Author’s reply to: Comments on “Asymptotically stable equilibrium points in new chaotic systems”
DOI:
https://doi.org/10.21640/ns.v9i19.1208Keywords:
chaotic systems, asymptotically stable equilibrium, non-existence of Shilnikov chaos, Lyapunov exponentsAbstract
Since theorem 1 of (Elhadj and Sprott, 2012) is incorrect, some of the systems found in the article (Casas-García et al. 2016) may have homoclinic or heteroclinic orbits and may seem chaos in the Shilnikov sense. However, the fundamental contribution of our paper was to find ten simple, three-dimensional dynamic systems with non-linear quadratic terms that have an asymptotically stable equilibrium point and are chaotic, which was achieved. These were obtained using the Monte Carlo method applied specifically for the search of these systems.
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Algaba A., Fernández-Sánchez F., Merino M., and Rodríguez-Luis A. J. (2013) 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. (2012a) “Comment on ‘Existence of heteroclinic orbits of the Shilnikov type in a 3D quadratic autonomous chaot-ic system’ [J. Math. Anal. Appl. 315, 106-119 (2006)],” J. Math. Anal. Appl., 392, 99-101.
Algaba A., Fernández-Sánchez F., Merino M., and Rodríguez-Luis A. J. (2012b) “Comment on “Analysis and application of a novel three-dimensional energy-saving and emission-reduction dynamical evolution system” [Energy 40, 291-299 (2012),” Energy 47, 630-633.
Carrillo, S., Casas-García, K., Flores-Godoy, J. J., Valencia, F. V., and Fernández-Anaya, G. (2015) Study of new chaotic flows on a family of 3-dimensional systems with quadratic non-linearities. Journal of Physics: Conference Series (Vol. 582, No. 1, p. 12016) IOP Publishing.
Casas-García, K., Quezada-Téllez L. A., Carrillo-Moreno S., Flores-Godoy J. J., and Fernán-dez-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 sys-tems. Applied Mathematics and Mechanics (English Edition), 33(3), 371-374.
Guochang Fang, Lixin Tian, Mei Sun, Min Fu (2012) Reply to: Comments on “Analysis and application of a novel three-dimensional energy-saving and emission-reduction dynamic evolu-tion system” [Energy 40 (2012) 291-299], Energy 47, 634-635.
Leonov, G. A., and Kuznetsov, N. V. (2015) On differences and similarities in the analysis of Lorenz, Chen, and Lu systems, Applied Mathematics and Computation, 256, 334–343.
Sprott, J. C., and Xiong, A. (2015) Classifying and quantifying basins of attraction. Chaos: An Interdiciplinary Journal of nonlinear Science, 25(8), 083101.
Zuo-Huan Zheng and Guanrong Chen (2012) “Author’s reply to: Comment on “Existence of heteroclinic orbits of the Shil’nikov type in a 3D quadratic autonomous chaotic system, [J. Math. Anal. Appl. 315 (2006) 106–119], J. Math. Anal. Appl., 392, 102.
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