Hyperchaotic attractors from a linearly controlled Lorenz system
type: Item
instance of: scholarly article
title: Hyperchaotic attractors from a linearly controlled Lorenz system
zbMATH Open document ID: 1175.37041
author: Kangming Zhang
author: Qi-Gui Yang
author: Guanrong Chen
published in: Nonlinear Analysis. Real World Applications
publication date: 2009-05-07T00:00:00Z
review text: Adding a linear feedback controller to the classical Lorenz system, the authors obtain a hyperchaotic system \[ \begin{cases} \dot{x}=10\left( y-x\right) ,\\ \dot{y}=28x-y-xz+w,\\ \dot{z}=-\frac{8}{3}z+xy,\\ \dot{w}=k_{1}x+k_{2}y, \end{cases} \] where \(k_{1}\) and \(k_{2}\) are two parameters determining chaotic and hyperchaotic nature of the system. They focus attention on the study of the following properties of a new system: (a) existence of a periodic orbit with two zero Lyapunov exponents; (b) existence of a chaotic orbit with two zero Lyapunov exponents; (c) dependence of chaos on initial values of \(w_{0};\) (d) chaos with only one equilibrium; (e) hyperchaos with only one equilibrium. Furthermore, the theory of normal forms and symbolic computations are employed for the analysis of a Hopf bifurcation in the system.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 37C27
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 5551925
zbMATH Keywords: Lorenz system
zbMATH Keywords: chaos and hyperchaos
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: Lyapunov exponents
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2008.02.008
OpenAlex ID: W2028923894
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DOI: 10.1016/J.NONRWA.2008.02.008
description: scientific article; zbMATH DE number 5551925