Related papers: Constructing Higher-Dimensional Digital Chaotic Sy…

We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…

In the paper, combinatorial synthesis of structure for applied Web-based systems is described. The problem is considered as a combination of selected design alternatives for system parts/components into a resultant composite decision (i.e.,…

Deep learning techniques have shown promise in many domain applications. This paper proposes a novel deep reservoir computing framework, termed deep recurrent stochastic configuration network (DeepRSCN) for modelling nonlinear dynamic…

Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…

High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant…

Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties…

We present CryptoChaos, a novel hybrid cryptographic framework that synergizes deterministic chaos theory with cutting-edge cryptographic primitives to achieve robust, post-quantum resilient encryption. CryptoChaos harnesses the intrinsic…

The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for…

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…

Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a new technique based on the…

Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. We demonstrate spatiotemporal chaos prediction using a machine learning architecture…

As an alternative approach for predicting complex dynamical systems where physics-based models are no longer reliable, reservoir computing (RC) has gained popularity. The hybrid approach is considered an interesting option for improving the…

A hierarchical Model Predictive Control (MPC) formulation is presented for coupled discrete-time linear systems with state and input constraints. Compared to a centralized approach, a two-level hierarchical controller, with one controller…

In recent years, a lot of research has gone into creating multi-layer chaotic mapping-based cryptosystems. Random-like behavior, a continuous broadband power spectrum, and a weak baseline condition dependency are all characteristics of…

Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…

Using the machine learning approach known as reservoir computing, it is possible to train one dynamical system to emulate another. We show that such trained reservoir computers reproduce the properties of the attractor of the chaotic system…

Computing the state-space topology of a dynamical system from scalar data requires accurate reconstruction of those dynamics and construction of an appropriate simplicial complex from the results. The reconstruction process involves a…

State estimation has long been a fundamental problem in signal processing and control areas. The main challenge is to design filters with ability to reject or attenuate various disturbances. With the arrival of big data era, the…

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…