% plotBEModeCurves
b=1; % basal branching rate
% The parameter E giving the dependence of branch rate on the number of terminal segments will varied
scrsz = get(0,'ScreenSize');
figure(1)
set(gcf,'Position',[1, 1 , scrsz(4) , scrsz(4) ])
clf
hold on
nplotrange=1:5:101;
for E=0:0.25:1
% Calculate numerical solutions
[T,Y,mun,sigman,validPoints]=cBEModel(b,E);
% Plot top row: temporal development for the probabilities $p(n,t)$ for
% $n=1,6,11,...,101$ and three different values of $E$: $E=0$ (left),
% $E=\frac{1}{2}$ (middle) and $E=1$ (right) in all cases lower
% $n$-values lead to earlier $p(n,t)$-peaks, while late peaking traces
% might peak outside the window shown.
subplot(3,3,1)
if(E==0)
plot(T(validPoints),Y(validPoints,nplotrange))
end
axis([0,4,0,0.2])
subplot(3,3,2)
if(E==0.5)
plot(T(validPoints),Y(validPoints,nplotrange))
end
axis([0,25,0,0.2])
subplot(3,3,3)
if(E==1)
plot(T(validPoints),Y(validPoints,nplotrange))
end
axis([0,25,0,0.2])
% Plot middle row: expectation value and variance for the number of terminal
% segments for three different values of $E$ (matching those in the top
% row) calculated using the first 1000 $p(n,t)$'s while keeping
% $p_{high}< 10^{-6}$.
subplot(3,3,4)
hold on
if(E==0)
plot(T(validPoints),mun(validPoints),'k-')
plot(T(validPoints),sigman(validPoints),'k--')
end
axis([0,4,0,30])
subplot(3,3,5)
hold on
if(E==0.5)
plot(T(validPoints),mun(validPoints),'k-')
plot(T(validPoints),sigman(validPoints),'k--')
end
axis([0,10,0,30])
subplot(3,3,6)
hold on
if(E==1)
plot(T(validPoints),mun(validPoints),'k-')
plot(T(validPoints),sigman(validPoints),'k--')
legend('\mu(n)','\sigma(n )','p_{high}10^7 ','Location','NorthWest')
end
axis([0,25,0,30])
% Plot bottom row left: comparison expectation value (solid grey lines) with
% mean field prediction (dashed black lines) for five different $E$
% values: $E= 0,0.25, 0.5, 0.75, 1$; at $E$-values $0, 1$ the mean
% field solutions coincide with the exact solution.
subplot(3,2,5)
hold on
plot(T(validPoints),mun(validPoints),'k-')
if(E==0)
plot(T(validPoints),exp(T(validPoints)),'r--')
else
plot(T(validPoints),(E*T(validPoints)+1).^(1/E),'r--')
legend('\mu(n)','\mu_{MF}(n)','Location','SouthEast')
end
axis([0,25,0,30])
% Plot bottom row right: comparison of mean field solution and numerical
% results; after an initial growth of the relative error for
% intermediate values of $E$ , i.e. $E= 0.25, 0.5, 0.75$, the
% relative error attenuates. The standard deviation and mean for $E=0$
% and $E=1$ correspond within the numerical error with the exact
% solutions.
markers=['.';'+';'d';'o';'-'];
subplot(3,2,6)
hold on
if(E==0 )
plot(T(validPoints),(exp(T(validPoints))./mun(validPoints)'),markers(1+round(E/0.25)))
else
plot(T(validPoints),((E*T(validPoints)+1).^(1/E)./mun(validPoints)'),markers(1+round(E/0.25)))
end
legend('E=0','E=0.25','E=0.50','E=0.75','E=1','Location','SouthEast')
axis([0,25,0.99,1.1])
end
%% Save figure to file (pdf)
figure(1)
saveas(gcf,'figures/BEModel.pdf')