Finding periodic orbits: close recurrences

The state-space trajectories of (transient) turbulence of previous movie, as well as this of transient trajectory initiated from the unstable manifold of the UB equilibrium, exhibit close passes to other equilibria, such as the LB lower-branch equilibrium.
We can quantify this by plotting in a time-delay plot the distance between the trajectory at a set of initial times t and times t+T later:
recurrence plot Dark regions correspond to close recurrences: triangles and circles denote equilibria and periodic orbits determined by using a dark region as initial guess for a Newton search.
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