Inferring instantaneous, multivariate and nonlinear sensitivities for the analysis of feedback processes in a dynamical system: Lorenz model case-study

As an alternative to classical linear feedback analysis, we present a nonlinear approach for the determination of the sensitivities of a dynamical system from observations of its variations. The new methodology consists of statistical estimates of all the pair-wise relationships among the system state variables based on a neural-network modelling of the system dynamics (its time evolution). The model can then be used to estimate the instantaneous, multivariate, nonlinear sensitivities. Classical feedback analysis is re-examined in terms of these sensitivities, which are shown to be more fundamental in the analysis of feedback processes than estimates of feedback factors and to provide a more appropriate representation of the system's behaviour. The method is described and tested on synthetic observations of the time variations of the Lorenz low-order atmospheric model where the correct sensitivities can be evaluated analytically.