The intensification rate (IR) equation, derived from a time-dependent simplified energetically based dynamical system (EBDS), serves to connect tropical cyclone (TC) intensity, IR, and their evolutions, suggesting a linkage between the timing of TC lifetime maximum intensity (LMI) and the occurrence of maximum intensification rate (MIR). This study demonstrates that the IR equation predicts MIR typically preceding LMI by 0-36 hours, as confirmed by idealized numerical simulation and analysis of best track data. It was observed that 77.5% (48.5%) of global TCs reached LMIs within 36 (12) hours after MIR from 1982 to 2023. This consistency between observational data, numerical simulation and analytical analysis underscores the EBDS-based IR equation's ability in capturing the timing relationship between MIR and LMI. The intrinsic link between the timing of LMI and MIR highlights the critical importance of predicting the timing of MIR for effectively forecasting the timing of LMI.
 

tropical cyclone, lifetime maximum intensity, intensification rate