Search results for "attractor"

Hidden attractors in Chua circuit: mathematical theory meets physical experiments

2022

AbstractAfter the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in dynamical systems arose. Despite the key role of this first discovery, later on a number of works have appeared supposing that chaotic attractors of the considered dynamical models are rather artificial, computer-induced objects, i.e., they are generated not due to the physical nature of the process, but only by errors arising from the application of approximate numerical methods and finite-precision computations. Further justification for the possibility of a real exi…

D3 Dihedral Logistic Map of Fractional Order

2021

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.

The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension

2020

On the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global stability are estimated and the difficulties of numerically studying the birth of self-excited and hidden attractors, caused by the loss of global stability, are discussed. The problem of reliable numerical computation of the finite-time Lyapunov dimension along the trajectories over large time intervals is discussed. Estimating the Lyapunov dimension of attractors via the Pyragas time-delayed feedback control technique and the Leonov method is demonstrated. Taking into accoun…

EXPERIMENTAL INVESTIGATION OF DILUTE SOLID-LIQUID SUSPENSION IN AN UNBAFFLED STIRRED VESSELS BY A NOVEL PULSED LASER BASED IMAGE ANALYSIS TECHNIQUE

2009

The availability of experimental information on solid distribution inside stirred tanks is a topic of great importance in several industrial applications. The measurement of solid particle distribution in turbulent multiphase flow is not simple and the development of suitable measurement techniques is still in progress. In this work a novel non-intrusive technique for measuring particle concentration fields in solid-liquid systems is employed. The technique makes use of a laser sheet, a high sensitivity digital camera for image acquisition and a Matlab procedure for post-processing the acquired images. Experimental data are here obtained for the case of an unbaffled stirred tank. Stable tor…

Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system

2018

In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of fractional order is analyzed. It is found that without equilibria, the system has hidden attractors.

Localization and dimension estimation of attractors in the Glukhovsky-Dolzhansky system

2016

Polarisation attraction and incoherent modulation instability in optical fibers

2006

This thesis, entitled « Polarisation attraction and incoherent modulation instability in optical fibers », presents a theoretical and experimental study of two new processes from the nonlinear optic in optical fibers domain. We introduce in the first chapter some theoretical notions useful for the comprehension of this work. Then, we demonstrate in the second chapter that it is possible to generate some modulation instability in optical fibers using a partially coherent optical beam. We highlight and observe the main properties of the phenomenon. We study the polarisation attraction in isotropic fibers process in the third chapter. Our work proves the existence of the phenomenon, and permit…

Hidden Oscillations In The Closed-Loop Aircraft-Pilot System And Their Prevention

2016

The paper is devoted to studying and prevention of a special kind of oscillations-the Pilot Involved Oscillations (PIOs) which may appear in man-machine closed-loop dynamical systems. The PIO of categories II and III are defined as essentially non-linear unintended steady fluctuations of the piloted aircraft, generated due to pilot efforts to control the aircraft with a high precision. The main non-linear factor leading to the PIO is, generally, rate limitations of the aircraft control surfaces, resulting in a delay in the response of the aircraft to pilot commands. In many cases, these oscillations indicate presence of hidden, rather than self-excited attractors in the aircraft-pilot state…

Highly occupied gauge theories in 2 + 1 dimensions : a self-similar attractor

2019

Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in 2+1 dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this non-thermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with sc…

Singular tori as attractors of four-wave-interaction systems

2009

We study the spatiotemporal dynamics of the Hamiltonian four-wave interaction in its counterpropagating configuration. The numerical simulations reveal that, under rather general conditions, the four-wave system exhibits a relaxation process toward a stationary state. Considering the Hamiltonian system associated to the stationary state, we provide a global geometrical view of all the stationary solutions of the system. The analysis reveals that the stationary state converges exponentially toward a pinched torus of the Hamiltonian system in the limit of an infinite nonlinear medium. The singular torus thus plays the role of an attractor for the spatiotemporal wave system. The topological pr…