Related papers: Symbolic Toolkit for Chaos Explorations
The idea that chaos could be a useful tool for analyze nonlinear systems considered in this paper and for the first time the two time scale property of singularly perturbed systems is analyzed on chaotic attractor. The general idea…
We review the occurrence of the patterns of the onset of chaos in low-dimensional nonlinear dissipative systems in leading topics of condensed matter physics and complex systems of various disciplines. We consider the dynamics associated…
We present a tensor network model (TNM) for forecasting nonlinear and chaotic dynamics, bridging quantum many-body methods with classical complex systems. The TNM leverages hierarchical tensor contractions to encode non-Markovian temporal…
We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…
Chaotic iterations, a tool formerly used in distributed computing, has recently revealed various interesting properties of disorder leading to its use in the computer science security field. In this paper, a comprehensive study of its…
The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions.…
This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange…
This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…
Chaotic attractors commonly contain periodic solutions with unstable manifolds of different dimensions. This allows for a zoo of dynamical phenomena not possible for hyperbolic attractors. The purpose of this Letter is to demonstrate these…
A web-based tool called ADFilter was developed to process collision events using autoencoders based on a deep unsupervised neural network. The autoencoders are trained on a small fraction of either collision data or Standard Model Monte…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
In this paper, we present a unified framework of multiple attractors including multistability, multiperiodicity and multichaos. Multichaos, which means that the chaotic solution of a system lies in different disjoint invariant sets with…
In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based…
The structure of the Lorenz-84 attractor is investigated in this study. Its dynamics belonging to weakly dissipative chaos, classical approaches cannot be used to analyze its structure. The color tracer mapping is introduced for this…
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches---such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)---amount to multi-linear factorization. They are…
In this letter, taking the well known (2+1)-dimensional soliton systems, Davey-Stewartson (DS) model and the asymmetric Nizhnik-Novikov-Veselov (ANNV) model, as two special examples, we show that some types of lower dimensional chaotic…
This article is talking about the study constructive method of structural identification systems with chaotic dynamics. It is shown that the reconstructed attractors are a source of information not only about the dynamics but also on the…
We have found stable chaotic solutions for optomechanical systems coupled with a Two-Level System or qubit. In this system methods have been found which can be used to Tune in and out of Chaos as well as various n-period motions. This…
We demonstrate experimentally a new form of induced transparency, i.e., chaos-induced transparency, in a slightly deformed microcavity which support both continuous chaotic modes and discrete regular modes with Q factors exceeding 3X?10^7.…
We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…