Eigenvalues equilibrium in bifurcation zero hopf

Numerical Bifurcation Analysis Toolbox in Matlab

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Eigenvalues equilibrium in bifurcation zero hopf

Forum: Open Discussion

Creator: Sergey Novak

Created: 2023-09-19

Updated: 2023-09-19

Sergey Novak - 2023-09-19

Hello, i find zero hopf bifurcation and I decided to check the eigenvalues of the equilibrium
This codimension two bifurcation is characterized by the conditions λ1=0 and Re λ2,3=0, but I don't see the imaginary part being zero
I don't quite understand how matcont discovered this bifurcation
Thank you for help

output.png

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hilmeijer - 2023-09-19

Classify this as a Zero-Neutral Saddle. The testfunction for the Hopf bifurcation vanishes as two eigenvalues have zero sum, but both are real. At the command line, this is probably mentioned, and then you can ignore this as a codim 2 case.

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- Sergey Novak - 2023-09-19
  
  Thank you so much for your help
  There is a message about this in the console
  I didn't pay attention to her before
  
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