Search results for "Chaotic dynamics"
showing 10 items of 197 documents
"Table 2" of "Inclusive J/psi production in pp collisions at sqrt(s) = 2.76 TeV"
2016
The $\sqrt{s}$-dependence of $\langle p_{\rm T}\rangle$ for inclusive J/$\psi$ production (forward rapidity).
"Table 3" of "Inclusive J/psi production in pp collisions at sqrt(s) = 2.76 TeV"
2016
the $\sqrt{s}$-dependence of $\langle p_{\rm T}\rangle$ for inclusive J/$\psi$ production (forward rapidity).
"Table 1" of "Measurements of the Nuclear Modification Factor for Jets in Pb+Pb Collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV with the ATLAS Detect…
2015
The $\langle T_{\mathrm{AA}} \rangle $ and $\langle N_{\mathrm{part}} \rangle$ values and their uncertainties in each centrality bin.
"Table 1" of "Search for a heavy top-quark partner in final states with two leptons with the ATLAS detector at the LHC"
2012
(1) Number of generated MC events for the scalar top signal grid (2) Relative Cross section uncertainties for the scalar top signal grid.
Lyapunov dimension formula for the global attractor of the Lorenz system
2016
The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first by G.A. Leonov in 2002. Leonov used the construction technique of special Lyapunov-type functions, which was developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters, of the system, such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values including all parameters, which sati…
Internal perturbations of homoclinic classes:non-domination, cycles, and self-replication
2010
Conditions are provided under which lack of domination of a homoclinic class yields robust heterodimensional cycles. Moreover, so-called viral homoclinic classes are studied. Viral classes have the property of generating copies of themselves producing wild dynamics (systems with infinitely many homoclinic classes with some persistence). Such wild dynamics also exhibits uncountably many aperiodic chain recurrence classes. A scenario (related with non-dominated dynamics) is presented where viral homoclinic classes occur. A key ingredient are adapted perturbations of a diffeomorphism along a periodic orbit. Such perturbations preserve certain homoclinic relations and prescribed dynamical prope…
Singular hyperbolic systems
1999
We construct a class of vector fields on 3-manifolds containing the hyperbolic ones and the geometric Lorenz attractor. Conversely, we shall prove that nonhyperbolic systems in this class resemble the Lorenz attractor: they have Lorenz-like singularities accumulated by periodic orbits and they cannot be approximated by flows with nonhyperbolic critical elements.
The Lyapunov dimension, convergency and entropy for a dynamical model of Chua memristor circuit
2018
For the study of chaotic dynamics and dimension of attractors the concepts of the Lyapunov exponents was found useful and became widely spread. Such characteristics of chaotic behavior, as the Lyapunov dimension and the entropy rate, can be estimated via the Lyapunov exponents. In this work an analytical approach to the study of the Lyapunov dimension, convergency and entropy for a dynamical model of Chua memristor circuit is demonstrated.
Estimation of Lyapunov dimension for the Chen and Lu systems
2015
Nowadays various estimates of Lyapunov dimension of Lorenz-like systems attractors are actively developed. Within the frame of this study the question arises whether it is possible to obtain the corresponding estimates of dimension for the Chen and Lu systems using the reduction of them to the generalized Lorenz system. In the work (Chen and Yang, 2013) Leonov's method was applied for the estimation of Lyapunov dimension, and as a consequence the Lyapunov dimension of attractors of the Chen and Lu systems with the classical parameters was estimated. In the present work an inaccuracy in (Chen and Yang, 2013) is corrected and it is shown that the revised domain of parameters, where the estima…
A lower-bound estimate of the Lyapunov dimension for the global attractor of the Lorenz system
2019
In this short report, for the classical Lorenz attractor we demonstrate the applications of the Pyragas time-delayed feedback control technique and Leonov analytical method for the Lyapunov dimension estimation and verification of the Eden's conjecture. The problem of reliable numerical computation of the finite-time Lyapunov dimension along the trajectories over large time intervals is discussed.