Question: Which option is the correct one? Consider the nonlinear ODE * = f ( ) with equilibrium 0 E RS. In which case can you

Which option is the correct one?

Which option is the correct one? Consider the
Consider the nonlinear ODE * = f ( ) with equilibrium 0 E RS. In which case can you not conclude whether O is asymptotically stable or unstable? O The eigenvalues of D f(0) are -1 (algebraic multiplicity 1) and 1 (algebraic multiplicity 2) The eigenvalues of D f (0) are -1 (algebraic multiplicity 2) and 1 (algebraic multiplicity 1). The eigenvalues of D f (0) are i, -i, -1 (all algebraic multiplicity 1). O The eigenvalues of Df (0) are -1 and 1, one with algebraic multiplicity 1 and the other with algebraic multiplicity 2, but we do not know which one is which

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