title: Parametric spatiotemporal oscillation in reaction-diffusion systems.
abstract: We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.
authors.affiliation: Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India.
authors.forename: Shyamolina
authors.initials: S
authors.lastname: Ghosh
authors.affiliation: Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India.
authors.forename: Deb Shankar
authors.initials: DS
authors.lastname: Ray