Related papers: Constructing Higher-Dimensional Digital Chaotic Sy…
This study redefines the analysis of Devaney chaos in multiple mappings from a set-valued perspective and introduces new conditions to characterize their chaotic behavior. As an innovative advancement, we develop computational algorithms to…
Unstable periodic orbits (UPOs) are the non-chaotic, dynamical building blocks of spatio-temporal chaos, motivating a first-principles based theory for turbulence ever since the discovery of deterministic chaos. Despite their key role in…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…
The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient computation of reachable sets…
Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional…
The paper presents higher dimension consensus (HDC) for large-scale networks. HDC generalizes the well-known average-consensus algorithm. It divides the nodes of the large-scale network into anchors and sensors. Anchors are nodes whose…
This paper introduces a new watermarking algorithm based on discrete chaotic iterations. After defining some coefficients deduced from the description of the carrier medium, chaotic discrete iterations are used to mix the watermark and to…
Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…
Predictive multiplicity and chaotic dynamics represent two fundamental challenges in machine learning that have evolved independently despite their conceptual connections. We bridge this gap by introducing horizon-constrained Rashomon sets,…
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatio-temporal systems including fluid turbulence is supported by non-chaotic, exactly recurring time-periodic solutions of the…
Investigating how to construct a secure hash algorithm needs in-depth study, as various existing hash functions like the MD5 algorithm have recently exposed their security flaws. At the same time, hash function based on chaotic theory has…
Stochastic balancing domain decomposition by constraints (BDDC) algorithms are developed and analyzed for the sampling of the solutions of linear stochastic elliptic equations with random coefficients. Different from the deterministic BDDC…
Chaotic iterations have been introduced on the one hand by Chazan, Miranker [5] and Miellou [9] in a numerical analysis context, and on the other hand by Robert [11] and Pellegrin [10] in the discrete dynamical systems framework. In both…
This paper discusses mixing of chaotic systems as a dependable method for secure communication. Distribution of the entropy function for steady state as well as plaintext input sequences are analyzed. It is shown that the mixing of chaotic…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
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…
This paper presents a density-based topology optimization method for designing three-dimensional (3D) compliant mechanisms and loadbearing structures with design-dependent pressure loading. Instead of interface-tracking techniques, the…
We propose a novel approach which exploits chaos to enhance classification accuracy. Specifically, the available data that need to be classified are treated as vectors that are first lifted into a higher-dimensional space and then used as…
This paper addresses the problem of building global topological maps from 3D LiDAR point clouds for autonomous mobile robots operating in large-scale, dynamic, and unknown environments. Adaptive Resonance Theory-based Topological Clustering…