Bifurcation diagram error>Hello. I am currently studying the paper "(Nonlinear dynamics in the Cournot duopolygame with heterogeneous players)" by (H.N. Agiza, A.A. Elsadany) and trying to implement the bifurcation diagram in Python. However, I am encountering an error and I think there are errors in my mathematical input and code. Would it be possible to help me?(The equation I entered is equation (13) in the paper, which can be found on page 516.)
# Parametersa = 10.0 # Parameter ab = 0.5 # Parameter bc1 = 3.0 # Parameter c1c2 = 5.0 # Parameter c2# Alpha value rangealpha_min = 0.0 # Minimum alpha valuealpha_max = 5.0 # Maximum alpha valuealpha_step = 0.1 # Alpha value step# Alpha values listalpha_values = np.arange(alpha_min, alpha_max, alpha_step)def q1(alpha): q1_prev = 0.0 # Initialize q1_prev for i in range(iterations): q1_next = q1_prev + alpha * q1_prev(a - c1 - 2 * b * q1_prev - b * q2(alpha)) q1_prev = q1_next return q1_nextdef q2(alpha): return 1 / (2 * b) * (a - c2 - b * q1(alpha))def bifurcation_diagram(): # Data storage lists q1_vals = [] q2_vals = [] for alpha in alpha_values: # Initial value setting q1 = 0.5 q2 = 0.5 # Simulation execution for i in range(iterations): q1_next = q1(alpha) # Pass current alpha to q1 function q2_next = q2(alpha) # Pass current alpha to q2 function # Data storage if i > 100: q1_vals.append(q1_next) q2_vals.append(q2_next) # Update to the next value q1 = q1_next q2 = q2_next # Plotting plt.plot(alpha_values, q1_vals, label="q1") plt.plot(alpha_values, q2_vals, label="q2") plt.legend() plt.show()# Number of iterationsiterations = 5000# Generate bifurcation diagrambifurcation_diagram()I am still a beginner, so I lack in many areas.I think there are errors in my mathematical input and code.Would it be possible to help me?