Entrainment of marginally stable excitation waves by spatially extended sub-threshold periodic forcing

We introduce a novel approach of stabilizing the dynamics of excitation waves by spatially extended sub-threshold periodic forcing. Entrainment of unstable primary waves has been studied numerically for different amplitudes and frequencies of additional sub-threshold stimuli. We determined entrainment regimes under which excitation blocks were transformed into consistent 1:1 responses. These responses were spatially homogeneous and synchronized in the entire excitable medium. Compared to primary pulses, pulses entrained by secondary stimulations were stable at considerably shorter periods which decreased at higher amplitudes and greater number of secondary stimuli. Our results suggest a practical methodology for stabilization of excitation in reaction-diffusion media such as nerve tissue with regions of reduced excitability.