Thresholding Distance Plots Using True Recurrence Points

Recurrence plots (RP) visualize multi-dimensional state spaces and represent the recurrence of states of a system. Recurrence points can be divided into true recurrence points and false recurrence points (also called sojourn points). We introduce the true recurrence point recurrence plot, TRP, a variant of the traditional RP excluding the sojourn points. This is a cleaned up RP free from recurrence points originating from tangential motion, and hence a more robust representation of unstable periodic orbits. The method is demonstrated with three simple systems, a periodic sine wave, a quasi-periodic torus and the x-component of the chaotic Lorenz system