Zero-Hopf Bifurcation at the Origin and Infinity for a Class of Generalized Lorenz System (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, the zero-Hopf bifurcations are studied for a generalized Lorenz system. Firstly, by using the averaging theory and normal formtheory, we provide sufficient conditions for the existence of small amplitudeperiodic solutions that bifurcate from zero-Hopf equilibria under appropriateparameter 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 theabove theoretical results, some related illustrations are given by means of thenumerical simulation.