Related papers: Large deviations in chaotic systems: exact results…
We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…
The affect of demographic stochasticity of a system of globally coupled chaotic maps is considered. A two-step model is studied, where the intra-patch chaotic dynamics is followed by a migration step that coupled all patches; the…
We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios…
Synchronization transitions are investigated in coupled chaotic maps. Depending on the relative weight of linear versus nonlinear instability mechanisms associated to the single map two different scenarios for the transition may occur. When…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
The climate system is a complex, chaotic system with many degrees of freedom and variability on a vast range of temporal and spatial scales. Attaining a deeper level of understanding of its dynamical processes is a scientific challenge of…
We show that the probability distribution function that best fits the distribution of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space deviates from the exponential statistics by a…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
Two replicas of spatially extended chaotic systems synchronize to a common spatio-temporal chaotic state when coupled above a critical strength. As a prototype of each single spatio-temporal chaotic system a lattice of maps interacting via…
In the present study, we investigate the dynamics of impulsive differential equations driven by a chaotic system. We rigorously prove that, likewise the drive, the response impulsive system is also chaotic. Our results are based on the…
Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…
A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
We conduct a comprehensive investigation into the dynamics of gradient descent using large-order constant step-sizes in the context of quadratic regression models. Within this framework, we reveal that the dynamics can be encapsulated by a…
In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…
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…
Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method utilizes deep neural networks (DNNs) to construct a model for…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.