Hello,
I see that there are no complex conjugate numbers with a purely imaginary part on the Hopf curve. I don't quite understand if this is really a Hopf curve or something else.
Indeed, along your curve you follow a neutral saddle, not a Hopf point. The test function checks if the sum of two eigenvalues is zero, in this case they are real, so this is correct. This probably happened because you started from a BT point and then in one direction you'll have a true Hopf curve, and in the other direction it follows the neutral saddles.
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Hello,
I see that there are no complex conjugate numbers with a purely imaginary part on the Hopf curve. I don't quite understand if this is really a Hopf curve or something else.
Thank you for help
Last edit: Sergey Novak 2023-11-25
Indeed, along your curve you follow a neutral saddle, not a Hopf point. The test function checks if the sum of two eigenvalues is zero, in this case they are real, so this is correct. This probably happened because you started from a BT point and then in one direction you'll have a true Hopf curve, and in the other direction it follows the neutral saddles.
Thank you for help