In this work, we compare the behavior of a stand-alone reactor with that of a coupled nonlinear reactor-separator system. The coupling between the two units arises because of the recycle of the reactant-rich stream from the downstream separator. The reaction considered is an elementary autocatalytic reaction of the form A + 2B → 3B. The reactor is assumed to be isothermal. Three different modes of operation of the coupled system corresponding to three different control strategies are investigated. The nonlinear system behavior is analyzed for these cases using singularity theory and the D-partition method. We obtain the preferred control strategy as that in which the reactor effluent flow rate and the fresh feed flow rate are flow-controlled and the reactor holdup is allowed to vary.