Endogenous Reachability Collapse (ERC) — Ensemble Behavior
A minimal extension exploring how loss of recoverability may emerge at the level of initial condition distributions.
While the minimal model shows that a stable attractor may become dynamically inaccessible, this work examines how that transition appears across an ensemble of initial states.
As internal constraint increases, the fraction of initial conditions that return to the base attractor contracts and may collapse abruptly beyond a critical range, providing an operational measure of accessibility.
This suggests that loss of function may first appear at the ensemble level, as a rapid collapse in the fraction of recoverable initial conditions, before becoming absolute at the level of individual trajectories.
Within the explored range, this transition appears consistent with a threshold-like behavior in accessibility.
The attractor remains present in the state space, but becomes reachable only from a diminishing subset of initial conditions.
This suggests that system robustness may depend not only on structure, but on how accessibility is distributed across state space under constraint..
This ensemble perspective introduces an operational and measurable indicator of recoverability loss, linking dynamical accessibility to observable system-level transitions.
