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. The effect of parametric periodic forcing on oscillatory reaction diffusion systems are being studied with renewed interest to see frequency entrainment and resulting multi-phase, steady as well as traveling, orders separated by phase fronts [1, 2, 3, 4]. Existence of multiphase oscillations are theoretically accounted for by showing the stability of phase separated oscillatory orders in complex Ginzburg Landau equation or in some reaction diffusion models. The mechanism that can possibly cause a slow drift in overall phases of oscillation under periodic forcing, and thus produce stable phase-separated regions, is an important subject for investigation. In view of that, we are going to investigate the effect of periodic forcing in time, on an oscillatory system, on multiple time scales. In almost all reactions diffusion systems, one of the reacting species is dependent on the other for its production and thus does not need be externally supplied. This situation causes *