TY - JOUR
T1 - Zero-Hopf Bifurcation at the Origin and Infinity for a Class of Generalized Lorenz System
AU - Liu , Hongpu
AU - Huang , Wentao
AU - Wang , Qinlong
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 621
EP - 636
PY - 2023
DA - 2023/08
SN - 5
DO - http://doi.org/10.12150/jnma.2023.621
UR - https://global-sci.org/intro/article_detail/jnma/21955.html
KW - Generalized Lorenz system, zero-Hopf bifurcation, averaging theory, normal form theory, Poincaré compactification.
AB - <p style="text-align: justify;">In this paper, the zero-Hopf bifurcations are studied for a generalized Lorenz system. Firstly, by using the averaging theory and normal form
theory, we provide sufficient conditions for the existence of small amplitude
periodic solutions that bifurcate from zero-Hopf equilibria under appropriate
parameter perturbations. Secondly, based on the Poincaré compactification,
the dynamic behavior of the generalized Lorenz system at infinity is described,
and the zero-Hopf bifurcation at infinity is investigated. Additionally, for the
above theoretical results, some related illustrations are given by means of the
numerical simulation.</p>