A multistable slow-fast model of affective state switching under circadian drive

Abstract

Rhythmic mood fluctuations are often associated with circadian timing, but it remains unclear how daily rhythms that normally organize physiological affective variation also shape transitions into longer pathological episodes in bipolar disorder. We introduce a phenomenological slow-fast model of affective dynamics inspired by HPA-axis homeostatic feedback. A fast affective coordinate evolves on a multistable landscape whose geometry is shaped by a slow homeostatic variable, producing four stable wells: depression-like, physiological low, physiological high, and mania-like. Circadian input acts not as a local forcing term but as a periodic tilt of the global affective landscape. With intact barriers, this tilt entrains physiological low-high cycling; when outer barriers are weakened, it creates phase-dependent windows for stochastic escape into pathological wells, where prolonged occupancy can produce episode-like infradian cycling. Modeling persistent perturbations as an Ornstein-Uhlenbeck process, we derive a Kramers-type escape criterion linking pathological transitions to phase-dependent barrier height and perturbation strength. One-year simulations and scans over the parameter governing landscape geometry show that preserved circadian amplitude stabilizes physiological cycling, whereas reduced amplitude combined with stronger perturbations promotes entry into and occupancy within depression-like or mania-like wells. The model provides a dynamical framework for studying how circadian disruption, landscape geometry, and perturbation sensitivity jointly shape transitions between physiological mood cycling and episode-like pathological states. Lead ParagraphBipolar disorder involves large, persistent transitions among depressive, euthymic, and manic states, whereas everyday mood also shows smaller fluctuations over the day. Whether these two forms of affective variation can be understood within a single dynamical framework remains unclear. Here, we present a slow-fast affective landscape model in which a slow homeostatic variable shapes a multistable potential for a faster affective state. The landscape contains two inner physiological wells and two outer pathological wells. Circadian input does not force the affective state directly into particular wells; instead, it periodically tilts the global landscape, entraining daily cycling within the physiological low and high states under normal geometry. When circadian amplitude is weakened or outer barriers are reduced, persistent stochastic fluctuations can promote escape into hard-to-exit depression-like or mania-like states. The central issue is therefore not simply whether such escapes can occur, but how circadian disruption, landscape geometry, and perturbation sensitivity determine the balance of dwell time across physiological and pathological states over clinically meaningful observation windows.