Vulnerability Windows as Lyapunov Stability Margins: A Dynamical Systems Model of Gestational Oxygen Sensitivity

Each fetal organ system passes through a developmental period during which it is maximally sensitive to oxygen disruption. This paper provides the dynamical systems formalisation of that mapping. Each developing organ system is modelled as a dynamical system with stable equilibrium trajectories corresponding to normal maturation. The Lyapunov stability margin — the maximum perturbation from which the system can return to normal trajectory — varies as a function of gestational age. Three results follow. First, the super-window of 23–36 weeks gestation corresponds to the period of minimum aggregate Lyapunov stability margin across all simultaneously developing systems. Second, Prigogine's dissipative structure framework identifies the fetus as a far-from-equilibrium system maintained by continuous oxygen throughput — withdrawal produces a phase transition to an alternative attractor, not graceful degradation. Third, the HIF-1α / PHD-VHL molecular oscillation under intermittent hypoxia is modelled as a Lotka-Volterra predator-prey dynamic, with oscillation amplitude determining whether the system remains within or is expelled from the stability basin.