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

TL;DR

This study investigates how spatially extended sub-threshold periodic forcing can entrain and stabilize excitation waves in reaction-diffusion systems, transforming unstable waves into synchronized, stable responses across the medium.

Contribution

It provides a numerical analysis of entrainment regimes and demonstrates a method to stabilize excitation waves in media with reduced excitability.

Findings

Entrainment transforms unstable waves into stable 1:1 responses.

Secondary stimulations enable stable pulses at shorter periods.

Higher amplitudes and more stimuli increase stability and reduce periods.

Abstract

We analyze the effects of spatially extended periodic forcing on the dynamics of one-dimensional excitation waves. 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 with regions of reduced excitability.