This work aimed to develop and validate a novel non-linear model to characterize RR interval (RRi) time-dependent fluctuations throughout a rest-exercise-recovery protocol, offering a more precise and physiologically relevant representation of cardiac autonomic responses than traditional HRV metrics or linear approaches. Using data from a cohort of 272 elderly participants, the model employs logistic functions to capture the non-stationary and transient nature of RRi time-dependent fluctuations, with parameter estimation achieved via Hamiltonian Monte Carlo. Sobol sensitivity analysis identified baseline RRi (α) and recovery proportion (c) as the primary drivers of variability, underscoring their critical roles in autonomic regulation and resilience. Validation against real-world RRi data demonstrated robust model performance (R