Dynamics of a Hénon–Lozi-type map
Identifieur interne : 000F68 ( France/Analysis ); précédent : 000F67; suivant : 000F69Dynamics of a Hénon–Lozi-type map
Auteurs : M. A. Aziz-Alaoui [France] ; Carl Robert [États-Unis] ; Celso Grebogi [États-Unis]Source :
- Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena [ 0960-0779 ] ; 2001.
Abstract
We present and analyze a smooth version of the piecewise linear Lozi map. The principal motivation for this work is to develop a map, which is better amenable for an analytical treatment as compared to the Hénon map and is one that still possesses the characteristics of a Hénon-type dynamics. This paper is a first step. It does the comparison of the Lozi map (which is a piecewise linear version of the Hénon map) with the map that we introduce. This comparison is done for fixed parameters and also through global bifurcation by changing a parameter. If ε measures the degree of smoothness, we prove that, as ε→0, the stability and the existence of the fixed points are the same for both maps. We also numerically compare the chaotic dynamics, both in the form of an attractor and of a chaotic saddle.
Url:
DOI: 10.1016/S0960-0779(00)00192-2
Affiliations:
- France, États-Unis
- Californie, Haute-Normandie, Massachusetts, Région Normandie
- College Park (Maryland), Le Havre
- Université du Maryland
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ISTEX:48D149B18EEB87956510D820449F5514DA1CFC91Le document en format XML
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The principal motivation for this work is to develop a map, which is better amenable for an analytical treatment as compared to the Hénon map and is one that still possesses the characteristics of a Hénon-type dynamics. This paper is a first step. It does the comparison of the Lozi map (which is a piecewise linear version of the Hénon map) with the map that we introduce. This comparison is done for fixed parameters and also through global bifurcation by changing a parameter. If ε measures the degree of smoothness, we prove that, as ε→0, the stability and the existence of the fixed points are the same for both maps. We also numerically compare the chaotic dynamics, both in the form of an attractor and of a chaotic saddle.</div></front></TEI><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Californie</li><li>Haute-Normandie</li><li>Massachusetts</li><li>Région Normandie</li></region><settlement><li>College Park (Maryland)</li><li>Le Havre</li></settlement><orgName><li>Université du Maryland</li></orgName></list><tree><country name="France"><noRegion><name sortKey="Aziz Alaoui, M A" sort="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M" first="M. A." last="Aziz-Alaoui">M. A. Aziz-Alaoui</name></noRegion><name sortKey="Aziz Alaoui, M A" sort="Aziz Alaoui, M A" uniqKey="Aziz Alaoui M" first="M. A." last="Aziz-Alaoui">M. A. Aziz-Alaoui</name></country><country name="États-Unis"><region name="Californie"><name sortKey="Robert, Carl" sort="Robert, Carl" uniqKey="Robert C" first="Carl" last="Robert">Carl Robert</name></region><name sortKey="Grebogi, Celso" sort="Grebogi, Celso" uniqKey="Grebogi C" first="Celso" last="Grebogi">Celso Grebogi</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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