Search results for "Chaotic dynamics"
showing 10 items of 197 documents
Finite-time and exact Lyapunov dimension of the Henon map
2017
This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the finite-time Lyapunov exponents by different algorithms is discussed. A new adaptive algorithm for the finite-time Lyapunov dimension computation in studying the dynamics of dimension is used. Analytical estimates of the Lyapunov dimension using the localization of attractors are given. A proof of the conjecture on the Lyapunov dimension of self-excited attractors and derivation of the exact Lyapunov dimension formula are revisited.
Homoclinic orbit and hidden attractor in the Lorenz-like system describing the fluid convection motion in the rotating cavity
2014
In this paper a Lorenz-like system, describing the process of rotating fluid convection, is considered. The present work demonstrates numerically that this system, also like the classical Lorenz system, possesses a homoclinic trajectory and a chaotic self-excited attractor. However, for considered system, unlike the classical Lorenz one, along with self-excited attractor a hidden attractor can be localized. Analytical-numerical localization of hidden attractor is presented.
Superconvergent Perturbation Theory, KAM Theorem (Introduction)
2001
Here we are dealing with an especially fast converging perturbation series, which is of particular importance for the proof of the KAM theorem (cf. below).
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
2015
In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attra…
Global attractors from the explosion of singular cycles
1997
Abstract In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.
Up, down, two-sided Lorenz attractor, collisions, merging and switching
2021
We present a slightly modified version of the well known "geometric Lorenz attractor". It consists in a C1 open set O of vector fields in R3 having an attracting region U containing: (1) a unique singular saddle point sigma; (2) a unique attractor Lambda containing the singular point; (3) the maximal invariant in U contains at most 2 chain recurrence classes, which are Lambda and (at most) one hyperbolic horseshoe. The horseshoe and the singular attractor have a collision along the union of 2 co-dimension 1 sub-manifolds which divide O in 3 regions. By crossing this collision locus, the attractor and the horseshoe may merge in a two-sided Lorenz attractor, or they may exchange their nature:…
"Table 10" of "Properties of jet fragmentation using charged particles measured with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV"
2021
$\langle \zeta \rangle$, combined jet.
"Table 3" of "Properties of jet fragmentation using charged particles measured with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV"
2020
$\langle \zeta \rangle$, forward jet.
"Table 3" of "Properties of jet fragmentation using charged particles measured with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV"
2021
$\langle \zeta \rangle$, forward jet.
"Table 4" of "Properties of jet fragmentation using charged particles measured with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV"
2021
$\langle \zeta \rangle$, central jet.