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 : 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 : 1 we show the generation of spatial order as a result of global forcing of a Hopf state. (c) 2006 Elsevier B.V. All rights reserved.