Related papers: Universal visibility patterns of unimodal maps
We examine the problem of making reconciled forecasts of large collections of related time series through a behavioural/Bayesian lens. Our approach explicitly acknowledges and exploits the 'connectedness' of the series in terms of…
As the parameters of a map are varied an attractor may vary continuously in the Hausdorff metric. The purpose of this paper is to explore the continuation of chaotic attractors. We argue that this is not a helpful concept for smooth…
Time evolution of diluted neural networks with a nonmonotonic transfer function is analitically described by flow equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviours: fixed-point, periodicity and…
Classical chaos theory rests on the notion of universality, whereby disparate dynamical systems share identical scaling laws. Existing universality classes, however, implicitly assume Markovian dynamics. Here, a logistic map endowed with…
Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding the universal aspects of these phenomena is of fundamental interest, yet typically bound to numerical observations in ad-hoc models…
Visibility graph reconstruction, which asks us to construct a polygon that has a given visibility graph, is a fundamental problem with unknown complexity (although visibility graph recognition is known to be in PSPACE). We show that two…
This paper investigates the origin and onset of chaos in a mathematical model of an individual neuron, arising from the intricate interaction between 3D fast and 2D slow dynamics governing its intrinsic currents. Central to the chaotic…
We give a definition of chaos for a continuous self-map of a general topological space. This definition coincides with the Devanney definition for chaos when the topological space happens to be a metric space. We show that in a uniform…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
A traversal of a connected graph is a linear ordering of its vertices all of whose initial segments induce connected subgraphs. Traversals, and their refinements such as breadth-first and depth-first traversals, are computed by various…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
The visibility graph of a simple polygon represents visibility relations between its vertices. Knowing the correct order of the vertices around the boundary of a polygon and its visibility graph, it is an open problem to locate the vertices…
Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of…
The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. We extend this visibility graph and create a directed limited penetrable horizontal visibility graph and an image…
The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to…
We predict synchronization of the chaotic dynamics of two atomic ensembles coupled to a heavily damped optical cavity mode. The atoms are dissipated collectively through this mode and pumped incoherently to achieve a macroscopic population…
Disorder and noise in physical systems often disrupt spatial and temporal regularity, yet chaotic systems reveal how order can emerge from unpredictable behavior. Complex networks, spatial analogs of chaos, exhibit disordered, non-Euclidean…
Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to…
Causality analysis is an important problem lying at the heart of science, and is of particular importance in data science and machine learning. An endeavor during the past 16 years viewing causality as real physical notion so as to…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…