A Formal Account of Reversal Triggers: Allostatic Regulation as a Hybrid Dynamical System in Reversal Theory

Reversal Theory explains motivation as switching between paired metamotivational states, but its three reversal triggers (satiation, frustration and contingent events) have remained verbal. We formalise them for one state pair as a discrete-time hybrid dynamical system. Each of two continuous need-satisfaction levels follows a leaky-integrator update: it decays exponentially, is refilled all the time but with substantially higher rates while its state is active, and drops with contingent events. A discrete binary state records the active state and switches when one of three guard conditions holds, which is slightly different from Reversal Theory’s setting that considers the three combined. Satiation occurs only if the need’s steady state under supply exceeds its target, and takes sharply longer as the two approach. Simulations show regular alternation under satiation alone, reversals by contingent events and by frustration, and a floor effect: frustration defined as a recent drop cannot fire once a need is already depleted, so a person can remain in an unsatisfying state; simulated individuals also differ widely in the same scenario. We place the model on a predictive-processing account of interoception (EPIC on Predictive Forward-Forward learning), outline how it could be fitted to multimodal recordings time-aligned with retrospective self-reports, and sketch a probabilistic version that combines the three triggers into one reversal probability and can be fitted by maximum likelihood. Code and parameters are available from the author on request.