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Amaral GF, Letellier C, Aguirre LA. Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems. Chaos. 2006;16(1):013115doi: 10.1063/1.2149527.
Amaral, G. F., Letellier, C., & Aguirre, L. A. (2006). Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems. Chaos (Woodbury, N.Y.), 16(1), 013115. https://doi.org/10.1063/1.2149527
Amaral, Gleison F V, et al. "Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems." Chaos (Woodbury, N.Y.) vol. 16,1 (2006): 013115. doi: https://doi.org/10.1063/1.2149527
Amaral GF, Letellier C, Aguirre LA. Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems. Chaos. 2006 Mar;16(1):013115. doi: 10.1063/1.2149527. PMID: 16599746.
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Chaos. 2006 Mar;16(1):013115. doi: 10.1063/1.2149527.

Piecewise affine models of chaotic attractors: the Rossler and Lorenz systems.

Chaos (Woodbury, N.Y.)

Gleison F V Amaral, Christophe Letellier, Luis Antonio Aguirre

Affiliations

  1. Departamento de Engenharia Elétrica, Universidade Federal de São João del-Rei, Pça Frei Orlando 170, 36307-352 São João del-Rei, Minas Gerais, Brazil.

PMID: 16599746 DOI: 10.1063/1.2149527

Abstract

This paper proposes a procedure by which it is possible to synthesize Rossler [Phys. Lett. A 57, 397-398 (1976)] and Lorenz [J. Atmos. Sci. 20, 130-141 (1963)] dynamics by means of only two affine linear systems and an abrupt switching law. Comparison of different (valid) switching laws suggests that parameters of such a law behave as codimension one bifurcation parameters that can be changed to produce various dynamical regimes equivalent to those observed with the original systems. Topological analysis is used to characterize the resulting attractors and to compare them with the original attractors. The paper provides guidelines that are helpful to synthesize other chaotic dynamics by means of switching affine linear systems.

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