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Quasiperiodic Patterns in Boundary-Modulated Excitable Waves

Sendiña-Nadal, Irene; Pérez-Muñuzuri, Vicente; Eguíluz, Víctor M.; Hernández-García, Emilio; Oreste, Piro
Physical Review E 64, 046208 (1-5) (2001)

We investigate the impact of the domain shape on wave propagation in excitable media.
Channelled domains with sinusoidal boundaries are considered. Trains of fronts generated
periodically at an extreme of the channel are found to adopt a quasiperiodic spatial configuration
stroboscopically frozen in time. The phenomenon is studied in a model for the photo-sensitive
Belousov-Zabotinsky reaction, but we give a theoretical derivation of the spatial return maps
prescribing the height and position of the successive fronts that is valid for arbitrary excitable
reaction-diffusion systems.