CIFT bifurcation

The hooked turns seen in isochrons of biological models are attributed to intrinsic phase sensitivity in the system, which generally comes about as the timescale separation parameter increases. To define these turns, we introduced the notion of backwards-time isochrons for a repelling periodic orbit, which have the equivalent set of properties as the regular forward-time isochrons, but where time is reversed. By considering the interaction of the set of forward- and backward-time isochrons, we are able to define the occurence of the hooked turns