Fig 3. Visualization of three-dimensional linear Koopman system from Eq (25) along with projection of dynamics onto the x₁-x₂ plane.

The attracting slow manifold is shown in red, the constraint $y_3=y_1^2$ is shown in blue, and the slow unstable subspace of Eq (25) is shown in green. Black trajectories of the linear Koopman system in y project onto trajectories of the full nonlinear system in x in the y₁-y₂ plane. Here, μ = −0.05 and λ = 1. Figure is reproduced with Code 1 in S1 Appendix.