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

Joseph M Starobin,Vivek Varadarajan

doi:10.1186/1753-4631-5-8

Joseph M Starobin, Vivek Varadarajan

Open Access

https://doi.org/10.1186/1753-4631-5-8

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Abstract

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.

Highlights

Dynamics of excitation waves in reaction-diffusion media can be altered by spatio-temporal periodic forcing
Unlike our recent work where we studied the dynamics initiated by a single excitation source [14], the adjusted model is set up to reflect the interference of several sources which deliver multiple stimuli of different amplitudes
As T0 is reduced to a critical limit, Tend, the system does not respond to every stimulus and exhibits unstable M : N (M >N ) excitation blocks which occur due to incomplete recovery of control variable v

Summary

Introduction

Dynamics of excitation waves in reaction-diffusion media can be altered by spatio-temporal periodic forcing. Locking of primary waves to the period of secondary stimulations occurs at particular values of forcing periods and amplitudes. This resonant shift is characterized by Arnold tongues which determine the margins of different types of M : N (M ≥ N, N ≥1) locking responses as a function of amplitude and frequency of external forcing [1,2]. Under the periodic forcing, spatially uniform two-dimensional BZ reaction oscillations were transformed into standing wave type labyrinths of complex geometry [1]. It was demonstrated that one-dimensional Turing patterns can be modulated by spatio-temporal forcing in the form of a travelling wave [3]

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