%Script file to produce a sequence of pictures illustrating
%  the pitchfork bifurcation of F(x)=lambda*x - x^3

%First, we illustrate the pitchfork.  Solving for 
%  F(x)=x, we got:  x( (lambda-1) -x^2 )=0 so that
%  x=0 or x^2+1=lambda:

t=linspace(-2,2,1500);
t1=t;
figure(1)  %Call up figure 1 for plotting

subplot(2,2,1)  %Creates a 2x2 array of plots in figure 1
t1= -t - t.^3;
y = -t1 - t1.^3;
plot(t,y,'k-',t,t,'r-.');
axis([-2,2,-2,2]);
grid on
title('\lambda = -1');

subplot(2,2,2)
t1=-t.^3;
y= -t1.^3;
plot(t,y,'k-',t,t,'r-.');
axis([-2,2,-2,2]);
grid on
title('\lambda = 0');

subplot(2,2,3)
t1= t - t.^3;
y= t1 -t1.^3;
plot(t,y,'k-',t,t,'r-.');
axis([-2,2,-2,2]);
grid on
title('\lambda = 1');

subplot(2,2,4)
t1=1.5*t-t.^3;
y= 1.5*t1 - t1.^3;
plot(t,y,'k-',t,t,'r-.');
axis([-2,2,-2,2]);
grid on
title('\lambda = 3/2');