab',30,'labo',0,-0.3);
0048 load('f2/p18');plotbra(p,5,1,'ms',ms,'lw',3, 'cl',[0 0 0]);
0049 text(.7,5.5,'h2','Fontsize',20,'color',[0.7 0 0]);
0050 text(2.2,5.2,'bb2','Fontsize',20,'color',[0 0.3 0.7]);
0051 text(1.4,3.7,'ss2','Fontsize',20,'color',[0 0.3 0]);
0052 text(2.5,1.4,'s2','Fontsize',20,'color',[0 0.4 0]);
0053 text(2.5,0.5,'c2','Fontsize',20,'color',[0 0 1]);
0054 text(3.25,2.0,'b2','Fontsize',20,'color',[0.7 0 0.3]);
0055 text(2,2.3,'f2','Fontsize',20,'color',[0 0 0]);
0056 %% plot of solutions
0057 plotsolf('s2','p30',4,1,2);plotsolf('b2','p5',5,1,2);
0058 plotsolf('c2','p25',6,1,2);plotsolf('ss2','p30',7,1,2);
0059 plotsolf('h2','p30',9,1,2);plotsolf('bb2','p60',8,1,2);