Related papers: Constructing Higher-Dimensional Digital Chaotic Sy…
Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were…
In this paper, a new approach for constructing integer domain chaotic systems (IDCS) is proposed, and its chaotic behavior is mathematically proven according to the Devaney's definition of chaos. Furthermore, an analog-digital hybrid…
This paper introduces a new notion of chaotic algorithms. These algorithms are iterative and are based on so-called chaotic iterations. Contrary to all existing studies on chaotic iterations, we are not interested in stable states of such…
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…
Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
This paper presents a new procedure of generating hash functions which can be evaluated using some mathematical tools. This procedure is based on discrete chaotic iterations. First, it is mathematically proven, that these discrete chaotic…
We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems. The deep hierarchy is encoded into the LSTM by…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
Clustering procedures suitable for the analysis of very high-dimensional data are needed for many modern data sets. In model-based clustering, a method called high-dimensional data clustering (HDDC) uses a family of Gaussian mixture models…
In this paper, a novel formulation of discrete chaotic iterations in the field of dynamical systems is given. Their topological properties are studied: it is mathematically proved that, under some conditions, these iterations have a chaotic…
We present a stochastic algorithm for constructing a topologically disordered (i.e., non-regular) spatial lattice with nodes of constant coordination number, the CC lattice. The construction procedure dramatically improves on an earlier…
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small…
This work describes the way that topological mixing and chaos in continua, as induced by discrete dynamical systems, can or can't be understood through topological conjugacy with symbolic dynamical systems. For example, there is no symbolic…
In this study, we address the problem of chaotic synchronization over a noisy channel by introducing a novel Deep Chaos Synchronization (DCS) system using a Convolutional Neural Network (CNN). Conventional Deep Learning (DL) based…
Higher-order brain connectivity (HOBC), which captures interactions among three or more brain regions, provides richer organizational information than traditional pairwise functional connectivity (FC). Recent studies have begun to infer…
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…
Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…
This article considers the $\mathcal{H}_\infty$ static output-feedback control for linear time-invariant uncertain systems with polynomial dependence on probabilistic time-invariant parametric uncertainties. By applying polynomial chaos…
The notion of topological phases extended to dynamical systems stimulates extensive studies, of which the characterization of non-equilibrium topological invariants is a central issue and usually necessitates the information of quantum…