I have a two dimensional, non-linear vector field [f_1(x_1,x_2); f_2(x_1,x_2)] with a fixed point at the origin. Is there a generally applicable, easy to understand (for engineers) method for getting the normal form?
Dear Jochen,
The procedure is more or less clearly written in Wiggins's (introduction to applied nonlinear dynamical system and chaos) book , but being a mathematician, it is not easy to judge how easy the treatment presented there for engineers. It can also be found in Lawrence Perko's book, probably a bit easier, but shorter.
Dear Tamás,
thank you for the suggestions. I briefly checked the two books and I found particularly Wiggins helpful. It is very comprehensive, but the procedure is explained clearly and step-by-step and, most important for most non-mathematicians, he doesn't get lost in lengthy proves. For (theoretically oriented) engineers understandable, I would say.
You need to check the linearization of the vector field.
Test the eigenvalues for resonances.
Resonance is defined as :m=\sigma{
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