schnak11demo

 demo-script for Schnakenberg on a small domain

0001 % demo-script for Schnakenberg on a small domain
0002 clear all; f=[]; t1=cputime; 
0003 fprintf('Initializing Schnakenberg on a small domain \n'); 
0004 spx=1; spy=1; nx=30; % 1 spot in x direction and 1 spot in y direction
0005 df=0.97; % deformation factor
0006 f=schnakinit(f,spx,spy,nx,df);
0007 f.parasw=2;f.bifchecksw=2;f.dsmin=0.01;f.ds=-0.1;f.nsteps=1; f.lammin=1.5; 
0008 f=cont(f); % 1 initial step
0009 fprintf('Using findbif to locate first 2 bifurcations from homog.branch \n');
0010 f=findbif(f,1); % find 1st and 2nd bifurcation from homogen.branch
0011 f=findbif(f,1);
0012 fprintf('Swibra to cold hexagons\n'); 
0013 c=swibra('f','bp2','c', 0.08);  
0014 % suitable parameters for first step
0015 c.dsmin=0.08;c.bifchecksw=0;c.mst=1;c.amod=1;c=pmcont(c); 
0016 % suitable parameters for further steps
0017 c.ds=0.1;c.dsmin=0.1;c.mst=10;c.imax=10;c.nsteps=100;c=pmcont(c);
0018 fprintf('Hot hexagons by loading cold hexagon and flip direction\n'); 
0019 load('c/p2');h=p;h=setfn(h);h.ds=-h.ds; 
0020 h.mst=2;h.dsmin=abs(h.ds);h.nsteps=2;h=pmcont(h);
0021 % suitable parameters for further cont:
0022 h.resfac=1E-7; % needed to avoid branch-switching!
0023 h.ds=-0.1;h.dsmin=0.1;h.mst=10;h.nsteps=100;
0024 h=pmcont(h);
0025 fprintf('Swibra to stripes, one direction\n'); 
0026 s=swibra('f','bp1','s', 0.01); 
0027 s.amod=1;s.nsteps=1;s.bifchecksw=2;s=pmcont(s);
0028 s.ds=0.1; s.nsteps=200; s=pmcont(s);
0029 fprintf('Swibra to stripes, other direction\n'); 
0030 ss=swibra('f','bp1','ss', -0.01); ss.amod=1;
0031 ss.nsteps=1; ss.bifchecksw=2; ss=pmcont(ss);
0032 ss.ds=-0.1;  ss.dsmax=0.1;ss.nsteps=20; ss.lammin=1.5; ss=pmcont(ss);
0033 fprintf('Swibra to cold beans, other direction\n'); 
0034 b=swibra('s','bp2','b',0.05);
0035 b.amod=1;b.mst=4;b.dsmin=0.05;b.nsteps=4;b=pmcont(b);
0036 fprintf('Swibra to hot beans, other direction\n'); 
0037 bb=swibra('ss','bp2','bb',0.05);
0038 bb.amod=1;bb.mst=4;bb.dsmin=0.05;bb.nsteps=4;bb=pmcont(bb);
0039 fprintf('Further continuation of the homogeneous branch\n');
0040 f.nsteps=20; f=cont(f);
0041 t2=cputime-t1; fprintf('\nTotal time=%g\n',t2);
0042 % -----------------------------------------------------------------
0043 fprintf('Plot bifurcation diagram\n'); 
0044 figure(5); clf; ms=10; 
0045 plotbraf('s','p29',5,2,'ms',ms,'lw',3,'cl',[0 0.4 0],'lab',30); 
0046 plotbraf('b','p10',5,2,'ms',ms,'lw',3,'cl',[0.7 0 0.3],'lp',9,'lab',5); 
0047 plotbraf('c','p26',5,2,'ms',ms,'lw',3, 'cl',[0 0 1],'lab',25); 
0048 plotbraf('ss','p41',5,1,'ms',ms,'lw',3, 'cl',[0 0.3 0],'lab',50); 
0049 plotbraf('h','p28',5,1,'ms',ms,'lw',3, 'cl',[0.7 0 0],'lab',30); 
0050 plotbraf('bb','p17',5,1,'ms',ms,'lw',3, 'cl',[0.3 0 0.7],'lp',14,'lab',10); 
0051 plotbraf('f','p13',5,1,'ms',ms,'lw',3, 'cl',[0 0 0]);
0052 text(1.5,6,'h','Fontsize',20,'color',[0.7 0 0]);
0053 text(2.4,5.2,'bb','Fontsize',20,'color',[0.3 0 0.7]);
0054 text(1.4,3.7,'ss','Fontsize',20,'color',[0 0.3 0]);
0055 text(2.5,1.2,'s','Fontsize',20,'color',[0 0.4 0]);
0056 text(2.5,0.5,'c','Fontsize',20,'color',[0 0 1]);
0057 text(3.25,2.0,'b','Fontsize',20,'color',[0.7 0 0.3]);
0058 text(2,2.3,'f','Fontsize',20,'color',[0 0 0]);
0059 % -----------------------------------------------------------------
0060 fprintf('Plot of some solutions\n'); 
0061 plotsolf('s','p29',4,1,2);
0062 plotsolf('b','p5',5,1,2);
0063 plotsolf('c','p25',6,1,2);
0064 plotsolf('ss','p41',7,1,2);
0065 plotsolf('h','p28',8,1,2);
0066 plotsolf('bb','p10',9,1,2);
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