Find the solution of the initial value problem ˙~x = F~ (~x) with ~x(0) = ~x0 for F~ (~x) = −µx1 −x2 + x 2 1 , ~x = x1 x2 , ~x0
= a b for arbitrarily chosen (a, b, µ) ∈ R 3 . Is the solution ~u(t; a, b, µ) a continuous function of all variables (t, a, b, µ) ∈ R 4 ? Give an interval t ∈ [−a, a] and an open neighbourhood (a, b, µ) ∈ U ⊂ R 3 such that ~u ∈ C([−a, a] × U, R 3 ).
