Search results for "attractors"
showing 4 items of 24 documents
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…
Coexistence of hidden attractors and multistability in counterexamples to the Kalman conjecture
2019
The Aizerman and Kalman conjectures played an important role in the theory of global stability for control systems and set two directions for its further development – the search and formulation of sufficient stability conditions, as well as the construction of counterexamples for these conjectures. From the computational perspective the latter problem is nontrivial, since the oscillations in counterexamples are hidden, i.e. their basin of attraction does not intersect with a small neighborhood of an equilibrium. Numerical calculation of initial data of such oscillations for their visualization is a challenging problem. Up to now all known counterexamples to the Kalman conjecture were const…