AN ASYMMETRICAL PHASE-LOCKING STRUCTURE FOR A NONEXCITABLE CELL MODEL

Phase-locking phenomena have been extensively studied in terms of non- invertible degree-1 circle maps, and synchronisation patterns describe d by these maps exhibit a symmetrical structure. Here we present an as ymmetrical structure of phase lockings, for a model that describes the synchronisation modes of intracellular Ca2+ oscillations in response to external signalling pulses. We compute the devil's staircases that form the synchronisation structure. The synchronisation zones in frequ ency-amplitude space are enclosed by tongues that contain inserted in them infinite self-similar cascades of narrower tongues organised in a n asymmetrical Farey tree. We call these structures devil's tongues. ( C) 1998 Elsevier Science Ltd. All rights reserved.