= Solution
An <equilibrium point of a dynamical system> is a state $\mathbf x_*$ with $\mathbf f(\mathbf x_*)=0$, so the trajectory stays there. In a planar <phase portrait>, an <unstable spiral> has a complex-conjugate pair of <Jacobian matrix> <eigenvalues> with positive real part: nearby trajectories rotate while moving outward. An <attractor> is an invariant set approached by trajectories from a neighborhood, its basin of attraction. It can be an <equilibrium point>, a <limit cycle>, or a more complicated set; outward spiralling near one <equilibrium point> does not preclude attraction to a larger set.
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