Invariant Analysis for an Extended Lorenz System

One of the well-known chaotic systems is the Lorenz system. The algebraic properties of the Lorenz system have been studied extensively since 1960s. In this study we investigate the algebraic invariants of an extended Lorenz system which stands as a normal form for some class of codim-3 bifurcations. We also give conditions on the parameters where a Hopf bifurcation can occur.