Comments on “Asymptotically stable equilibrium points in new chaotic systems”
DOI:
https://doi.org/10.21640/ns.v9i19.1114Keywords:
chaotic systems, asymptotically stable equilibrium, non-existence of Shilnikov chaos, Lyapunov exponentsAbstract
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.
Downloads
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.
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Nova Scientia
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Conditions for the freedom of publication: the journal, due to its scientific nature, must not have political or institutional undertones to groups that are foreign to the original objective of the same, or its mission, so that there is no censorship derived from the rigorous ruling process.
Due to this, the contents of the articles will be the responsibility of the authors, and once published, the considerations made to the same will be sent to the authors so that they resolve any possible controversies regarding their work.
The complete or partial reproduction of the work is authorized as long as the source is cited.
