Related papers: Statistical Distance For Chaotic Maps
In graph analysis, a classic task consists in computing similarity measures between (groups of) nodes. In latent space random graphs, nodes are associated to unknown latent variables. One may then seek to compute distances directly in the…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
We discuss the possibility of applying some standard statistical methods (the least square method, the maximum likelihood method, the method of statistical moments for estimation of parameters) to deterministically chaotic low-dimensional…
Uncertainty in the initial conditions of dynamical systems can cause exponentially fast divergence of trajectories, a signature of deterministic chaos. Here, we derive a classical uncertainty relation that sets a speed limit on the rates of…
We begin with an interpretation of the L1-distance between two power spectral densities and then, following an analogous rationale, we develop a natural metric for quantifying distance between respective covariance matrices.
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Recent progress toward classifying low-dimensional chaos measured from time series data is described. This classification theory assigns a template to the time series once the time series is embedded in three dimensions. The template…
More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics.…
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…
Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the…
For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…
On long enough timescales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The solar system is no exception: diffusive processes take part in the transportation of small bodies and provide…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
When we represent a network of sensors in Euclidean space by a graph, there are two distances between any two nodes that we may consider. One of them is the Euclidean distance. The other is the distance between the two nodes in the graph,…