Hidden attractors from the switching linear systems

F. Delgado-Aranda, I. Campos-Cantón, E. Tristán-Hernández, P. Salas-Castro

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.


Keywords


Chaos; Hidden attractor; Equilibrium; Linear system

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

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Revista Mexicana de Física

ISSN: 2683-2224 (on line), 0035-001X (print)

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