The H₂+ O₂ reaction is one of the simplest chemical oscillators and of great practical significance. In a well stirred flow system, equimolar mixtures support oscillatory ignitions, with a simple periodic waveform, over a range of ambient temperature and operating pressure. Here we report a series of experiments in which the outputs from the monitoring thermocouple and photomultiplier are data captured onto computer. These ‘time series’ are then treated via a number of techniques from dynamical systems theory, including fast Fourier transforms and attractor reconstructions. This allows the routes by which oscillations set in and are extinguished to be recognised. New responses have then been predicted in the light of these theories and observed experimentally. With a stoichiometric 2H₂+ O₂ mixture, complex mixed-mode oscillations and birhythmicity are also observed over some range of experimental conditions.