Related papers: On Raw Coding of Chaotic Dynamics
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints…
The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fr\'{e}chet space. The other is about…
We suggest and implement an approach for the bottom-up description of systems undergoing large-scale structural changes and chemical transformations from dynamic atomically resolved imaging data, where only partial or uncertain data on…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…
The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to…
This paper investigates the use of dynamical chaotic systems to encrypt and exchange images between different devices. Two devices were used to simulate the Cubic Map, having the same set of initial conditions, to generate an encryption…
Numerical study of the parametric motion of energy levels in a model system built on Random Matrix Theory is presented. The correlation function of levels' slopes (the so called velocity correlation function) is determined numerically and…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
Preliminary results of our investigations on solving indefinite qua\-dra\-tic programs by dynamical systems are given. First, dynamical systems corresponding to two fundamental DC programming algorithms to deal with indefinite quadratic…
Manifestation of dynamical instability and Hamiltonian chaos in the fundamental near-resonant matter-radiation interaction has been found analitically and in a Monte Carlo simulation in the behavior of atoms moving in a rigid optical…
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…