Question: if the trace is negative and the determinant changes sign then we go from 2 negative eigenvalues WLOG to 1 negative and one positive eigenvalue

if the trace is negative and the determinant changes sign then we go from 2 negative eigenvalues WLOG to 1 negative and one positive eigenvalue which implies a saddle . so we have gone from a fixed point to a saddle which is a characteristic of a pitchfork bifurcation

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