Dynamics of an Henon-Lozi Type Map

Celso Grebogi, C. Robert, M. A. Aziz-Alaoui

Research output: Contribution to journalArticle

31 Citations (Scopus)

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 Henon map and is one that still possesses the characteristics of a Henon-type dynamics. This paper is a first step. It does the comparison of the Lozi map (which is a piecewise linear version of the Henon map) with the map that we introduce. This comparison is done for fixed parameters and also through global bifurcation by changing a parameter. If epsilon measures the degree of smoothness, we prove that, as epsilon --> 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. (C) 2001 Elsevier Science Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)2323-2341
Number of pages18
JournalChaos, Solitons & Fractals
Volume12
Publication statusPublished - 2001

Keywords

  • BORDER-COLLISION BIFURCATIONS
  • CHAOTIC ATTRACTORS
  • SYSTEMS
  • CRISES

Cite this

Grebogi, C., Robert, C., & Aziz-Alaoui, M. A. (2001). Dynamics of an Henon-Lozi Type Map. Chaos, Solitons & Fractals, 12, 2323-2341.

Dynamics of an Henon-Lozi Type Map. / Grebogi, Celso; Robert, C.; Aziz-Alaoui, M. A.

In: Chaos, Solitons & Fractals, Vol. 12, 2001, p. 2323-2341.

Research output: Contribution to journalArticle

Grebogi, C, Robert, C & Aziz-Alaoui, MA 2001, 'Dynamics of an Henon-Lozi Type Map', Chaos, Solitons & Fractals, vol. 12, pp. 2323-2341.
Grebogi C, Robert C, Aziz-Alaoui MA. Dynamics of an Henon-Lozi Type Map. Chaos, Solitons & Fractals. 2001;12:2323-2341.
Grebogi, Celso ; Robert, C. ; Aziz-Alaoui, M. A. / Dynamics of an Henon-Lozi Type Map. In: Chaos, Solitons & Fractals. 2001 ; Vol. 12. pp. 2323-2341.
@article{be7540e095784aabbd046380fe409d45,
title = "Dynamics of an Henon-Lozi Type Map",
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 Henon map and is one that still possesses the characteristics of a Henon-type dynamics. This paper is a first step. It does the comparison of the Lozi map (which is a piecewise linear version of the Henon map) with the map that we introduce. This comparison is done for fixed parameters and also through global bifurcation by changing a parameter. If epsilon measures the degree of smoothness, we prove that, as epsilon --> 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. (C) 2001 Elsevier Science Ltd. All rights reserved.",
keywords = "BORDER-COLLISION BIFURCATIONS, CHAOTIC ATTRACTORS, SYSTEMS, CRISES",
author = "Celso Grebogi and C. Robert and Aziz-Alaoui, {M. A.}",
year = "2001",
language = "English",
volume = "12",
pages = "2323--2341",
journal = "Chaos, Solitons & Fractals",
issn = "0960-0779",
publisher = "Elsevier Limited",

}

TY - JOUR

T1 - Dynamics of an Henon-Lozi Type Map

AU - Grebogi, Celso

AU - Robert, C.

AU - Aziz-Alaoui, M. A.

PY - 2001

Y1 - 2001

N2 - 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 Henon map and is one that still possesses the characteristics of a Henon-type dynamics. This paper is a first step. It does the comparison of the Lozi map (which is a piecewise linear version of the Henon map) with the map that we introduce. This comparison is done for fixed parameters and also through global bifurcation by changing a parameter. If epsilon measures the degree of smoothness, we prove that, as epsilon --> 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. (C) 2001 Elsevier Science Ltd. All rights reserved.

AB - 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 Henon map and is one that still possesses the characteristics of a Henon-type dynamics. This paper is a first step. It does the comparison of the Lozi map (which is a piecewise linear version of the Henon map) with the map that we introduce. This comparison is done for fixed parameters and also through global bifurcation by changing a parameter. If epsilon measures the degree of smoothness, we prove that, as epsilon --> 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. (C) 2001 Elsevier Science Ltd. All rights reserved.

KW - BORDER-COLLISION BIFURCATIONS

KW - CHAOTIC ATTRACTORS

KW - SYSTEMS

KW - CRISES

M3 - Article

VL - 12

SP - 2323

EP - 2341

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

SN - 0960-0779

ER -