This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart rate) before, during, and after excitations taking the system out of its equilibrium (e.g., physical effort during cardiac stress testing). Dynamical modeling can be applied to a broad range of outcomes such as physiological processes in medicine and psychosocial processes in social sciences, and it allows to extract simple characteristics of the signal studied. The model we propose is based on a first order linear differential equation defined by three main parameters corresponding to the initial equilibrium value, the dynamic characteristic time, and the reaction to the excitation. In this paper, several estimation procedures for this model are considered and tested in a simulation study, that clarifies under which conditions accurate estimates are provided. Finally, applications of this model are illustrated using cardiology data recorded during effort tests.
