In this study, we report the experimental and numerical investigation of the behaviour of a spontaneously oscillatory reaction in a fed-batch reactor (FBR). We use a cerium catalysed BZ model with a modified Oregonator mechanism. In fed-batch mode, we observe phase-locked, quasiperiodic and period-doubling responses, depending on the amplitude and period of the replacement cycle. A series of single pulse experiments is used to construct phase transition curves, from which limit point (Arnold tongues) and period-doubling bifurcation boundaries can be constructed. Experimental boundaries are compared with boundaries determined numerically using a path following analysis. The results are used to determine the variation, in terms of the mean rate of production of the oxidised catalyst, with the operating conditions of the FBR for a fixed residence time. (C) 2003 Elsevier Ltd. All rights reserved.