On the integrability and the zero-Hopf bifurcation of a Chen–Wang differential system

© 2015, Springer Science+Business Media Dordrecht. The first objective of this paper was to study the Darboux integrability of the polynomial differential system (Formula presented)and the second one is to show that for (Formula presented) sufficiently small this model exhibits two small amplitude periodic solutions that bifurcate from a zero-Hopf equilibrium point localized at the origin of coordinates when (Formula presented). We note that this polynomial differential system introduced by Chen and Wang (Nonlinear Dyn 71:429–436, 2013) is relevant in the sense that it is the first system in (Formula presented) exhibiting chaotic motion without having equilibria.