Search results for " attractors"
showing 10 items of 21 documents
Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity
2015
Abstract In this paper a Lorenz-like system, describing convective fluid motion in rotating cavity, is considered. It is shown numerically that this system, like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic self-excited attractor. However, for the considered system, unlike the classical Lorenz system, along with self-excited attractor a hidden attractor can be localized. Analytical-numerical localization of hidden attractor is demonstrated.
Scenario of the Birth of Hidden Attractors in the Chua Circuit
2017
Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.
Numerical analysis of dynamical systems : unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimens…
2019
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rössler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rössler system. Using the example of the Vallis system describing the El…
On lower-bound estimates of the Lyapunov dimension and topological entropy for the Rossler systems
2019
In this paper, on the example of the Rössler systems, the application of the Pyragas time-delay feedback control technique for verification of Eden’s conjecture on the maximum of local Lyapunov dimension, and for the estimation of the topological entropy is demonstrated. To this end, numerical experiments on computation of finite-time local Lyapunov dimensions and finite-time topological entropy on a Rössler attractor and embedded unstable periodic orbits are performed. The problem of reliable numerical computation of the mentioned dimension-like characteristics along the trajectories over large time intervals is discussed. peerReviewed
APPROXIMATE INERTIAL MANIFOLDS FOR THERMODIFFUSION EQUATIONS
2004
In this paper, we consider the two dimensional equations of thermohydraulics, i.e. the coupled system of equations of fluid and temperature in the Boussinesq approximation. We construct a family of approximate Inertial Manifolds whose order decreases exponentially fast with respect to the dimension of the manifold. We give the explicit expression of the order of the constructed manifolds.
Stability and Chaotic Attractors of Memristor-Based Circuit with a Line of Equilibria
2019
This report investigates the stability problem of memristive systems with a line of equilibria on the example of SBT memristor-based Wien-bridge circuit. For the considered system, conditions of local and global partial stability are obtained, and chaotic dynamics is studied. peerReviewed
Structural Stability
2020
The notion of structural stability was first introduced by the Russian math- ematicians Alexandr Andronov and Lev Pontryagin (cf. Andronov and Potryangin 1937). However, there are traces of such a concept in the work of the French math- ematician Henry Poincaré (cf. Poincaré 1880). In more recent years, interesting developments about structural stability included writings of important math- ematicians like Mauricìo Peixoto (cf. at least Peixoto 1960), Stephen Smale (cf. at least Smale 1971) and René Thom (1972, 1980) (see structural morpho- dynamics). From an intuitive point of view, structural stability refers to a particular systemic property known as robustness. Put in general terms, a s…
Hidden attractors in electromechanical systems with and without equilibria
2016
This paper studies hidden oscillations appearing in electromechanical systems with and without equilibria. Three different systems with such effects are considered: translational oscillator-rotational actuator, drilling system actuated by a DC-motor and drilling system actuated by induction motor. We demonstrate that three systems experience hidden oscillations in sense of mathematical definition. While some of these hidden oscillations can be easily seen in natural physical experiments, the localization of others requires special efforts. peerReviewed
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…
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…