Hidden attractors from the switching linear systems | Zendy

F. Delgado-Aranda | Zendy; I. Campos-Cantón | Zendy; Edgar TristánHernández | Zendy; P. Salas-Castro | Zendy

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Hidden attractors from the switching linear systems

Author(s) -

F. Delgado-Aranda,

I. Campos-Cantón,

Edgar TristánHernández,

P. Salas-Castro

Publication year - 2020

Publication title -

revista mexicana de física

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.181

H-Index - 25

eISSN - 2683-2224

pISSN - 0035-001X

DOI - 10.31349/revmexfis.66.683

Subject(s) - attractor , chaotic , lyapunov exponent , quadratic equation , statistical physics , matrix (chemical analysis) , mathematics , computer science , physics , mathematical analysis , artificial intelligence , geometry , materials science , composite material

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 Rouche-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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