Is it possible that changing initial boundary conditions fi(0) (i=1..n) will affect the stability of a fixed point in an ODE, when the stability is based on the linearization of the ODE.
I would say the answer is no. The reason is that when you solve (by setting ODE=0) for fixed points and find the eigenvalues of the Jacobian matrix, you do not use fi(0). Please tell me why if I am wrong.
