The Lü system is a particular case of the Lorenz system

Keywords:Lorenz-like systems Lorenz system Chen system Lu system Lyapunov exponent Chaotic analog of 16th Hilbert problem a b s t r a c t Currently it is being actively discussed the question of the equivalence of various Lorenzlike systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a(Algaba et al., ,b, 2014bChen, 2013;Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed.

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“…Recently a very interesting discussion on the equivalence of the Lorenz, the Chen and the Lu systems was initiated in [2,3,11].…”

Section: Recent Discussion On Equivalence Of the Lorenz Chen And Lumentioning

confidence: 99%

“…Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior [2][3][4][5]11,14,35] in view of the possibility of reduction of such systems to the same form with the help of various transformations.…”

Section: Introductionmentioning

confidence: 99%

On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

Леонов

Kuznetsov

2015

Applied Mathematics and Computation

103

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“…Desde entonces han aparecido en la literatura sistemas caóticos con estructura similar al de Lorenz a los que se les ha llamado sistemas Tipo Lorenz: sistema de Chen [2,5], sistema de Lü [3,6,18], Li-Wang [12] y otros [7,8,16,19,22].…”

Section: Introductionunclassified

Tratamiento analítico de la bifurcación de Hopf en una extensión del sistema de Lü

Saavedra

Aguirre

Mena

2018

RMTA

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En este artículo se hace un análisis de la bifurcación de Hopf del sistema tridimensional tipo Lorenz introducido por Xianyi Li y Qianjun Ou (2011), este análisis consiste en identificar una región de parámetros del sistema donde la bifurcación de Hopf es no degenerada y supercrítica, aspecto que no es abordado en el artículo de Xianyi Li y Qianjun Ou. Para lograr este objetivo se utiliza el Teorema de la Variedad Central y el Teorema de Hopf. Además, para ilustrar los resultados, se muestran gráficas de algunas trayectorias del sistema, las cuales fueron obtenidas mediantesimulación numérica.

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“…9 (2) We would like to add a last comment. Chen's and Lü's systems, cited in the commented paper, are only particular cases of the Lorenz system as it is demonstrated in (Algaba et al, 2013b(Algaba et al, , 2013c, by using a linear scaling in time and state variables. This fact is illustrated in (Algaba et al, 2014(Algaba et al, , 2015(Algaba et al, , 2016.…”

Section: Introductionmentioning

confidence: 99%