i wish to take that plot and add it to the below plot : let # Define the fixed point functions x2(mu) = 0.5 + (1 / (2 * mu)) * sqrt(mu^2 - mu * (64 / 27)) x3(mu) = 0.5 - (1 / (2 * mu)) * sqrt(mu^2 - mu * (64 / 27)) # Create ranges for mu_values_full = 0:0.01:4.0 # Full range for x*_1 mu_values_partial = (64/27):0.01:4.0 # Start from 64/27 for x*_2 and x*_3 mu_values_stable = (64/27):0.01:(256/81) # Stable range for x*_2 mu_values_unstable = (256/81):0.01:4.0 # Unstable range for x*_2 # Compute the fixed points x2_values_stable = [x2(mu) for mu in mu_values_stable] x2_values_unstable = [x2(mu) for mu in mu_values_unstable] x3_values = [x3(mu) for mu in mu_values_partial] # Plot the fixed points plot(mu_values_full, fill(0, length(mu_values_full)), label="x*_1 = 0 (stable)", xlabel="",ylabel="x", xlims=(0, 4.1), ylims=(-0.1, 1), title="The (Real) Positions of the Three Fixed Points of f(x, ) for 0 4 in (, x) Space") plot!(mu_values_stable, x2_values_stable, label="x*_2 (stable)", linestyle=:solid, color=:blue) plot!(mu_values_unstable, x2_values_unstable, label="x*_2 (unstable)", linestyle=:dash, color=:blue) plot!(mu_values_partial, x3_values, label="x*_3 (unstable)", linestyle=:dash)