A recoverability boundary in a minimal rate-limited dynamical system

This work presents a minimal dynamical model to explore whether system failure depends only on total load, or also on the rate at which load is applied. The model describes a recovery-limited system subject to transient forcing with fixed total input (AUC) and variable timescale. Under these conditions, system behavior appears to separate into recoverable and non-recoverable regimes. Results are consistent with the emergence of an operational recoverability boundary in the joint space of load and forcing timescale. Key observations include:– Minimum state depends primarily on total input (AUC)– Recovery time depends primarily on forcing timescale– Recoverability depends jointly on both variables– Prior subcritical exposure can shift system behavior (history dependence) The model is intentionally minimal and does not aim to represent a specific biological system. Instead, it is designed to test a general rate-limited failure mechanism under controlled assumptions. All simulations and figures are fully reproducible from the accompanying code repository. Independent replication and extension of the model are encouraged.