Plot of two-dimensional bifurcation diagram for minimal demo

This script requires to have minimal_demo.html, minimal_demo_stst_psol.html, minimal_demo_extra_psol.html, minimal_demo_extra_nmfm.html to have run beforehand.

(c) DDE-BIFTOOL v. 3.1.1(75), 31/12/2014

Contents

%#ok<*SAGROW>
figure(3);clf
hold on
get_par=@(x,i)arrayfun(@(y)y.parameter(i),x.point);

give super- and subcritical Hopf bifurcations different color

ih=0;
for i=1:length(hopfref)
    ih=ih+1;
    hopfcrit{ih}=hopfref{i};
    hopfcrit{ih}.point=hopfref{i}.point(1:ind_genh(i));
    ih=ih+1;
    hopfcrit{ih}=hopfref{i};
    hopfcrit{ih}.point=hopfref{i}.point(ind_genh(i):end);
end

bifurcations of periodic orbits

The solutions may switch to equilibria at degenerate points. So we remove solutions with zero amplitude

pobranches={pbranch,trbranch1,trbranch2};
amp=@(x)max(max(x.profile(1:2,:),[],2)-min(x.profile(1:2,:),[],2));
for i=1:length(pobranches)
    amps=arrayfun(amp,pobranches{i}.point);
    pobranches{i}.point=pobranches{i}.point(amps>1e-4);
end

Plot Codimension-1 bifurcations as curves

branches=[hopfcrit,pobranches];
colors='rmrmbkk';
pl=[];
for i=1:length(branches)
    pl(i)=plot(get_par(branches{i},indtau),get_par(branches{i},indb),...
        [colors(i),'.-'],'linewidth',2);
end
pl=pl([1:2,5:end-1]);
lgtext={'subcrit. Hopf','supercrit. Hopf','POFold','torus bif'};

Codimension-2 bifurcations along Hopf bifurcations

plotted as points in the two-parameter plane

for i=1:length(genh)
    plgenh=plot(genh{i}.parameter(indtau),genh{i}.parameter(indb),...
        'ks','linewidth',2);
end
pl(end+1)=plgenh;
lgtext{end+1}='generalized Hopf';
for i=1:length(hoho)
    plhoho=plot(hoho{i}.parameter(indtau),hoho{i}.parameter(indb),...
        'ko','linewidth',2);
end
pl(end+1)=plhoho;
lgtext{end+1}='Hopf-Hopf';
legend(pl,lgtext);
xlabel('tau');
ylabel('b');
axis([0,20,0,0.6]);
grid on
title('2d bif diagram of eqs and p.o''s in (tau,b)')

Published with MATLAB® 7.14