Year: 2023
Author: Hongpu Liu, Wentao Huang, Qinlong Wang
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 3 : pp. 621–636
Abstract
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2023.621
Journal of Nonlinear Modeling and Analysis, Vol. 5 (2023), Iss. 3 : pp. 621–636
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Generalized Lorenz system zero-Hopf bifurcation averaging theory normal form theory Poincaré compactification.