supercritical pitchfork.txt

通过此程序希望大家对基本的分岔过程有一个感性的认识。

%% Animation for a Supercritical Pitchfork bifurcation (same structure as the Saddle Node case, limited annotation)

xmin = -3;
xmax = 3;
x = xmin:0.1:xmax
ax = (0.0).*x;

rmin = -4
rmax = 4
imax = 21

ymin = -20;
ymax = 20;
ky = ymin:0.1:ymax
ay = (0.0).*ky

for i = 1:imax
%calculate r value 
r = rmin + (i-1)*(rmax-rmin)/(imax-1)
%create title string
strr = num2str(r);
strt = ['r=' strr]; 

%calculate dxdt
y = r.*x - x.^3

%plot x-axis
plot(x,ax,'--');
axis([xmin xmax ymin ymax])
hold on
%plot y-axis
plot(ay,ky,'--')

%plot f(x)
plot(x,y,'r');

%plot fixed points
if (r < 0) 
plot(0,0,'o','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
end
if(r == 0.0) 
plot(0,0,'*','MarkerSize',10,'MarkerEdgeColor','k');
end
if (r > 0) 
plot(0,0,'o','MarkerSize',10,'MarkerEdgeColor','k');
plot(r.^(0.5),0,'o','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
plot(-r.^(0.5),0,'o','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
end

%plot flow direction
if(r <= 0)
plot(-2.5,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
plot(2.5,0,'<','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
end

if(r > 0) 
plot(-2.5,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k'); 
plot(-r.^(0.5)/2,0,'<','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
plot(r.^(0.5)/2,0,'>','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
plot(2.5,0,'<','MarkerSize',10,'MarkerEdgeColor','k','MarkerFaceColor','k');
end

%plot labels
xlabel('x','FontSize',20)
ylabel('dx/dt','FontSize',20)
text(-2,15,'dx/dt = rx - x^3','Color','r','FontSize',20)
text(1,15,strt,'FontSize',20)
title('Supercritical Pitchfork Bifurcation','FontSize',20)

%getframe
h = gcf;
M(i) = getframe(h,[5 5 480 380]);
hold off
end

%play and save movie
movie(M);
movie2avi(M,'SuperPitchfork','fps',1);