Related papers: Chaos in the Lorenz equations: a computer-assisted…
We present a new solution for fundamental problems in nonlinear dynamical systems: finding, verifying, and stabilizing cycles. The solution we propose consists of a new control method based on mixing previous states of the system (or the…
This paper focuses on an interesting phenomenon when chaos meets computers. It is found that digital computers are absolutely incapable of showing true long-time dynamics of some chaotic systems, including the tent map, the Bernoulli shift…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
We present a measurement noise reduction scheme based on information flow of a chaotic system. This scheme operates on conditions of chaoticity and well-defined noise level, not depending on other detailed characteristics of noise. Starting…
With the constant increase of the number of autonomous vehicles and connected objects, tools to understand and reproduce their mobility models are required. We focus on chaotic dynamics and review their applications in the design of…
We derive quantitative sufficient conditions for rotational chaos and diffusion in annular homeomorphisms, building on the topological criteria established in [31]. These conditions depend only on basic properties of the maps, making their…
This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot…
We deal with a mechanism of generating distributional chaos in planar nonautonomous ODEs and try to measure chaosity in terms of topological entropy. It is based on the interplay between simple periodic solutions. We prove the existence of…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The increase in data traffic on the internet has significantly increased the relevance of data and image encryption. Among the techniques most used in cryptography, chaotic systems have received great attention due to their easy…
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise…
In finite-dimensional, chaotic, Lorenz-like wave-particle dynamical systems one can find diffusive trajectories, which share their appearance with that of laminar chaotic diffusion [Phys. Rev. Lett. 128, 074101 (2022)] known from delay…
The problem of Turing pattern formation has attracted much attention in nonlinear science as well as physics, chemistry and biology. So far all Turing patterns have been observed in stationary and oscillatory media only. In this letter we…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about…
In this article we consider the possibility of controlling the dynamics of nonlinear discrete systems. A new method of control is by mixing states of the system (or the functions of these states) calculated on previous steps. This approach…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…