Citation: In G.A. Carpenter (Ed.), Some Mathematical Questions in Biology Circadian Rhythms, American Mathematical Society, Lectures on Mathematics in the Life Sciences, 19, 151-203.
Abstract: A neural network model provides behavioral, physiological, and anatomical predictions of how circadian rhythms are generated by the suprachiasmatic nuclei (SCN) of the mammalian hypothalamus. The 4-dimensional basic gated pacemaker model is defined in terms of on-cell/off-cell populations whose positive feedback signals are gated by slowly accumulating transmitter substances. The slow accumulation rate determines the approximate (circadian) period of the pacemaker. The relative insensitivity of period to other parameters demonstrates the clocklike nature of the model. Chaotic solutions, period-doubling, and slow modulation of the envelope of solutions can occur in some parameter ranges. The model consists of two symmetric pairs of fast-slow equations with inhibitory cross-coupling. In the uncoupled or weakly coupled state, no oscillations occur. Augmented versions of the model include fatigue, a negative feedback signal which decays on an ultradian time scale; and a very slow gain control process, which buffers the pacemaker on a time scale of months.