Abstract

DELGADO-ARANDA, F.; CAMPOS-CANTON, I.; TRISTAN-HERNANDEZ, E.  and  SALAS-CASTRO, P.. Hidden attractors from the switching linear systems. Rev. mex. fis. [online]. 2020, vol.66, n.5, pp.683-691.  Epub Jan 31, 2022. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.66.683.

Recently, chaotic behavior has been studied in dynamical systems that generate 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. The basic chaotic properties of the attractors are verified by the Lyapunov exponents.

Keywords : Chaos; hidden attractor; equilibrium; linear system.