Hidden attractors from the switching linear systems

Authors

  • F. Delgado-Aranda Instituto de Investigación en Comunicación Óptica. Universidad Autónoma de San Luis Potosí
  • I. Campos-Cantón Facultad de Ciencias. Universidad Autónoma de San Luis Potosí
  • E. Tristán-Hernández Instituto de Investigación en Comunicación Óptica. Universidad Autónoma de San Luis Potosí
  • P. Salas-Castro Universidad Politécnica de San Luis Potosí

DOI:

https://doi.org/10.31349/RevMexFis.66.683

Keywords:

Chaos, Hidden attractor, Equilibrium, Linear system

Abstract

Recently, chaotic behavior has been studied in dynamical systems that generates hidden attractors. Most of these systems have quadratic nonlinearities. This paper introduces a new methodology to develop a family of three-dimensional hidden attractors from the switching of linear systems. This methodology allows to obtain strange attractors with only one stable equilibrium, attractors with an infinite number of equilibria or attractors without equilibrium. The main matrix and the augmented matrix of every linear system are considered in Rouché-Frobenius theorem to analyze the equilibrium of the switching systems. Also, a systematic search assisted by a computer is used to find the chaotic behavior. Basic chaotic properties of the attractors are verified by the Lyapunov exponents.

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Published

2020-09-01

How to Cite

[1]
F. Delgado-Aranda, I. Campos-Cantón, E. Tristán-Hernández, and P. Salas-Castro, “Hidden attractors from the switching linear systems”, Rev. Mex. Fís., vol. 66, no. 5 Sept-Oct, pp. 683–691, Sep. 2020.

Issue

Vol. 66 No. 5 Sept-Oct (2020): Revista Mexicana de Física

Section

14 Other areas in Physics

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.