Projected Failure Margins in Biological Chaos: Cardiac Arrhythmias and Neural Dynamics as Thickening

This paper applies the reachability framework of Doucette (2026a) to biological chaos-control results reported in the Handbook of Chaos Control, asking whether the handbook's successes can be read as restorations of a positive distance between a projected reachable set and a failure set. The author distinguishes local instability from operational consequence: a continuous projection maps the state space onto low-dimensional observables, and a closed failure set marks forbidden regions. Instability is called thin when the projected reachable set stays at positive distance from failure, thick when instability participates in transport that meets failure, and transitional when the distance remains positive but shrinks. For cardiac preparations, the projection is taken to be the sequence of inter-beat intervals, with failure defined as intervals shorter than a conduction-block threshold or longer than a threshold associated with loss of mechanical coordination. For neural models, the projection extracts local field-potential amplitude or a coherence index, with failure defined as sustained hypersynchrony. The paper's central proposition states that a positive uncontrolled margin survives sufficiently small feedback applied only in a buffer zone adjacent to the failure set, provided the perturbation's effect on the return map is bounded relative to the margin. The rabbit ventricular and human atrial fibrillation experiments are then read as margin restoration: uncontrolled intervals approach short-interval failure values, while captured segments collapse onto orbits bounded away from failure. The neural stabilization results satisfy the same geometry. Factors such as increased dispersion of refractoriness, failure of local linearization, elevated extracellular potassium, and stronger synaptic coupling are described as enlarging the projected reachable set toward failure. The author explicitly limits the claims, noting that delay-coordinate reconstruction may distort distances, local stimuli leave other tissue unaffected, physiological parameters drift, and failure thresholds are empirical clinical choices. The account introduces no new measurements and asserts no clinical advantage; it merely renders the handbook results comparable under a single explicit margin criterion.