An Asymmetrical Phase Locking Structure for aNon-excitable Cell Model

Phase-locking phenomena have been extensively studied in terms of non-invertibledegree-1 circle maps, and synchronisation patterns described by these maps exhibit asymmetrical structure. Here we present an asymmetrical structure of phase lockings, fora model that describes the synchronisation modes of intracellular Ca2 oscillations inresponse to external signalling pulses. We compute the devils staircases that form thesynchronisation structure. The synchronisation zones in frequency–amplitude space are enclosedby tongues that contain inserted in them infinite self-similar cascades of narrower tonguesorganised in an asymmetrical Farey tree. We call these structures devils tongues.