There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter $\mu$ gives rise to a ‘space-invariant’ solution, and $\mu$ versus the ratio of the diffusion coefficients gives rise to a ‘time-invariant’ solution. We consider the case where both solution types may be possible. This leads to a refinement of the Turing model of pattern formation. We add convection to the system and investigate its effect. M...