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Dynamics and bifurcations of sleep-wake behavior

Victoria Booth, University of Michigan
Tuesday March 16, 12-1pm
Zoom Link:聽

Abstract:聽Transitions between sleep and wake states are regulated by the interactions among a number of brainstem and hypothalamic neuronal populations and the expression of their neurotransmitters. The timing of these transitions is strongly modulated by the 24 h circadian rhythm and the homeostatic sleep drive, the irresistible urge for sleep after being awake. We have been developing and analyzing mathematical models of sleep-wake regulatory networks to understand how the interaction of these processes dictate the timing and durations of sleep and wake episodes. To investigate model dynamics related to the circadian modulation of sleep patterns, we have reduced the dynamics of sleep-wake regulatory network models to a one-dimensional circle map, a classic technique for analyzing coupled oscillator systems. The sleep-onset maps, which track the phase of the circadian rhythm at which sleep onset occurs on successive days, have interesting properties such as non-monotonicity and discontinuities. In this talk, I鈥檒l discuss how the properties of these maps reflect and influence sleep-wake patterns and their bifurcations.