Show that the linearization of the system in (7) at .5; 2/ is u0 D 5v, v0 D 2u. Then show that the coefficient matrix of this linear system has conjugate imaginary eigenvalues 1, 2 D i p10. Hence .0; 0/ is a stable center for the linear system. Although this is the indeterminate case of Theorem 2 in Section 6.2, Fig. 6.3.16 suggests that .5; 2/ also is a stable center for (7).

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