Pacemaker-guided noise-induced spatial periodicity in excitable media

We study the impact of subthreshold periodic pacemaker activity and internal noise on the spatial dynamics of excitable media. For this purpose, we examine two systems that both consist of diffusively coupled units. In the first case, the local dynamics of the units is driven by a simple one-dimensional model of excitability with a piece-wise linear potential. In the second case, a more realistic biological system is studied, and the local dynamics is driven by a model for calcium oscillations. Internal noise is introduced via the ττ-leap stochastic integration procedure and its intensity is determined by the finite size of each constitutive system unit. We show that there exists an intermediate level of internal stochasticity for which the localized pacemaker activity maps best into coherent periodic waves, whose spatial frequency is uniquely determined by the local subthreshold forcing. Via an analytical treatment of the simple minimal model for the excitable spatially extended system, we explicitly link the pacemaker activity with the spatial dynamics and determine necessary conditions that warrant the observation of the phenomenon in excitable media. Our results could prove useful for the understanding of interplay between local and global agonists affecting the functioning of tissue and organs.