Phase instabilities generated by parametric modulation in reaction–diffusion systems

Effect of external periodic force on an oscillatory order in a reaction–diffusion system (Gierer–Meinhardt model) has been investigated. The 2:12:1 resonance situation is found susceptible for the generation of a band of phase instabilities. These phase instabilities, captured on multiple time scales, produces a mismatch between the oscillation frequency of reacting species. For all other forcing frequencies which are not in the ratio 2:12:1 we show the generation of spatial order as a result of global forcing of a Hopf state.