We revisit the analysis of a reactor network consisting of two coupled continuous stirred tank reactors (CSTRs) arranged in series (Chem. Eng. J. 59 (1995) 169). The main idea proposed in this earlier work is to improve process conversion by generating periodic behaviour in the first reactor (by appropriate choice of design and operational parameters) which then 'forces' the second reactor. The performance of this cascade system was shown to be greatly enhanced using the above strategy. In this paper we show some conceptual errors in the analysis in the original paper. We also show that by employing a systematic bifurcation analysis, including the use of a path following software, greater insights can be gained regarding the system's behaviour. Using these techniques we show that operation and design parameters can be readily identified to ensure that the cascade has a superior performance to a single CSTR.