%Script file to produce the "bifurcation diagram"
%  for F(x) = lambda x - x ^3
%  This will show the pitchfork for period 1 points
%    and the 2-cycle bifurcation.

t1=linspace(-2,5);
y1=zeros(size(t1));  %This is our fixed point at the origin.

t2=linspace(-3,3);   %We'll plot (y2,t2) for the sideways parabola
y2=t2.^2+1;

t3=linspace(-3,3);
y3=t3.^2-1;

plot(t1,y1,'r-',y2,t2,'k-',y3,t3,'m-')
axis([-2,3,-2,2])
legend('x_0=0','Period 1 Bifurcation','Period 2 Bifurcation')

title('Bifurcation Diagram:  \lambda x - x^3: Note Fig 6.15')
xlabel('\lambda')
ylabel('Fixed Point/Period 2 Point');