On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
type: Item
instance of: scholarly article
title: On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
zbMATH Open document ID: 1338.37046
published in: Applied Mathematics and Computation
publication date: 2016-06-22T00:00:00Z
full work available at URL: https://arxiv.org/abs/1409.8649
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 6596819
zbMATH Keywords: Lorenz-like systems
zbMATH Keywords: Lorenz system
zbMATH Keywords: Chen system
zbMATH Keywords: Lu system
zbMATH Keywords: Lyapunov exponent
zbMATH Keywords: chaotic analog of 16th Hilbert problem
Wikidata QID: Q30052533
author: G. A. Leonov
author: N. V. Kuznetsov
MaRDI profile type: Publication
OpenAlex ID: W2091402091
arXiv ID: 1409.8649
cites work: Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems
cites work: Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system
cites work: The Lü system is a particular case of the Lorenz system
cites work: Centers on center manifolds in the Lorenz, Chen and Lü systems
cites work: Comment on ``A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family''
cites work: Hausdorff and fractal dimension estimates for invariant sets of non-injective maps
cites work: Q3025196
cites work: Q4002244
cites work: Complicated basins and the phenomenon of amplitude death in coupled hidden attractors
cites work: The Chen system revisited
cites work: YET ANOTHER CHAOTIC ATTRACTOR
cites work: Lorenz Equations Part I: Existence and Nonexistence of Homoclinic Orbits
cites work: THE NONEQUIVALENCE AND DIMENSION FORMULA FOR ATTRACTORS OF LORENZ-TYPE SYSTEMS
cites work: Introduction to the theory of infinite-dimensional dissipative systems. Transl. from the Russian by Constantin I. Chueshov, edited by Maryna B. Khorolska
cites work: The Lorenz system does not have a polynomial flow
cites work: INVARIANT ALGEBRAIC SURFACES OF THE CHEN SYSTEM
cites work: On the shape and dimension of the Lorenz attractor
cites work: Q3886544
cites work: On completeness of quadratic systems
cites work: Some advances on generic properties of the Oseledets splitting
cites work: Maximum local Lyapunov dimension bounds the box dimension of chaotic attractors
cites work: Q4283491
cites work: Hopf bifurcation analysis in the \(T\) system
cites work: Preturbulence: A regime observed in a fluid flow model of Lorenz
cites work: Co-existing hidden attractors in a radio-physical oscillator system
cites work: Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor
cites work: Cost Function Based on Gaussian Mixture Model for Parameter Estimation of a Chaotic Circuit with a Hidden Attractor
cites work: Criteria for the existence of homoclinic orbits of systems Lu and Chen
cites work: Formulas for the Lyapunov dimension of attractors of the generalized Lorenz system
cites work: Shilnikov chaos in Lorenz-like systems
cites work: The Tricomi problem on the existence of homoclinic orbits in dissipative systems
cites work: Q3202465
cites work: On estimates of the bifurcation values of the parameters of a Lorentz system
cites work: Q3362126
cites work: Q3361169
cites work: Q2930458
cites work: Q4930147
cites work: General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems
cites work: Lyapunov functions in the attractor dimension theory
cites work: Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
cites work: Q4867828
cites work: TIME-VARYING LINEARIZATION AND THE PERRON EFFECTS
cites work: Hidden attractors in dynamical systems. from hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits
cites work: Localization of hidden Chua's attractors
cites work: Hidden attractor in smooth Chua systems
cites work: The dimension formula for the Lorenz attractor
cites work: Frequency-Domain Methods for Nonlinear Analysis: Theory and Applications
cites work: Coexisting Hidden Attractors in a 4-D Simplified Lorenz System
cites work: Invariant algebraic surfaces of the Lorenz system
cites work: Deterministic Nonperiodic Flow
cites work: ON A GENERALIZED LORENZ CANONICAL FORM OF CHAOTIC SYSTEMS
cites work: Is that Really Hidden? The Presence of Complex Fixed-Points in Chaotic Flows with No Equilibria
cites work: Dynamics and Synchronization of a Novel Hyperchaotic System Without Equilibrium
cites work: Theory of pseudo-orbit shadowing in dynamical systems
cites work: On the boundedness of solutions of the Chen system
cites work: Q4947577
cites work: When Two Dual Chaotic Systems Shake Hands
cites work: New Chaotic Regimes in the Lorenz and Chen Systems
cites work: Infinite-dimensional dynamical systems in mechanics and physics

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On differences and similarities in the analysis of Lorenz, Chen, and Lu systems (DOI)
DOI: 10.1016/J.AMC.2014.12.132