Now we want to look at the phase portraits of systems with complex Eigenvalues. The equilibrium of a system with complex Eigenvalues that have no real part is a stable center around which the trajectories revolve, without ever getting closer to or further from equilibrium. The equilibrium of a system with complex Eigenvalues with a positive real part is an unstable spiral that repels all trajectories. The equilibrium of a system with complex Eigenvalues with a negative real part is an asymptotically stable spiral that attracts all trajectories.

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