The instability of the cerium-bromate-bromide system in an open-flow (CSTR) system was investigated near the critical point. Near this critical point Hopf s bifurcation occurs, causing stable states to become unstable. Domains of single or three unstable steady states occur, with possible oscillations around them. A good agreement is obtained between the calculated and experimental oscillation domains on the various subspaces of constraints. This oscillator is the simplest chemical oscillator fully understood in terms of elementary reactions.