Bifurcation Diagram of Henon Map

I am trying to create a bifurcation diagram of the henon map. Currently, my code just produces a straight line, instead of the bifurcation diagram. I am new to Matlab, so bear with me. Here is my code:

a = 3:-.01:-3;
b=0.3;
x=rand(1)*10^-3;
y=-1+rand(1)*10^-3;
for i=0:1:200;
    x=1-a*x^2+y;
    y=b*x;
    hold all
    plot(a,x)
end

What's wrong with it?

Thanks, Joe

Answer 1

[Rajiv Singh]

Bifurcation map is the plot of equilibrium values vs parameters. For the henon map, the equilibrium solutions are x* = ((b-1) +/- sqrt((1-b)^2+4*a))/(2*a) and y* = b*x*. You could draw these parametric curves directly for a range of x* and y*, no? Unless I am missing something (like if you are actually trying to show the progression of solutions to their equilibria for various a,b values).