Comments on “Asymptotically stable equilibrium points in new chaotic systems”

Antonio Algaba, Fernando Fernández-Sánchez, Manuel Merino, Alejandro José Rodríguez-Luis

Abstract


In the commented paper ten nonlinear chaotic systems are presented. Authors state that these systems do not exhibit Shilnikov chaos. Unfortunately, this assertion is not correctly proved because they use an erroneous theorem from the literature.


Keywords


chaotic systems, asymptotically stable equilibrium, non-existence of Shilnikov chaos, Lyapunov exponents

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References


Algaba A., Fernández-Sánchez F., Merino M. and Rodríguez-Luis A.J. (2013a). Comments on “Non-existence of Shilnikov chaos in continuous-time systems”, Applied Mathematics and Mechanics (English Edition), 34(9), 1175-1176.

Algaba A., Fernández-Sánchez F., Merino M. and Rodríguez-Luis A.J. (2013b). Chen's attractor exists if Lorenz repulsor exists: The Chen system is a special case of the Lorenz system, Chaos 23, 033108.

Algaba A., Fernández-Sánchez F., Merino M. and Rodríguez-Luis A.J. (2013c). The Lü system is a particular case of the Lorenz system. Physics Letters A 377, 2771-2776.

Algaba A., Fernández-Sánchez F., Merino M. and Rodríguez-Luis A.J. (2014). Centers on center manifolds in the Lorenz, Chen and Lü systems. Communications in Nonlinear Science and Numerical Simulation 19, 772-775.

Algaba A., Domínguez-Moreno M.C., Merino M. and Rodríguez-Luis A.J. (2015). Study of the Hopf bifurcation in the Lorenz, Chen and Lü systems. Nonlinear Dynamics 79, 885-902.

Algaba A., Domínguez-Moreno M.C., Merino M. and Rodríguez-Luis A.J. (2016). Takens-Bogdanov bifurcations of equilibria and periodic orbits in the Lorenz system. . Communications in Nonlinear Science and Numerical Simulation 30, 328-343.

Casas-García K., Quezada-Téllez L.A., Carrillo-Moreno S., Flores-Godoy J.J. and Fernández-Anaya G. (2016) Asymptotically stable equilibrium points in new chaotic systems, Nova Scientia 8(16), 41-58.

Elhadj Z. and Sprott J.C. (2012). Non-existence of Shilnikov chaos in continuous-time systems. Applied Mathematics and Mechanics (English Edition), 33(3), 371-374.




DOI: https://doi.org/10.21640/ns.v9i19.1114

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Nova Scientia is a multidisciplinary, electronic publication that publishes biannually in the months of May and November; it is published by the Universidad De La Salle Bajío and aims to distribute unpublished and original papers from the different scientific disciplines written by national and international researchers and academics. It does not publish reviews, bibliographical revisions, or professional applications.

Nova Scientia, year 10, issue 21, November 2018 – April 2019, is a biannual journal printed by the Universidad De La Salle Bajío, with its address: Av. Universidad 602, Col. Lomas del Campestre, C. P. 37150, León, Gto. México. Phone: (52) 477 214 3900, e-mail: http://nova_scientia.delasalle.edu.mx. Chief editor: Ph.D. Ramiro Rico Martínez. ISSN 2007 - 0705. Copyright for exclusive use No. 04-2008-092518225500/102, Diffusion rights via computer net 04 - 2008 – 121011584800-203 both granted by the Instituto Nacional del Derecho de Autor.

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