Dynamical analysis in a self-regulated system undergoing multiple excitations: first order differential equation approach
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In this paper, we discuss a novel approach for studying longitudinal data of self-regulating systems experiencing multiple excitations (or inputs). We developed a model focusing on the evolution of a signal (e.g., heart rate) before, during, and after temporal perturbations taking the system out of its equilibrium state (e.g., cardiac stress testing on a bicycle ergometer). This approach, using multilevel regression and first order differential equations, allows to model a broad range of signals or outcomes such as physiological processes in medicine and psychosocial processes in social sciences, and to extract simple characteristics of the dynamical system studied. In a first step, we present the model (including readily available statistical code) and the three main parameters estimated: the initial equilibrium, the damping time, and the reaction to the excitation. We then show simulation studies clarifying under which conditions the model provides accurate estimates. These simulations showed that the estimates are robust to noise, thus giving the opportunity to use it in a wide panel of studies. Finally, application of this model is illustrated using cardiological data recorded during effort test.
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