Posts tagged asymptotically stable attractor spiral
Phase portraits for systems of differential equations with complex Eigenvalues

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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