Dynamics of a Hénon-Lozi-type map
type: Item
instance of: scholarly article
title: Dynamics of a Hénon-Lozi-type map
zbMATH Open document ID: 1005.37013
DOI: 10.1016/S0960-0779(00)00192-2
author: Carl Robert
author: C. Grebogi
author: M. A. Aziz-Alaoui
published in: Chaos, Solitons and Fractals
publication date: 2002-06-13T00:00:00Z
review text: The main goal of this paper is to provide a basic analysis of the two-dimensional map \(L_{a,b,\varepsilon}\) along with detailed comparison with the Lozi map when \(\varepsilon\to 0\). Here \(L_{a,b,\varepsilon}\) is defined by \[ L_{a,b,\varepsilon}: \binom {x}{y} \mapsto \binom {1-aS_\varepsilon(x)+y}{bx}, \tag{1} \] where \(a,b\in \mathbb{R}\), \(b\neq 0\) and \(S_\varepsilon(x)\) is defined by \[ S_\varepsilon: \mathbb{R}\to \mathbb{R}, \quad x\mapsto S_\varepsilon(x)= \begin{cases} |x|&\text{if }|x|\geq \varepsilon,\\ \frac{x^2}{2\varepsilon}+ \frac{\varepsilon}{2} &\text{if }|x|\leq \varepsilon, \end{cases} \] where \(\varepsilon\) satisfies \(\varepsilon\in (0,1)\). The authors study existence and local stability of fixed points in different regions of the parameter space of \(a,b\) as the parameter \(\varepsilon\) varies. They also investigate the numerics to compare their chaotic dynamics with that of the Lozi map (period-doubling, fractal structure of the chaotic attractor, etc.) and the influence of \(\varepsilon\) on the Lyapunov exponent.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 1755332
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: Lozi map
reviewed by: Messoud Efendiev
describes a project that uses: Dynamics
MaRDI profile type: Publication
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full work available at URL: s0960-0779(00)00192-2
OpenAlex ID: W2050361523
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description: scientific article; zbMATH DE number 1755332