Bifurcation plot displays empty set after a certain value

As said, when plotting my bifurcation plot it does not show its chaotic tendency after r=4a nd it only plots two points at the last given value (in this case 5, but the same applies to any value over 4 or under -2).

def f (A, R):
        A = A*(R*((A/N)-1)-1)+N+A
        B = N-A
        return A

def bifurcation(r, iter):
    # One initial condition for each value of r
    a = np.linspace(0,1000,len(r))
    # We are first going to get rid of the transients
    for i in range(5000):
         a = f(a,r)
    # Assuming we are now on the limit cycle, we plot value of iter outputs
    for i in range(iter): 
        a = f(a,r)
        b = N-a
        plt.plot(r,a, '.', color = 'r', markersize = 1)
        plt.plot(r,b, '.', color = 'b', markersize = 1)

N = 1000
plt.figure()
r = np.arange(0, 5, 0.01)
iter = 100
bifurcation(r, iter)
plt.legend("AB")
plt.show()]

bifurcation plot