In order to further understand a self-exciting Faraday disc dynamo (Hide $\it{et al}$, in $\it{Proc. R. Soc}.$ A $\bf{452}$, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.
