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Zero–Hopf bifurcations in Yu–Wang type systems

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Abstract

In this paper, we study a three-dimensional system of differential equations which is a generalization of the system introduced by Yu and Wang (Eng Technol Appl Sci Res 3:352–358, 2013), a continuation of the study of chaotic attractors [see Yu and Wang (Eng Tech Appl Sci Res 2:209–215, 2012)]. We show that these systems admit a zero-Hopf non-isolated equilibrium point at the origin and prove the existence of a limit cycle emanating from it. We illustrate our results with some numerical simulations.

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Acknowledgements

Our deep gratitude to one of the anonymous referee for his/her excellent review, and for pointing us out the Ref. [1] which help us to improve our manuscript. The first and third authors have been partially supported from Asociación Mexicana de Cultura A.C., the National System of Researchers (SNI), and Conacyt-México Project A1S10112.

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Authors and Affiliations

  1. Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, Mexico City, Mexico

    Abimael Bengochea & Ernesto Pérez-Chavela

  2. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, C.P. 09340, Mexico City, Mexico

    Angel Garcia-Chung

  3. Tecnológico de Monterrey, Escuela de Ingeniería y Ciencias, Carr. al Lago de Guadalupe Km. 3.5, 52926, Monterrey, State of Mexico, Mexico

    Angel Garcia-Chung

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  1. Abimael Bengochea
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  2. Angel Garcia-Chung
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  3. Ernesto Pérez-Chavela
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Correspondence to Ernesto Pérez-Chavela.

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Bengochea, A., Garcia-Chung, A. & Pérez-Chavela, E. Zero–Hopf bifurcations in Yu–Wang type systems. Eur. Phys. J. Spec. Top. 231, 413–421 (2022). https://doi.org/10.1140/epjs/s11734-021-00347-y

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00347-y

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