A Systems Theory of Cardiac-Autonomic Trajectories and Equilibria

Heart rate variability (HRV) is conventionally summarized with static indices computed over fixed windows, which cannot show how cardiac autonomic regulation persists, transitions, responds to perturbation, and recovers. We develop the Systems Theory of Cardiac-Autonomic Trajectories and Equilibria (STATE), in which autonomic regulation is a low-dimensional latent stochastic dynamical system observed only through RR intervals, and we derive what the theory can and cannot claim. First, we prove that for isotropic linear dynamics the sympathetic and parasympathetic coordinates are not separately identifiable from a scalar RR signal, whereas distinct time scales or coupling restore observability. Second, we derive exact properties of a minimal bistable system (stationary law, mean escape time, critical forcing), and a Monte Carlo simulation agreed with the exact escape time within 6%. Third, in 2000 simulated replicates of a monostable and a bistable system that share the same linearization at rest, baseline variability (area under the receiver operating characteristic curve, AUC, 0.56) and peak displacement at the pulse used (AUC 0.42) did not discriminate the systems, yet sustained return after an identical pulse differed: 100% versus 7%. We define resilience as a multidimensional response profile, show that recovery descriptors depend on analyst-chosen tolerances that must be fixed a priori, and state four falsifiable hypotheses with the result that would refute each. The work is theoretical and computational; no empirical recordings were used.