In this contribution we study the onset of chaos via type-II intermittency within the framework of Horizontal Visibility graph theory. We construct graphs associated to time series generated by an iterated map close to a Neimark–Sacker bifurcation and study, both numerically and analytically, their main topological properties. We find well defined equivalences between the main statistical prope...

We study a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments S in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibilit...

Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one correspondence between vertices of G and bars in S, such that there is an edge between two vertices in G if and only if there exists an unobstructed vertical line of sight between their corresponding bars. If bars are a...

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-do...