Antiresonance and Stabilization in Spatio‐Temporal Dynamics of a Periodically Driven Gray‐Scott Reaction‐Diffusion System

Abstract

We consider the spatio‐temporal dynamics of a Gray‐Scott reaction diffusion system driven by a time periodic force. The drive excites the system through a direct transition and a parametric transition. The destructive interference of two simultaneous transitions gives rise to an antiresonance dip in the response function‐frequency spectrum. This is manifested in the stabilization of the dynamics in an intermediate frequency range centered at the dip, outside which one observes spatio‐temporal patterns due to instability. A theoretical scheme based on linear analysis followed by detailed numerical simulations of the reaction‐diffusion system has been carried out to explore this antiresonance‐induced dynamical stabilization. This is the first realization of anti‐resonance, an analog of Fano Resonance in auto ionization, in a reaction‐ diffusion system.