Eur. Phys. J. Spec. Top. (2022) 231: 413-421
https://doi.org/10.1140/epjs/s11734-021-00347-y

Regular Article

Zero–Hopf bifurcations in Yu–Wang type systems

¹ Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, Mexico City, Mexico
² Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, C.P. 09340, Mexico City, Mexico
³ Tecnológico de Monterrey, Escuela de Ingeniería y Ciencias, Carr. al Lago de Guadalupe Km. 3.5, 52926, Monterrey, State of Mexico, Mexico

^c ernesto.perez@itam.mx

Received: 12 June 2021
Accepted: 19 November 2021
Published online: 3 December 2021

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.