Hi kdvO,

After analyzing your code, the issue causing the plotted lines to appear straight instead of showing the expected Hopf bifurcation behavior lies in how the detection of Hopf bifurcation is implemented within the loop. The current logic for detecting the bifurcation relies on comparing the difference between the last value and the current value of `x_result` to a threshold of 0.01. However, this approach may not accurately capture the oscillatory behavior characteristic of a Hopf bifurcation.

To fix this, you need to modify the condition for detecting the Hopf bifurcation by considering both the real and imaginary parts of the solution. Specifically, you can check for changes in the sign of the imaginary part to identify oscillatory behavior. Here's how you can update the code:

% Check for Hopf bifurcation (change in stability)

% Look for oscillatory behavior in the solution

if i > 1

if sign(imag(Y(end, 1))) ~= sign(imag(x_result(i-1))) fprintf('Hopf bifurcation detected at eta = %f\n', eta); end end

By comparing the signs of the imaginary parts of `Y(end, 1)` and `x_result(i-1)`, you can detect when there is a change in stability, indicative of a Hopf bifurcation. Additionally, to enhance visualization and better observe the bifurcation behavior, you might consider increasing the number of points in `eta_values` or adjusting other parameters related to your system dynamics.

Once you make these changes, rerun your code to generate an accurate Hopf bifurcation diagram that showcases the expected behavior with oscillations and dynamic changes in stability. This adjustment should address the issue of getting straight lines in your plot and provide a more informative representation of the system's behavior. Good luck!