Optical single-channel recording by imaging Ca2+ flux through individual ion channels: theoretical considerations and limits to resolution

Abstract

A control scheme is applied between two different oscillators to study their phase synchronization. It utilizes unidirectional signal coupling and only measures the time interval when the trajectories to the two oscillators’ attractors cross the Poincaré surfaces respectively. By using this scheme, phase synchronization (without 2π phase slips) can be obtained between two different chaotic systems whose signal variables have large amplitude mismatch. This unidirectional signal coupling also provides a minimum information flow from the driving system to the response system. Therefore it can be used in synchronizing systems with substantially different dynamics via a channel with low information rate.