Circadian rhythms are established by the entrainment of our intrinsic body clock to periodic forcing signals provided by the external environment, primarily variation in light intensity
across the day/night cycle. Loss of entrainment can cause a multitude of physiological difficulties associated with misalignment of circadian rhythms, ...
Circadian rhythms are established by the entrainment of our intrinsic body clock to periodic forcing signals provided by the external environment, primarily variation in light intensity
across the day/night cycle. Loss of entrainment can cause a multitude of physiological difficulties associated with misalignment of circadian rhythms, including insomnia, excessive daytime
sleepiness, gastrointestinal disturbances, and general malaise. This can occur after travel to
different time zones, known as jet lag; when changing shift work patterns; or if the period of an
individual’s body clock is too far from the 24-hour period of environmental cycles. We consider
the loss of entrainment and the dynamics of re-entrainment in a two-dimensional variant of the
Forger-Jewett-Kronauer model of the human circadian pacemaker forced by a 24-hour light/dark
cycle. We explore the loss of entrainment by continuing bifurcations of one-to-one entrained orbits under variation of forcing parameters and the intrinsic clock period. We show that the
severity of the loss of entrainment is dependent on the type of bifurcation inducing the change
of stability of the entrained orbit, which is in turn dependent on the environmental light intensity. We further show that for certain perturbations, the model pblackicts a counter-intuitive
rapid re-entrainment if the light intensity is sufficiently high. We explain this phenomenon via
computation of invariant manifolds of fixed points of a 24-hour stroboscopic map and show how
the manifolds organise re-entrainment times following transitions between day and night shift
work.
