On bifurcations of Lorenz attractors in the Lyubimov–Zaks model

2021 ◽  
Vol 31 (9) ◽  
pp. 093118
Author(s):  
Alexey Kazakov
Keyword(s):  
Lorenz Attractors

scholarly journals Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors

2018 ◽  
Vol 57 (2) ◽  
pp. 269-292
Author(s):  
Carlos Gustavo T. Moreira ◽  
Maria José Pacifico ◽  
Sergio Romaña Ibarra
Keyword(s):  
Hausdorff Dimension ◽  
Dynamical Spectra ◽  
Lorenz Attractors

scholarly journals On the statistical stability of Lorenz attractors with a stable foliation

2018 ◽  
Vol 39 (12) ◽  
pp. 3169-3184 ◽  
Author(s):  
WAEL BAHSOUN ◽  
MARKS RUZIBOEV
Keyword(s):  
Stable Foliation ◽  
Statistical Stability ◽  
Lorenz Attractors

We prove statistical stability for a family of Lorenz attractors with a $C^{1+\unicode[STIX]{x1D6FC}}$ stable foliation.

Lorenz attractors in unfoldings of homoclinic-flip bifurcations

2010 ◽  
Vol 26 (1) ◽  
pp. 61-76 ◽  
Author(s):  
A. Golmakani ◽  
A.J. Homburg
Keyword(s):  
Lorenz Attractors

A degenerate singularity generating geometric Lorenz attractors

1995 ◽  
Vol 15 (5) ◽  
pp. 833-856 ◽  
Author(s):  
Freddy Dumortier ◽  
Hiroshi Kokubu ◽  
Hiroe Oka
Keyword(s):  
Vector Field ◽  
Normal Form ◽  
Vector Fields ◽  
Lorenz Attractor ◽  
Degenerate Singularity ◽  
Field Singularity ◽  
Lorenz Attractors ◽  
Geometric Lorenz Attractor

AbstractA degenerate vector field singularity in R3 can generate a geometric Lorenz attractor in an arbitrarily small unfolding of it. This enables us to detect Lorenz-like chaos in some families of vector fields, merely by performing normal form calculations of order 3.

scholarly journals Statistical stability of geometric Lorenz attractors

2014 ◽  
Vol 224 (3) ◽  
pp. 219-231 ◽  
Author(s):  
José F. Alves ◽  
Mohammad Soufi
Keyword(s):  
Statistical Stability ◽  
Lorenz Attractors

scholarly journals Ergodic Optimization for Hyperbolic Flows and Lorenz Attractors

2020 ◽  
Vol 21 (10) ◽  
pp. 3253-3283 ◽  
Author(s):  
Marcus Morro ◽  
Roberto Sant’Anna ◽  
Paulo Varandas
Keyword(s):  
Ergodic Optimization ◽  
Hyperbolic Flows ◽  
Lorenz Attractors

scholarly journals Monotonicity and non-monotonicity regions of topological entropy for Lorenz-like families with infinite derivatives

2020 ◽  
Vol 5 (2) ◽  
pp. 293-306
Author(s):  
M.I. Malkin ◽  
K.A. Safonov
Keyword(s):  
Normal Form ◽  
Topological Entropy ◽  
Lorenz Attractor ◽  
Homoclinic Loop ◽  
One Dimensional ◽  
Study Behavior ◽  
Saddle Value ◽  
Lorenz Attractors ◽  
Two Parameter ◽  
Lorenz Maps

AbstractWe study behavior of the topological entropy as the function of parameters for two-parameter family of symmetric Lorenz maps Tc,ɛ(x) = (−1 + c|x|1−ɛ) · sgn(x). This is the normal form for splitting the homoclinic loop in systems which have a saddle equilibrium with one-dimensional unstable manifold and zero saddle value. Due to L.P. Shilnikov results, such a bifurcation corresponds to the birth of Lorenz attractor (when the saddle value becomes positive). We indicate those regions in the bifurcation plane where the topological entropy depends monotonically on the parameter c, as well as those for which the monotonicity does not take place. Also, we indicate the corresponding bifurcations for the Lorenz attractors.

Neural reconstruction of Lorenz attractors by an observable

2002 ◽  
Vol 14 (1) ◽  
pp. 81-86 ◽  
Author(s):  
B. Cannas ◽  
S. Cincotti
Keyword(s):  
Lorenz Attractors
Sign in / Sign up

Export Citation Format

Share Document