Euzébio, Rodrigo D. [UNESP]Llibre, Jaume2018-12-112018-12-112017-10-01Nonlinear Analysis: Real World Applications, v. 37, p. 31-40.1468-1218http://hdl.handle.net/11449/174285A zero-Hopf equilibrium is an isolated equilibrium point whose eigenvalues are ±ωi≠0 and 0. In general for a such equilibrium there is no theory for knowing when it bifurcates some small-amplitude limit cycles moving the parameters of the system. Here we study the zero-Hopf bifurcation using the averaging theory. We apply this theory to a Chua system depending on 6 parameters, but the way followed for studying the zero-Hopf bifurcation can be applied to any other differential system in dimension 3 or higher. In this paper first we show that there are three 4-parameter families of Chua systems exhibiting a zero-Hopf equilibrium. After, by using the averaging theory, we provide sufficient conditions for the bifurcation of limit cycles from these families of zero-Hopf equilibria. From one family we can prove that 1 limit cycle bifurcates, and from the other two families we can prove that 1, 2 or 3 limit cycles bifurcate simultaneously.31-40engAveraging theoryChua systemPeriodic orbitZero Hopf bifurcationArtigo10.1016/j.nonrwa.2017.02.002Acesso aberto2-s2.0-850143126612-s2.0-85014312661.pdf